IEEE Transactions on Antennas and Propagation [volume 60 number 2 part I]

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FEBRUARY 2012

VOLUME 60

NUMBER 2

IETPAK

(ISSN 0018-926X)

PART I OF TWO PARTS

SPECIAL ISSUE ON MULTIPLE-INPUT MULTIPLE-OUTPUT (MIMO) TECHNOLOGY

Guest Editorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. W. Wallace, J. B. Andersen, B. K. Lau, B. Daneshrad, and J. Takada

Antenna Design, Modeling, and Analysis Design of a MIMO Dielectric Resonator Antenna for LTE Femtocell Base Stations . . . . . . . . J.-B. Yan and J. T. Bernhard A Compact Eighteen-Port Antenna Cube for MIMO Systems . . . . . . . . . . . . . . . . . . . J. Zheng, X. Gao, Z. Zhang, and Z. Feng Printed MIMO-Antenna System Using Neutralization-Line Technique for Wireless USB-Dongle Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S.-W. Su, C.-T. Lee, and F.-S. Chang Simple and Efficient Decoupling of Compact Arrays With Parasitic Scatterers . . . . . . . . . . . . . B. K. Lau and J. B. Andersen Reducing Mutual Coupling of MIMO Antennas With Parasitic Elements for Mobile Terminals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z. Li, Z. Du, M. Takahashi, K. Saito, and K. Ito A Compact Wideband MIMO Antenna With Two Novel Bent Slits . . . . . . . . .. . . . . . . . J.-F. Li, Q.-X. Chu, and T.-G. Huang Characteristic Mode Based Tradeoff Analysis of Antenna-Chassis Interactions for Multiple Antenna Terminals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. Li, Y. Tan, B. K. Lau, Z. Ying, and S. He Multiple Antenna Systems With Inherently Decoupled Radiators . . . . . . . . . M. Pelosi, M. B. Knudsen, and G. F. Pedersen A Pattern Reconfigurable U-Slot Antenna and Its Applications in MIMO Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P.-Y. Qin, Y. J. Guo, A. R. Weily, and C.-H. Liang Multiple Element Antenna Efficiency and its Impact on Diversity and Capacity . . . . . . . . . . . . . J. X. Yun and R. G. Vaughan On the Accuracy of Equivalent Circuit Models for Multi-Antenna Systems . . . . . . . . . . . . . . J. W. Wallace and R. Mehmood Channel Sounding and Modeling A Low-Cost MIMO Channel Sounder Architecture Without Phase Synchronization . .. . D. Pinchera and M. D. Migliore Impact of Incomplete and Inaccurate Data Models on High Resolution Parameter Estimation in Multidimensional Channel Sounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Landmann, M. Käske, and R. S. Thomä A General Coupling-Based Model Framework for Wideband MIMO Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Y. Zhang, O. Edfors, P. Hammarberg, T. Hult, X. Chen, S. Zhou, L. Xiao, and J. Wang

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438 445 456 464 473 482 490 503 516 529 540 548 557 574

(Contents Continued on p. 433)

(Contents Continued from Front Cover) Multi-Link MIMO Channel Modeling Using Geometry-Based Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Poutanen, F. Tufvesson, K. Haneda, V.-M. Kolmonen, and P. Vainikainen Land Mobile Satellite Dual Polarized MIMO Channel Along Roadside Trees: Modeling and Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Cheffena, F. P. Fontán, F. Lacoste, E. Corbel, H.-J. Mametsa, and G. Carrie Empirical-Stochastic LMS-MIMO Channel Model Implementation and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P. R. King, T. W. C. Brown, A. Kyrgiazos, and B. G. Evans System Performance Evaluation Effectiveness of Relay MIMO Transmission by Measured Outdoor Channel State Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K. Nishimori, N. Honma, T. Murakami, and T. Hiraguri Single and Multi-User Cooperative MIMO in a Measured Urban Macrocellular Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. K. Lau, M. A. Jensen, J. Medbo, and J. Furuskog User Influence on MIMO Channel Capacity for Handsets in Data Mode Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Ø. Nielsen, B. Yanakiev, I. B. Bonev, M. Christensen, and G. F. Pedersen Exposure Compliance Methodologies for Multiple Input Multiple Output (MIMO) Enabled Networks and Terminals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. Perentos, S. Iskra, A. Faraone, R. J. McKenzie, G. Bit-Babik, and V. Anderson MIMO Transmission Using a Single RF Source: Theory and Antenna Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . O. N. Alrabadi, J. Perruisseau-Carrier, and A. Kalis MIMO Capacity Enhancement Using Parasitic Reconfigurable Aperture Antennas (RECAPs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R. Mehmood and J. W. Wallace Eigen-Coherence and Link Performance of Closed-Loop 4G Wireless in Measured Outdoor MIMO Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Webb, M. Hunukumbure, and M. Beach Multipath Simulator Measurements of Handset Dual Antenna Performance With Limited Number of Signal Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P. Hallbjörner, J. D. Sánchez-Heredia, P. Lindberg, A. M. Martínez-González, and T. Bolin On Small Terminal Antenna Correlation and Impact on MIMO Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Yanakiev, J. Ø. Nielsen, M. Christensen, and G. F. Pedersen Compensating for Non-Linear Amplifiers in MIMO Communications Systems . . . . . . . . . S. A. Banani and R. G. Vaughan

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CALL FOR PAPERS

Call for Papers: Special Issue on Antennas and Propagation at Millimeter and Sub-millimeter Waves . . . . . . . . . .. . . . . . . . . .

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION Is the leading international engineering journal on the general topics of electromagnetics, antennas and wave propagation. The journal is devoted to antennas, including analysis, design, development, measurement, and testing; radiation, propagation, and the interaction of electromagnetic waves with discrete and continuous media; and applications and systems pertinent to antennas, propagation, and sensing, such as applied optics, millimeter- and sub-millimeter-wave techniques, antenna signal processing and control, radio astronomy, and propagation and radiation aspects of terrestrial and space-based communication, including wireless, mobile, satellite, and telecommunications. Author contributions of relevant full length papers and shorter Communications are welcomed. See inside back cover for Editorial Board.

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Digital Object Identifier 10.1109/TAP.2012.2186030

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 60, NO. 2, FEBRUARY 2012

Guest Editorial for the Special Issue on Multiple-Input Multiple-Output (MIMO)

W

E are pleased to present this special issue on multiple-input multiple-output (MIMO), which represents a breakthrough in the use of antenna arrays in wireless transmission. Unlike traditional phased array or diversity techniques that enhance one signal of interest, MIMO systems employ antenna arrays jointly at the transmitter and receiver to spatially multiplex signals, providing tremendous capacity gains. Although there has already been intense research in MIMO wireless communications, and many obstacles in signal processing, modulation, and coding for MIMO systems have been overcome, outstanding questions in the areas of antennas and propagation remain, making MIMO a timely topic for our community. The need for research in this area becomes even more apparent as new standards such as IEEE 802.11n, LTE Advanced, and WiMAX that include MIMO operation are implemented, revealing that physical devices, antennas, and channels can no longer be oversimplified or neglected. This special issue is organized into three main sections: 1) antenna design, modeling, and analysis, 2) channel sounding and modeling, and 3) system performance evaluation. A. Antenna Design, Modeling, and Analysis

Although signal processing treatments of MIMO may treat antennas as isotropic elements that are not affected by nearby antennas or scatterers, real antennas exhibit non-isotropic patterns and inter-element coupling. This section contains papers that consider the challenges of designing compact MIMO antennas with good performance, as well as novel and rigorous ways to model and analyze such antenna systems. Exploiting multiple polarizations is a possible method of achieving a compact MIMO design with low coupling. Yan and Bernhard present a clever design allowing two orthogonal resonant modes of a compact dielectric resonator antenna (DRA) for LTE700 femtocell applications, achieving polarization and angle diversities and 30 dB isolation. A low profile tri-polarized antenna consisting of a dual-polarized ring patch and a disk-loaded monopole is explored in Zheng et al. to build an 18-port antenna cube, exhibiting lower mutual coupling and simpler feeding than a dipole MIMO cube. Several papers address the challenge of MIMO antenna design for compact user terminals exhibiting higher mutual coupling and correlation. Su et al. implement a printed neutralization line along one ground plane edge to decouple a twomonopole array for a USB dongle application at 2.4 GHz, requiring little modification of the ground plane. The use of parasitic structures for coupling mitigation is explored in several contributions. Lau and Bach Andersen introduce the theory of parasitic decoupling, whereby two arbitrary antennas of a given antenna spacing can be perfectly decoupled with a reactively loaded parasitic element acting as a reflector. Experiments reveal that decoupling is achieved with only a small penalty in total efficiency. Z. Li et al. introduce a complementary perspective that the parasitic elements create a second path for couDigital Object Identifier 10.1109/TAP.2012.2183909

pling cancellation, demonstrating the principle by decoupling two closely-coupled slot antennas using two monopoles as parasitic elements. J. Li et al. design an efficient wideband MIMO antenna by combining a parasitic decoupling strip with right-angled slits in the ground plane to obtain 2.4 GHz–6.55 GHz operation and 18 dB isolation. The ground plane of compact user terminals can play a major role in the radiation of MIMO antennas at low frequency where the chassis is excited. The theory of characteristic mode is explored by H. Li et al. in the context of designing efficient MIMO antennas by placing the elements to avoid simultaneous excitation of the chassis by more than one antenna element. A tradeoff analysis shows that MIMO performance is significantly improved by the increased isolation. Pelosi et al. carry out a comprehensive study on the performance of small narrowband antennas with and without a user in either MIMO mode or transceiver separation mode (TSM). This approach can relax the duplex filter requirement in TSM, although user effects may largely influence the antenna performance. In order to further improve MIMO antenna performance in a time-varying propagation channel, reconfigurable antenna elements may be employed to optimize the antenna-channel interaction. Qin et al. show that two pattern reconfigurable U-slot antenna elements can provide capacity gain in measured line-ofsight (LOS) and non-LOS channels, relative to two omnidirectional reference antennas. Metrics and models for MIMO antennas are considered by two contributions. Yun and Vaughan isolate the role of antenna efficiencies from correlation in the diversity and capacity performance of a given MIMO antenna. Thereafter, the MIMO antenna can be represented with an equivalent number of ideal antenna branches that are called diversity order and capacity order, respectively. The question of the validity and accuracy of equivalent circuit models for MIMO arrays is addressed by Wallace and Mehmood, where a method-of-moments analysis based on first principles reveals that such models are exact under normal circumstances, and that transmit and receive modes can be analyzed with a single unified model. B. Channel Sounding and Modeling This section focuses on accurate channel characterization through sounding and modeling, which is vital to correctly assess the benefits of MIMO transmission, allowing critical tradeoffs and design decisions to be made. Two papers in this section directly consider the topic of channel sounding. Pinchera and Migliore present an interesting measurement approach using a parasitic array instead of a switched array. Using low cost switched parasitic elements instead of a large multiport microwave switch dramatically reduces the cost of MIMO channel sounding with only modest reduction in accuracy. The impact of an imperfect underlying model on the accuracy of high-resolution double-directional MIMO channel estimation is studied by Landmann et al. It is shown that modeling this uncertainty allows multipath to be correctly classified as discrete or diffuse, and that imperfect calibration can lead to large error in multipath estimates.

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Sounder-based channel modeling is considered in two papers. Zhang et al. extend tensor-based MIMO modeling approaches to the case of wide bandwidth, which is required for today’s wireless standards. The model is assessed using measured indoor channels, indicating a tradeoff between complexity and accuracy when generating synthetic MIMO channel data. Poutanen et al. propose a method for extending geometry-based stochastic channel models to the case of multiple links, which is important to analyze MIMO systems using coordinated transmission or relays. This model is accomplished by having certain clusters that are shared by the links, creating dependence in the statistics of the MIMO channels. Finally, this section includes two papers that present measurement of land mobile satellite (LMS) channels. Cheffena et al. consider the effect of signal shadowing by trees in MIMO-LMS links, proposing a multipath model for trees based on multiple scattering theory. The model is compared with direct FDTD simulation, indicating that good accuracy can be obtained with modest complexity. King et al. investigate the use of multiple antennas to increase the capacity of LMS networks, where a Markov chain is employed to characterize the time-variant nature of shadowing and depolarization effects. The utility of the proposed technique is illustrated through direct measurements with an artificial LMS platform. C. System Performance Evaluation The final section deals principally with system-level aspects, indicating how detailed characteristics of the propagation channel, antennas, and devices affect the performance of the overall MIMO system or network. Two papers consider the emerging topic of relays and coordinated MIMO transmission. Nishimori et al. evaluate the capacity of relay-enhanced multi-antenna transmission in a cellular environment through direct propagation measurements taken in Yokkaichi City, Japan. This study shows that characterizing path-loss differences is critical and that relay-enhanced MIMO can provide a 50% improvement in capacity. Lau et al. analyze urban propagation measurements involving three coherent base stations and a mobile unit equipped with four antennas. Capacity for cooperative transmission from the base stations is analyzed, revealing dramatic sum-rate capacity gains compared to non-cooperative methods. User influence and exposure limits are considered in two contributed papers. Nielsen et al. provide a detailed study of user influence on the outage capacity for mobile devices in the data mode operation. Six different handsets at two bands are characterized for twelve different users, showing that handset design and hand position critically impact body loss, mean effective gain, and outage capacity. Perentos et al. consider compliance and exposure testing of MIMO devices, which is important as multi-antenna technology is increasingly incorporated into advanced devices. The developed methodologies allow such testing to be performed with scalar field probes, avoiding expensive upgrades of existing test equipment. The use of parasitic arrays for MIMO transmission are considered in two papers, providing reduced complexity or capacity enhancement compared to classical MIMO systems. Alrabadi et al. develop the methodology of using a switched parasitic array (SPA) with only a single active RF source to replace a full MIMO transmitter with reduced cost and complexity. The generalized method for forming the required orthogonal bases is demonstrated through simulation and direct measurement with

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a prototype SPA. Mehmood and Wallace propose flexible reconfigurable aperture (RECAP) antennas to increase MIMO capacity in interference-limited scenarios. Multi-user simulations with a detailed noise model suggest that high reconfigurability can lead to many-fold capacity increase. Finally, four papers are included that extend or verify assumptions made in existing modeling approaches for MIMO systems. Webb et al. consider the coherence time and bandwidth of channel state information in measured time-varying urban channels, indicating how sensitive feedback methods are to time and frequency offsets. The study shows that controlling the feedback rate can lead to significant improvements in mobile MIMO systems. Hallbjörner et al. explore the impact of sparse multipath on antenna correlation and diversity, in contrast to classical treatments where infinite and uniform arrivals are assumed. Multipath channels are simulated using antenna arrays in an anechoic chamber, showing that sparse multipath can lead to high variability or spread of channel statistics like correlation. Yanakiev et al. study the use of correlation as a metric in the design stage to predict handset performance in terms of MIMO capacity in real scenarios. The surprising result is that correlation may have little bearing on capacity, indicating correlation may be a misleading figure of merit. Finally, Banani and Vaughan investigate the effect of non-linear amplifiers in practical MIMO systems and how to compensate the resulting degradations to channel capacity. A model for non-linear MIMO systems is introduced, and a blind channel-estimation technique is developed to estimate and track the channel in the presence of non-linearities. To conclude this guest editorial, we would like to thank the former Editor-in-Chief Dr. Trevor S. Bird and his successor Prof. Michael A. Jensen, for providing us with the opportunity to coordinate and organize this special issue and for their continued support throughout the process. We are also grateful to the many anonymous reviewers who helped make the special issue possible. We believe that the issue provides a true snapshot of the state-of-the-art in antennas and propagation research in MIMO systems, serving as interesting reading as well as a useful reference for years to come. JON W. WALLACE, Guest Editor School of Engineering and Science Jacobs University Bremen, Germany JØRGEN BACH ANDERSEN, Guest Editor Department of Electronic Systems Aalborg University Aalborg, Denmark BUON KIONG LAU, Guest Editor Department of Electrical and Information Technology Lund University Lund, Sweden BABAK DANESHRAD, Guest Editor Department of Electrical Engineering University of California, Los Angeles Los Angeles, CA JUN-ICHI TAKADA, Guest Editor Graduate School of Engineering Tokyo Institute of Technology Tokyo, Japan

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ON

Jon W. Wallace (S’99–M’03) received the B.S. (summa cum laude) and Ph.D. degrees in electrical engineering from Brigham Young University (BYU), Provo, UT, in 1997 and 2002, respectively. From 1995 to 1997, he worked as an Associate of Novell, Inc., Provo, and during 1997 he was a Member of Technical Staff for Lucent Technologies, Denver, CO. He received the National Science Foundation Graduate Fellowship in 1998 and worked as a Graduate Research Assistant at BYU until 2002. From 2002 to 2003, he was with the Mobile Communications Group, Vienna University of Technology, Vienna, Austria. From 2003 to 2006, he was a Research Associate with the BYU Wireless Communications Laboratory. Since 2006, he has been Assistant Professor of electrical engineering at Jacobs University, Bremen, Germany. His current research interests include wireless channel sounding and modeling, physical-layer security, MIMO communications, cognitive radio, and ultrawideband (UWB) systems. Dr. Wallace currently serves as an Associate Editor of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. He was awarded the H. A. Wheeler paper award in the IEEE TRANSACTIONS PROPAGATION in 2002.

ANTENNAS AND

Jørgen Bach Andersen (M’68–SM’78–F’92–LF’02) received the M.Sc. and Dr.Techn. degrees from the Technical University of Denmark (DTU), Lyngby, Denmark, in 1961 and 1971, respectively. In 2003 he was awarded an honorary degree from Lund University, Sweden. From 1961 to 1973, he was with the Electromagnetics Institute, DTU and since 1973 he has been with Aalborg University, Aalborg, Denmark, where he is now a Professor Emeritus and Consultant. He was head of a research center, Center for Personal Communications, CPK, from 1993–2003. He has been a Visiting Professor in Tucson, AZ; Christchurch, New Zealand; Vienna, Austria; and Lund, Sweden. He has published widely on antennas, radio wave propagation, and communications, and has also worked on biological effects of electromagnetic systems. He has coauthored a book, Channels, Propagation and Antennas for Mobile Communications (IEE, 2003). He was on the management committee for COST 231 and 259, a collaborative European program on mobile communications. Prof. Andersen is a former Vice President of the International Union of Radio Science (URSI) from which he was awarded the John Howard Dellinger Gold Medal in 2005.

Babak Daneshrad received the B.Eng. and M.Eng. degrees with emphasis in communications from McGill University, Montreal, Quebec, Canada, in 1986 and 1988, respectively, and the Ph.D. degree with emphasis in integrated circuits and systems from the University of California, Los Angeles (UCLA), in 1993. In January 2001, he co-founded Innovics Wireless, a company focused on developing 3G cellular mobile terminal antenna diversity solutions and in 2004 he co-founded Silvus Communications. From 1993 to 1996, he was a member of technical staff with the Wireless Communications Systems Research Department, AT&T Bell Laboratories, where he was involved in the design and implementation of systems for high-speed wireless packet communications. Currently, he is a Professor with the Electrical Engineering Department, UCLA. His research interests are in the areas of wireless communication system design, experimental wireless systems, and VLSI for communications. His current research interests are cross disciplinary in nature and deal with addressing practical issues associated with the realization of advanced wireless systems. The work is focused on low power MIMO wireless systems, as well as cognitive radio communications. Prof. Daneshrad is the recipient of the 2005 Okawa Foundation award, a coauthor of the best paper award at PADS 2004, and was awarded first prize in the DAC 2003 design contest. He is the beneficiary of the endowment for “UCLA-Industry Partnership for Wireless Communications and Integrated Systems.”

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Buon Kiong Lau (S’00–M’03–SM’07) received the B.E. degree (with honors) from the University of Western Australia, Perth, Australia and the Ph.D. degree from Curtin University of Technology, Perth, in 1998 and 2003, respectively, both in electrical engineering. During 2000 to 2001, he worked as a Research Engineer with Ericsson Research, Kista, Sweden. From 2003 to 2004, he was a Guest Research Fellow at the Department of Signal Processing, Blekinge Institute of Technology, Sweden. Since 2004, he has been at the Department of Electrical and Information Technology, Lund University, where he is now an Associate Professor. He has been a Visiting Researcher at the Department of Applied Mathematics, Hong Kong Polytechnic University, China, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, and Takada Laboratory, Tokyo Institute of Technology, Japan. His primary research interests are in various aspects of multiple antenna systems, particularly the interplay between antennas, propagation channels and signal processing. Dr. Lau is an Associate Editor for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. From 2007 to 2010, he was a Co-Chair of Subworking Group 2.2 on “Compact Antenna Systems for Terminals” (CAST) within EU COST Action 2100. Since 2011, he is a Swedish national delegate and the Chair of Subworking Group 1.1 on “Antenna System Aspects” within COST IC1004.

Jun-ichi Takada (SM’11) received B.E. and D.E. degrees from Tokyo Institute of Technology (Tokyo Tech), Japan, in 1987 and 1992, respectively. He was a Research Associate at Chiba University from 1992 to 1994, and an Associate Professor at Tokyo Tech from 1994 to 2006 where he has been a Professor since 2006. From 2003 to 2007, he was also a Researcher at the National Institute of Information and Communications Technology (NICT), Japan. His current interests include the radiowave propagation and channel modeling for various wireless systems, and regulatory issues of spectrum sharing.

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Design of a MIMO Dielectric Resonator Antenna for LTE Femtocell Base Stations Jie-Bang Yan, Member, IEEE, and Jennifer T. Bernhard, Fellow, IEEE

Abstract—A novel multiple-input multiple-output (MIMO) dielectric resonator antenna (DRA) for long term evolution (LTE) femtocell base stations is described. The proposed antenna is able to transmit and receive information independently using TE and HE modes in the LTE bands 12 (698–716 MHz, 728–746 MHz) and 17 (704–716 MHz, 734–746 MHz). A systematic design method based on perturbation theory is proposed to induce mode degeneration for MIMO operation. Through perturbing the boundary of the DRA, the amount of energy stored by a specific mode is changed as well as the resonant frequency of that mode. Hence, by introducing an adequate boundary perturbation, the TE and HE modes of the DRA will resonate at the same frequency and share a common impedance bandwidth. The simulated mutual coupling between the modes was as low as . It was estimated that in a rich scattering environment with an Signal-to-Noise Ratio (SNR) of 20 dB per receiver branch, the proposed MIMO DRA was able to achieve a channel capacity of 11.1 b/s/Hz (as compared to theoretical maximum 2 2 capacity of 13.4 b/s/Hz). Our experimental measurements successfully demonstrated the design methodology proposed in this work. Index Terms—Dielectric resonator antenna (DRA), long term evolution (LTE), multiple-input multiple-output (MIMO) antenna, mutual coupling, perturbation method.

I. INTRODUCTION

T

HE Federal Communications Commission (FCC) recently released the 700 MHz spectrum which was previously used for analog television broadcasting [1]. A new nationwide wireless broadband network based on long term evolution (LTE) technology has been proposed to operate in the 700 MHz spectrum [2], [3]. In the LTE Evolved UMTS terrestrial radio access (E-UTRA) air interface, multiple-input multiple-output (MIMO) technology plays an important role in increasing the system’s spectral efficiency [4], [5]. Given the lower operating frequency of the LTE system, as compared to the WiFi and cellular standards, the antenna in handheld devices such as a smartphone or a netbook must be electrically

Manuscript received May 27, 2010; revised December 14, 2010; accepted February 05, 2011. Date of publication October 28, 2011; date of current version February 03, 2012. This work was supported by the Motorola Center for Communications at the University of Illinois at Urbana-Champaign and a Croucher Foundation Scholarship. J.-B. Yan was with the Electromagnetics Laboratory, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA. He is now with the Center for Remote Sensing of Ice Sheets (CReSIS), University of Kansas, Lawrence, KS 66045 USA. J. T. Bernhard is with the Electromagnetics Laboratory, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2174021

small. This implies the mobile antennas are likely to be inefficient and the coverage of the system is therefore limited. This is especially true if MIMO operation is needed at both mobile and base station since the antenna efficiency would be further reduced due to strong mutual coupling between closely-packed mobile antennas. In view of this, LTE architecture includes a femtocell solution for coverage extension [6]. Femtocells can be considered as low-power access points serving indoor areas. To exploit the richness in multipath propagation in indoor scenarios, it is desired to employ MIMO antennas with a very low mutual coupling as the base station antenna in a femtocell. One possible solution would be the orthogonally polarized MIMO antennas proposed in [7]. However the problem is that such antennas would be oversized when scaled to operate at 700 MHz. Hence, a new MIMO antenna solution for LTE’s femtocell base station is necessary. In this work, a 700 MHz dual-mode MIMO dielectric resonator antenna (DRA) that is suitable for the new wireless system is proposed. Although the cost of DRAs may be high as compared to traditional PIFAs or microstrip antennas, they have the advantages of compact size, high radiation efficiency, and wide impedance bandwidth [8]. Another important feature of DRAs is that the three dimensional structure offers more degrees of freedom in exciting various orthogonal resonant modes, and each mode can be utilized to transmit and receive information independently. This makes the DRA an ideal candidate for application in MIMO communication systems. Indeed, a multi-mode usage of a single dielectric resonator has been suggested in [9], but the emphasis is not on MIMO applications. The concept of a MIMO DRA was first described and demonstrated by Ishimiya et al. in [10], [11]. It was experimentally shown that a cubic MIMO DRA is able to achieve a diversity gain of about 10 dB and has comparable performance to traditional MIMO dipole arrays in practical IEEE 802.11n systems. Nevertheless, in Ishimiya’s papers, no explicit design method has been described. The major difficulty of applying DRAs in MIMO systems is to make various modes to resonate at the same frequency while maintaining low coupling between the modes. Here, we introduce a systematic design method for MIMO DRAs. The key in MIMO DRA design is to induce degenerate modes (i.e., modes that have the same resonant frequency). Conventionally, only DRAs that exhibit symmetry can support degenerate modes [12] and this limits any further size reduction of MIMO DRAs. Hence, a novel mode degeneration method based on boundary perturbation is proposed and demonstrated in this work. Section II describes the base design for the proposed MIMO DRA, then, Section III introduces the boundary perturbation for

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YAN AND BERNHARD: DESIGN OF A MIMO DIELECTRIC RESONATOR ANTENNA FOR LTE FEMTOCELL BASE STATIONS

Fig. 1. Perspective view of the split-cylindrical DRA ( , , , and

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, ).

mode degeneration. In Section IV, we evaluate the performance of the perturbed antenna structure. Simulated results including those for MIMO capacity are provided. Following that, some experimental results are given in Section V as a validation to the developed design methodology. Finally a conclusion and a discussion of future work are given in Section VI. Fig. 2. Theoretical magnetic field distributions for the (a) mode. (b)

II. BASE DESIGN Consider a split-cylindrical DRA , with a radius of 44 mm and a length of 80 mm residing on a ground plane with dimensions as shown in Fig. 1. The mode and the mode can be excited simultaneously using appropriate excitation methods, such as probe feeds, aperture coupling or microstrip feeds. The value of the subscript ranges between zero and one, depending on the method of feeding [12]. Here, a 50 microstrip-fed rectangular slot and a probe feed were chosen to excite the and modes, respectively (see Fig. 1). FR-4 epoxy board with thickness of 1.6 mm is used as the substrate of the microstrip line. The dimensions of the slot are 50 mm 4 mm and the probe that excites the mode has a length of 27 mm. Fig. 2 shows the plots of the theoretical magnetic field distributions for the two modes inside the DRA computed using Wolfram Research Mathematica [13]. It can be seen that mode behaves as a magnetic dipole on the -axis while mode radiates as a short magnetic dipole oriented along the -axis. The two modes are therefore orthogonal to each other and should exhibit low mutual coupling. The resonant frequencies of the mode and mode can be derived from the separation equation [8] and are found to be 653 MHz and 520 MHz, respectively,

(1)

mode, and

Fig. 3. Simulated -parameters of the unperturbed cylindrical DRA.

simulation was performed using Ansys HFSS [14] and the simulated -parameters of the antenna are shown in Fig. 3. The theoretically predicted and simulated operating frequencies of the modes agree very well with each other. It can also be seen that the coupling between the two modes is very low as expected. III. DESIGN OF MIMO DRA

(2) where is the speed of light in free space, and and are the first zeros of the zero-order Bessel function and the derivative of the first-order Bessel function, respectively. A full-wave

A. Boundary Perturbation In order to work in a MIMO system, the two modes should have the same resonant frequency and have a shared impedance bandwidth. To accomplish this, we propose a mode degeneration method based on boundary perturbation. For an arbitrarily

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shaped dielectric resonator, the change in resonant frequency due to a change of the cavity wall can be determined using perturbation theory [15], and is given by,

(3)

Fig. 4. Boundary perturbation from the base of the split-cylindrical DRA (Cross-sectional ( -plane) view).

where and are the permittivity and the permeability of the dielectric resonator respectively, and are the resonant radian frequencies of the perturbed and unperturbed resonator, respectively, and are the volume perturbed and the original volume of the resonator, and and are the unperturbed fields. Equation (3) indicates that the change in resonant frequency is equal to the electric and magnetic energies removed by the perturbation divided by the total energy stored [15], i.e.,

(4) where and are time-averaged electric and magnetic energies originally contained in the volume perturbed and is the total energy stored in the unperturbed cavity. Now consider a boundary perturbation from the base of the split-cylindrical DRA as depicted in Fig. 4. The changes in resonant frequencies of the mode and mode can be computed using (3), and the result is shown in Fig. 5. It can be observed that as the electric boundary is moved up, the resonant frequency of the mode increases more rapidly than that of the mode. Hence, at a certain perturbation value, the two resonant frequencies should overlap and thus fulfill the primary requirement for MIMO antenna design. According to (4), the difference in the rate of change of resonant frequency can be explained by the difference in the energy stored by the two modes in the perturbation volume . To verify the boundary perturbation method, an HFSS simulation was carried out and the result is also shown in Fig. 5. It can be seen that the result predicted by the boundary perturbation method starts to deviate from the result obtained from HFSS when the perturbation, , increases. This is due to the substitution of the original fields into the perturbed fields during the derivation of (3). The difference between the original fields and the perturbed fields would be intolerable when the perturbation is too large. Thus, the deviation at large perturbations is inherent in the perturbation analysis. Nonetheless, the boundary perturbation method gives a good initial guess on how much perturbation is required to make the two modes resonate at the same frequency. According to the HFSS simulation result, the two modes both resonate at 700 MHz when the perturbation, , is 13 mm. In (3), there is no specific constraint on the geometry of the cavity, hence, the proposed boundary perturbation method can be applied to DRAs of any other shapes with arbitrary perturbations. However, the difficulty of analysis of such structures might be the evaluation of the integrals in (3).

Fig. 5. Plot of change of resonant frequency eter .

against the perturbation param-

Fig. 6. Elliptical approximation of the perturbed cylindrical boundary (Crosssectional ( -plane) view).

Fig. 7. Simulated -parameters of the perturbed cylindrical DRA.

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Fig. 8. Comparison of the simulated and measured radiation patterns of Port 1 (HE mode).

Fig. 9. Comparison of the simulated and measured radiation patterns of Port 2 (TE mode).

B. Boundary Approximation While the above described boundary perturbation method obtains the solutions by approximating the fields, boundary approximation estimates the change in resonant frequency by approximating the structure of the resonator. According to Fig. 6, a perturbed cylindrical boundary can be modeled by a half ellipse. The accuracy of this method depends on how well the perturbed circular arc is approximated by an elliptic arc. The resonant frequencies of various modes in an elliptical DRA can be found by expanding the fields inside the cavity in Mathieu functions and applying the technique of separation of variables. A detailed analysis of an elliptical DRA can be found in [16]. The resonant frequencies of a series of split-elliptical DRAs of various minor axes, which corresponded to the previously described set of perturbed cylindrical DRAs, are computed, and the change in resonant frequency estimated by this boundary approximation method is plotted in Fig. 5. The results obtained agree very well with those calculated by both the boundary perturbation method and full-wave simulations. IV. SIMULATED ANTENNA PERFORMANCE A. Antenna Characteristics mode and the mode From Section III-A, the of a split-cylindrical DRA will both resonate at 700 MHz when

the perturbation, , is 13 mm. The dimensions of the perturbed DRA are 80 mm 84 mm 31 mm. Given the same resonant frequency and a half-wavelength antenna separation, the dimensions of a two-element MIMO PIFA would be 107 mm 214 mm 5 mm. Since coupling between antenna ports is another important parameter to characterize MIMO antennas, the proposed antenna structure was simulated in HFSS. The simulated -parameters of the antenna were obtained with 50 terminations at both ports and are given in Fig. 7. It can be observed that the mutual coupling between the two modes is insensitive to the perturbation (see Fig. 3) and is less than . This is significantly lower than the mutual coupling in conventional MIMO antennas that are based on dipole antennas, patch antennas or PIFAs [17]–[20]. The impedance bandwidths (defined as ) of the mode and the mode are 10 MHz and 35 MHz respectively. The mode has a relatively narrow bandwidth and limits the overall bandwidth of the antenna. Nevertheless, the bandwidth of the mode can be improved using well known bandwidth broadening techniques, such as inserting an air gap between the ground plane and the DRA [21], [22], or adding a matching stub at the end of the microstrip line [23]. The simulated gains of the and modes are 3.96 and 3.19 dBi, respectively. The simulated radiation patterns of the two modes, which are orthogonal to each other, are given in Figs. 8 and 9. Hence, the antenna is

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Fig. 10. The floor plan (16 m 19 m) of the office environment that was used to estimate the MIMO channel capacity (notice that there is no line-of-sight (LOS) path between the transmitter and any of the receivers). Fig. 11. Estimated channel capacity of the proposed MIMO DRA.

able to exploit polarization diversity and the pattern orthogonality leads to low mutual coupling between the ports. the transmit antennas, the flat-fading MIMO channel capacity of the -th link, , can be calculated by [25]–[27]

B. MIMO Performance Evaluation The channel capacity gain by using the proposed antenna was evaluated with the aid of Remcom Wireless Insite [24]. In the simulation setup, a single transmitter and 1000 identical receivers were placed in an office environment as shown in Fig. 10. The office environment was constructed to resemble a rich scattering environment (i.e., the channel statistics are approximately Rayleigh distributed). In order to resemble a timevarying MIMO channel, the receivers were randomly spread across the designated area of the office such that a 1000 nonline-of-sight (NLOS) communication links were established. In all the simulations, there were 80 paths for each channel realization. The simulated complex radiation patterns (including both polarizations, and ) of the proposed antennas were used at the transmitter and all the receivers. 1000 samples of the unnormalized channel matrix were then obtained from the simulation [25],

(5) communication links, and where there are is the unnormalized channel matrix of the -th link. Here, represents the -th sample of the complex channel gain between port of the transmitter and port of the receiver, where subscripts , 2 and , 2:

(6) Here is the number of path in the -th link; is the received power contributed by the -th path in the -th link; is the phase of the -th path in the -th link. From the simulated channel data, it was found that the coherence bandwidth of the wireless channel was much larger than the bandwidth of the proposed antenna. Hence, for equal power distributed among

(7) where and denote the number of transmit and receiver antennas, respectively; is an identity matrix with dimension ; is the mean signal-to-noise ratio (SNR) per receive branch; represents a complex conjugate transpose; and is the -th normalized channel matrix

(8)

where denotes a Frobenius norm. The mean capacity and the maximum achievable capacity obtained by using the proposed antenna are plotted in Fig. 11. Fig. 11 also gives the theoretical channel capacities for single-input single-output (SISO), 2 2 and 3 3 channels with zero mean, unity variance, i.i.d. complex Gaussian distributed channel elements for comparison. The results indicate that the estimated mean channel capacity is 11.1 b/s/Hz at an SNR of 20 dB per receiver branch. The maximum achievable capacity is very close to the theoretical maximum 2 2 MIMO capacity of 13.4 b/s/Hz. The small discrepancy between the theoretical and simulated capacities may be due to the non-ideal scattering environment and finite mutual coupling between the modes. Nevertheless, the simulation results reflect the utility of the antenna design, and a prototype antenna is presented in Section V. V. MEASUREMENT RESULTS The perturbed cylindrical DRA was built and tested in the Electromagnetics Laboratory at University of Illinois at Urbana-Champaign. The dielectric material ( and ) was supplied by Countis Laboratories [28]. The dielectric block was bonded onto the ground plane

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REFERENCES

Fig. 12. Measured -parameters of the perturbed cylindrical DRA.

with silver epoxy so as to prevent any air gaps between the dielectric and ground plane. This is important because for DRAs with high permittivities, air gaps of less than 0.05 mm can be enough to significantly alter the expected input impedance [12]. The -parameters of the perturbed cylindrical DRA were measured using Agilent’s two-port Network Analyzer E8363B (with 50 reference impedance). The measured results are given in Fig. 12, which are very close to the simulated results given in Fig. 7. Both modes are well matched at 717 MHz. The coupling between the ports is less than at the operating frequency. The measured impedance bandwidths of the mode and the mode are 13.5 MHz and 35 MHz, respectively. The measured radiation patterns along the three principal cuts are given in Figs. 8 and 9. Despite a small distortion of the pattern at some angles, the measured patterns agreed reasonably well with the simulated ones. The complementary nature of the two orthogonal modes can still be observed clearly. VI. CONCLUSION A 2-port MIMO antenna based on a split-cylindrical DRA is described in this work. A mode degeneration method derived from perturbation theory is proposed to make the TE and HE modes of the split-cylindrical DRA resonate at the same frequency. The proposed method has been verified by both fullwave simulations and the boundary (elliptical) approximation method, and can be applied to DRAs of any shape. The fabricated MIMO DRA was tested and the experimental results show very good agreement with the simulated results. Indeed, given that the same operating frequency and the same dielectric material, the antenna described in this paper is smaller in volume, has lower profile, has a smaller ground plane and has much lower mutual coupling as compared to the work in [10], [11]. The proposed antenna is potentially suitable as the femtocell base station antenna in the forthcoming nationwide mobile broadband system based on LTE technology. Future work related to this paper will be a frequency reconfigurable MIMO DRA which can easily be adapted to other LTE bands and other wireless standards.

[1] Federal Communications Commission, “700 MHz band,” Auction 73 Feb. 2009. [2] News Archives AT&T Inc., 2008 [Online]. Available: http://www.att. com/ [3] News Archives Verizon Wireless, 2009 [Online]. Available: http://news.vzw.com/ [4] 3GPP TS36.300, “Evolved Universal Terrestrial Radio Access (E-UTRA) and Evolved Universal Terrestrial Radio Access Network (E-URRAN): Overall Description,”. [5] D. Astely, E. Dahlman, A. Furuskar, Y. Jading, M. Lindstrom, and S. Parkvall, “LTE: The evolution of mobile broadband—[LTE part II: 3GPP release 8],” IEEE Commun. Mag., vol. 47, no. 4, pp. 44–51, Apr. 2009. [6] V. Chandrasekhar and J. Andrews, “Femtocell networks: A survey,” IEEE Commun. Mag., vol. 46, no. 9, pp. 59–67, Sep. 2008. [7] C.-Y. Chiu, J.-B. Yan, and R. D. Murch, “Compact three-port orthogonally polarized MIMO antennas,” IEEE Antennas Wireless Propag. Lett., vol. 6, pp. 619–622, 2007. [8] K.-M. Luk and K.-W. Leung, Dielectric Resonator Antennas. Hertfordshire, England: Research Studies Press Ltd., 2003. [9] L. K. Hady, D. Kajfez, and A. A. Kishk, “Triple mode use of a single dielectric resonator,” IEEE Trans. Antennas Propag., vol. 57, no. 5, pp. 1328–1335, May 2009. [10] K. Ishimiya, J. Langbacka, Z. Ying, and J.-I. Takada, “A compact MIMO DRA antenna,” in Proc. IEEE Int. Workshop on Antenna Technology: Small Antennas and Novel Metamaterials (IWAT ’08), Chiba, Japan, Mar. 2008, pp. 286–289. [11] K. Ishimiya, Z. Ying, and J.-I. Takada, “A compact MIMO DRA for 802.11n application,” presented at the IEEE Antennas and Propagation Society Int. Symp., San Diego, CA, Jul. 2008. [12] A. Petosa, Dielectric Resonator Antenna Handbook. Norwood, MA: Artech House, 2007. [13] Mathematica, Wolfram Research Inc., 2010. [14] HFSS Ansys, Inc., 2010. [15] R. F. Harrington, Time-Harmonic Electromagnetic Fields. New York: IEEE Press, 2001. [16] A. Tadjalli and A. Sebak, “Resonance frequencies and far field patterns of elliptical dielectric resonator antenna: Analytical approach,” in Progress in Electromagnetic Research, PIER 64, 2006, pp. 81–98. [17] C.-C. Hsu, K. H. Lin, H.-L. Su, H.-H. Lin, and C.-Y. Wu, “Design of MIMO antennas with strong isolation for portable applications,” presented at the IEEE Antennas and Propagation Society Int. Symp., Charleston, SC, Jun. 2009. [18] H. Zhang, Z. Wang, J. Yu, and J. Huang, “A compact MIMO antenna for wireless communication,” IEEE Antennas Propag. Mag., vol. 50, no. 6, pp. 104–107, Dec. 2008. [19] K.-S. Min, D.-J. Kim, and M.-S. Kim, “Multi-channel MIMO antenna design for WiBro/PCS band,” in Proc. IEEE Antennas and Propagation Society Int. Symp., Hawaii, Jun. 2007, pp. 1225–1228. [20] K. Chung and J. H. Yoon, “Integrated MIMO antenna with high isolation characteristics,” Electron. Lett., vol. 43, no. 4, pp. 199–201, Feb. 2007. [21] M. Cooper, “Investigation of Current and Novel Rectangular Dielectric Resonator Antennas for Broadband Applications at L-band Frequencies,” M.Sc. thesis, Carleton University, Ottawa, ON, Canada, 1997. [22] S.-M. Deng, C.-L. Tsai, S.-F. Chang, and S.-S. Bor, “A CPW-fed suspended, low profile rectangular dielectric resonator antenna for wideband operation,” in Proc. IEEE Antennas and Propagation Society Int. Symp., Washington, D.C., Jul. 2005, vol. 4B, pp. 242–245. [23] P. V. Bijumon, S. K. Menon, M. N. Suma, M. T. Sebastian, and P. Mohanan, “Broadband cylindrical dielectric resonator antenna excited by modified microstrip line,” Electron. Lett., vol. 41, no. 7, pp. 385–387, Mar. 2005. [24] Wireless Insite, Remcom Inc., 2006. [25] J. D. Boerman and J. T. Bernhard, “Performance study of pattern reconfigurable antennas in MIMO communication systems,” IEEE Trans. Antennas Propag., vol. 56, no. 1, pp. 231–236, Jan. 2008. [26] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” in Wireless Personal Commun.. New York: Kluwer Academic Press, 1998, pp. 311–335. [27] Z. Tang and A. S. Mohan, “Experimental investigation of indoor MIMO Ricean channel capacity,” IEEE Antennas Wireless Propag. Lett., vol. 4, pp. 55–58, 2005. [28] Countis Laboratories [Online]. Available: http://www.countis.com/

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Jie-Bang Yan (S’09–M’11) received the B.Eng. degree (first class honors) in electronic and communications engineering from the University of Hong Kong, in 2006, the M.Phil. degree in electronic and computer engineering from the Hong Kong University of Science and Technology, in 2008, and the Ph.D. degree in electrical and computer engineering from the University of Illinois at Urbana-Champaign, in 2011. He was a Croucher Scholar from 2009 to 2011 while he did his Ph.D. at the University of Illinois at Urbana-Champaign. Upon graduation, he joined the Center for Remote Sensing of Ice Sheets (CReSIS), University of Kansas, where he is currently an Assistant Research Professor. His research interests include design and analysis of MIMO and reconfigurable antennas, RF propagation, radar antenna designs, and fabrication of on-chip antennas. He holds two U.S. patents and a U.S. patent application related to novel antenna technologies. Dr. Yan was the recipient of the Best Paper Award at the 2007 IEEE (HK) AP/MTT Postgraduate Conference and the 2011 Raj Mittra Outstanding Research Award at Illinois. He serves as a Reviewer for several journals and conferences on antennas and electromagnetics.

Jennifer T. Bernhard (S’89–M’95–SM’01–F’10) was born on May 1, 1966, in New Hartford, NY. She received the B.S.E.E. degree from Cornell University, Ithaca, NY, in 1988 and the M.S. and Ph.D. degrees in electrical engineering from Duke University, Durham, NC, in 1990 and 1994, respectively, with support from a National Science Foundation Graduate Fellowship. While at Cornell, she was a McMullen Dean’s Scholar and participated in the Engineering Co-op Program, working at IBM Federal Systems Division in Owego, New York. During the 1994–95 academic year she held the position

of Postdoctoral Research Associate with the Departments of Radiation Oncology and Electrical Engineering at Duke University, where she developed RF and microwave circuitry for simultaneous hyperthermia (treatment of cancer with microwaves) and MRI (magnetic resonance imaging) thermometry. From 1995–1999, she was an Assistant Professor in the Department of Electrical and Computer Engineering, University of New Hampshire, where she held the Class of 1944 Professorship. Since 1999, she has been with the Electromagnetics Laboratory, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, where she is now a Professor. Her industrial experience includes work as a Research Engineer with Avnet Development Labs and, more recently, as a private consultant for members of the wireless communication and sensors community. Her research interests include reconfigurable and wideband microwave antennas and circuits, wireless sensors and sensor networks, high speed wireless data communication, electromagnetic compatibility, and electromagnetics for industrial, agricultural, and medical applications, and has four patents on technology in these areas. Prof. Bernhard is a member of URSI Commissions B and D, Tau Beta Pi, Eta Kappa Nu, Sigma Xi, and ASEE. She is a Fellow of the IEEE. She was an organizing member of the Women in Science and Engineering (WISE) Project at Duke, a graduate student-run organization designed to improve the climate for graduate women in engineering and the sciences. In 1999 and 2000, she was a NASA-ASEE Summer Faculty Fellow at the NASA Glenn Research Center, Cleveland, OH. She received the NSF CAREER Award in 2000. She is also an Illinois College of Engineering Willett Faculty Scholar and a Research Professor in Illinois’ Coordinated Science Laboratory, and the Information Trust Institute. She and her students received the 2004 H. A. Wheeler Applications Prize Paper Award from the IEEE Antenna and Propagation Society for their paper published in the March 2003 issue of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. She served as an Associate Editor for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION from 2001–2007 and for IEEE Antennas and Wireless Propagation Letters from 2001–2005. She is also a member of the editorial board of Smart Structures and Systems. She served as an elected member of the IEEE Antennas and Propagation Society’s Administrative Committee from 2004–2006. She was President of the IEEE Antennas and Propagation Society in 2008.

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A Compact Eighteen-Port Antenna Cube for MIMO Systems Jianfeng Zheng, Xu Gao, Zhijun Zhang, Senior Member, IEEE, and Zhenghe Feng, Senior Member, IEEE

Abstract—An 18-port compact antenna cube is proposed in this , paper. The cube, which has a volume of 0.76 0.76 0.76 provides 18 individual channels and is ideal for multiple-input multiple-output (MIMO) wireless communications. On each of the total six faces of the cube, a three-port tri-polarization antenna is installed. All antennas adopt a metal backing configuration, so the ground of all antennas forms a well shield Faraday cage, in which other functional circuits can be installed. Experimental measurements were carried out to evaluate the performance of the antenna cube in different MIMO scenarios. The results show that MIMO systems with the proposed compact antenna cube outperform those with dipole antennas which occupy the same number of RF channels but with much larger space. When a vertical 3-dipole array, a horizontal 3-dipole array and a dual polarization antenna are used in the user end (UE), respectively, the capacity of the global selected MIMO systems with antenna cube is about 2.7, 4.6, and 2.9 bits/s/Hz more than the full MIMO systems with a vertical 3-dipole array as the access point (AP) antennas. It is 1.9, 3.9, and 2.0 bits/s/Hz more than the full MIMO systems with a vertical 5-dipole array as AP antennas. The performance differences between the MIMO systems using global and simplified selection circuits are small. Index Terms—Antenna cube, antenna selection, multiple-input multiple-output (MIMO), polarization.

I. INTRODUCTION

A

PPLYING multiple-input multiple-output (MIMO) technology especially with antenna selection in access points (AP) can improve the overall system capacity. However, to construct enough antennas within a small volume is always a challenge. In previous works, a number of compact MIMO antennas have been proposed consisting of up to four ports, compact antenna designs with more than 10 ports are less common and mainly consist of a flat panel approach and are used in large size base station. Recently an interesting approach, the antenna cube, emerges. An antenna cube takes advantage of spatial and polarization orthogonality to implement a large amount of antennas Manuscript received December 20, 2010; revised March 28, 2011; accepted August 15, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. This work was supported in part by the National Basic Research Program of China under Contract 2007CB310605, in part by the National Science and Technology Major Project of the Ministry of Science and Technology of China 2010ZX03007-001-01, in part by Qualcomm Inc., and in part by the Chuanxin Foundation of Tsinghua University. The authors are with the State Key Lab of Microwave and Communications, Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing 100084, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173449

within a constrained volume. In [1]–[3], MIMO cube accommodates up to 12 electrical dipole antennas on all its 12 edges. The 24-port and 36-port antenna cubes suitable for MIMO wireless communications are presented in [4]. However, existing cubes [1]–[4] demand a completely dedicated space for antennas. As the antenna elements in those cubes are omni-directional, the inner space must be kept empty to avoid performance degradation, i.e., other circuits cannot be installed in the space. To resolve the problem, a compact 18-port planar tri-polarization antenna cube for MIMO systems is proposed in this paper. A tri-polarization antenna makes full use of the promising polarization domain, which is considered an important resource for constructing compact antenna arrays and enhancing system performance [6]–[8]. The antenna cube employs tri-polarization antennas [9] as the basic elements. To form a compact antenna cube, six tri-polarization antennas are distributed on separate faces of a cube. This arrangement achieves low mutual coupling and wide coverage within a small volume mm with an operating frequency band of 2.40–2.48 GHz. In a real communication system, it is difficult to implement a large amount of RF channels even at AP. Thus some sorts of antenna switching must be involved for antenna-abundant MIMO systems [10]–[12]. Accompanying with the antenna cube, two simplified antenna switching schemes are proposed in this paper. Measurement results demonstrate that in an indoor environment, performance achieved by simplified switching schemes is almost as good as that of a fully switching system. Antenna design, measurement results and experimental verifications of the proposed compact planar tri-polarization antenna cube are described in Sections II–V. Specifically, the tripolarization antenna is briefly introduced in Section I. Measurement results of the 18-port antenna cube are presented and discussed in Section II. Measurement procedure and analysis framework are explained in Section III. Experimental results of MIMO systems between the antenna cube and various terminal antennas are discussed in Section IV. Conclusion is drawn in Section V. II. ANTENNA CUBE DESIGN The conformal and low-profile tri-polarization antenna which was proposed in [9] is a fundamental building block in the planar MIMO cube and is briefly introduced here. The configuration of the tri-polarization antenna is shown in Fig. 1. A ring patch, which functions as two independent orthogonal polarized antennas, and a disk-loaded monopole compose the tri-polarization antenna, and the operating frequency band is chosen to be 2.4–2.48 GHz.

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Fig. 1. Geometry of the tri-polarization antenna: (a) top view and (b) side view.

Different from antennas used in other MIMO cubes proposed in the literature, the planar tri-polarization antenna has a very low profile, and the total height of the tri-polarization antenna is 5.8 mm. Furthermore, the full 74 74 mm sized ground plane of the tri-polarization antenna makes it particularly suitable for antenna mounted on the equipments. The advantage of low profile together with the easiness of its conformal integration on a cube surface makes the tri-polarization antenna a good candidate to construct the MIMO cube. Apart from the above advantage of the tri-polarization antenna, most importantly, the patch antenna mode and the monopole antenna mode of the tri-polarization have the orthogonal polarization property to each other. With three ports of this antenna working independently, the far field of this antenna has three orthogonal linear polarizations. Specifically, when the tri-polarization antenna is placed as in Fig. 1, i.e., the monopole is along the -axis while the feed lines P1 and P2 are along the - and -axes in horizontal plane, respectively, the E-field radiated by the ring patch is parallel to the ground plane and can provide two orthogonal polarizations excited through P1 and P2, while the monopole provides the vertical polarization component and has an omni-directional radiation in the azimuth plane. Fig. 2 shows the measured radiation patterns of the tri-polarization antenna at 2.42 GHz. As shown, the radiation pattern of monopole mode (port M3) and patterns of the patch mode (port P1 and port P2) have orthogonal polarizations to each other. The gains of the directional slot-fed antennas at 2.42 GHz are 7.5 dBi for P1 and P2, while the gain of the omni-directional coaxial-fed disk-loaded monopole fed by M3 is 2.5 dBi. The main reason for the lower gain of M3 compared with the gains of other two ports is the different radiation properties between monopole and patch antennas.

The omni-directional radiation property gives the monopole mode lower gain compared to the directional patch mode. In real communication applications, the position of mobile terminals may rotate due to different communication scenarios and the arbitrariness of user’s behavior. For the fact that the three ports of this antenna radiate three polarized fields that are orthogonal to one another, this antenna could receive electromagnetic wave with any kind of polarization by switching among the ports of the antenna cube, thus avoid situations of the polarization mismatch. The tri-polarization antenna has a low planar profile and the complete common ground, thus it is easy to construct the planar tri-polarization antenna cube by embedding one tri-polarization antenna on each face of a cube. The structure of the planar tri-polarization antenna cube is shown in Fig. 3. As shown, the six planar tri-polarization antennas are fixed on the six faces of the cube. Each antenna has 3 ports, and the antenna cube has 18 ports, which can provide up to 18 individual communication channels. The antenna cube operates at 2.4–2.48 GHz, and the volume is 94 94 94 mm , about 0.76 0.76 0.76 where is the wavelength in vacuum. For convenience of description, the faces of the cube are numbered as shown in Fig. 3, the up face is #1, the front, right, back and left faces are numbered as #2, #3, #4, and #5 respectively, and the bottom face is #6. The three ports in a face are noted as P1, P2, and M3. Each port in the antenna cube is denoted with the numbers of faces and ports, for example, F#1-P1 represents the P1 port of the tri-polarization antenna in the #1 face of the cube. For the three ports of each tri-polarization antenna in the face have three orthogonal polarizations, it is easy to obtain the full radiation coverage in the whole sphere. Therefore, the MIMO cube can provide good convergence for user terminals with any rotation and position. An important aspect to construct the antenna cube is to maintain relative low mutual coupling between any individual ports, as mutual coupling will deteriorate the performance of MIMO wireless communication systems. For the compact tri-polarization antenna cube, relatively low mutual coupling between antennas of the proposed MIMO cube is mainly due to the choices of antenna types, positions and orientations. As the three antennas in a tri-polarization antenna employ orthogonal polarizations, the mutual coupling between each port is relatively low. The tri-polarization antenna has a ground backing, so the tri-polarization antennas in different faces radiate toward different directions and inherently have low mutual coupling. To verify the performance of the planar tri-polarization antenna cube, a prototype antenna cube was fabricated, and the photo of the cube is shown in Fig. 3. Due to the symmetric characteristic of the antenna cube, only the tri-polarization antenna #1 is measured. The measured reflection and transmission coefficients are shown in Fig. 4. The results are pretty much identical to the results reported in [9]. Between any two tri-polarization antennas in adjacent faces, there are nine sets of transmission coefficients. As shown in Fig. 5, there are three most significant results between antennas in face #1 and #3. The isolations at 2.4–2.48 GHz band are all better than 20 dB. The isolations between ports in opposite

ZHENG et al.: COMPACT EIGHTEEN-PORT ANTENNA CUBE FOR MIMO SYSTEMS

Fig. 2. Measured electrical patterns of the tri-polarization antenna: (a) – plane; (f) , – plane.

,

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plane; (b)

,

plane; (c)

,

plane; (d)

, – plane; (e)

,

Fig. 3. Structure and photograph of the planar tri-polarization antenna cube.

antennas are all better than 25 dB, which is not illustrated here for the reason of concision. Overall, these results show that the proposed planar tri-polarization antenna cube has good isolation among the individual ports, which satisfies the requirement of MIMO systems. III. MIMO SYSTEMS WITH THE ANTENNA CUBE In prior works, the antennas presented for MIMO systems were often validated by examining the channel capacity of the full MIMO systems between antenna cubes in a narrow frequency band. However, the full MIMO systems which support more than 10 individual channels are too expensive and complicated to use in personal wireless communication systems nowadays, such as WLAN equipments, and the communication systems mostly are wideband. To overcome these shortcomings, the performance of the MIMO systems employing the antenna cube is examined in typical indoor scenarios with antenna selection among the whole WLAN frequency bands. The measurements were carried out in Room 1010 on the 10th floor of Weiqing Building in Tsinghua University, which is a

Fig. 4. (a) Measured return loss of the tri-polarization antenna #1 in the cube. (b) Measured isolation between ports in antenna #1.

typical laboratory room as schemed in Fig. 6. The framework of the room is reinforced concrete, the walls are mainly built

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Fig. 7. Schematic of test-bench for MIMO system.

Fig. 5. Measured isolation between ports in adjacent tri-polarization antennas.

Fig. 8. Antennas used in measurement besides antenna cube: (a) vertical 5-dipole array; (b) vertical 3-dipole array; (c) horizontal 3-dipole array; (d) dual-polarization antenna.

Fig. 6. Structure of the measured office.

by brick and plaster, and the ceiling is made with plaster plates with aluminium alloy framework. The scheme of the test-bench is shown in Fig. 7. The measurement system consists of an Agilent E5071B network analyzer, AP antennas, user equipment (UE) antennas, RF switches, a computer, an auxiliary amplifier, and RF cables. The AP and the UE are connected to a 16-to-1 RF switch and a 4-to-1 RF switch respectively, and the switches are then connected to the network analyzer. The auxiliary amplifier is between the transmit antenna and the network analyzer to amplify the transmit signal. The computer controls the measurement procedure and records the data. In the measurement, the transmit power of network analyzer is set to 10 dBm, IFBW is 10 kHz, and sweep averaging is set on with sweep averaging factor as 16, the noise floor of the network analyzer is below than 90 dB when measuring S21. The loss of the cable is less than 15 dB, the insertion loss of the switch is about 4 dB and the power gain of the amplifier is about 10

dB. With the SNR limitation of 15 dB, the dynamic range of the measurement system is above 66 dB. For the conveniences of measurement and installation, the tri-polarization antenna in the bottom face of cube was removed, thus only 15 ports of the cube were used. The configurations of the measurements are listed in Table I. The measurement campaign was carried out for twelve representative MIMO systems, and the measured channel responses are noted as , here is the type number of AP antennas and is the one of UE antennas. On the AP side, four different arrays were used respectively. They are a vertical three-dipole array, a vertical five-dipole array, and an antenna cube with three/five selected branches. The separation between adjacent antennas of the dipole array is one wavelength, so the three/five-dipole array’s size is two/four wavelengths. On the UE side, three different arrays were used alternatively. They are a vertical threedipole array, a horizontal three-dipole array and a compact dual polarization antenna [13]. The size of three-dipole array is two wavelengths and the dual polarization antenna is 0.8 wavelength in size. The schemes of all dipole arrays and the dual-polarization antenna are shown in Fig. 8. In each measurement, the AP antenna was fixed in the center of the office room with a height of 1.2 m, and UE antennas were placed in the 10 locales around the room sequentially with a height of about 0.8 m. The locales UE2, 5, 8, 10 had Line-ofsight (LOS) paths and UE1, 3, 4, 6, 7, 9 only had non-line-ofsight (NLOS) paths, as illustrated in Fig. 6, where the locales UE5, 10 and the locales UE2, 8 were in the broad-sight and

ZHENG et al.: COMPACT EIGHTEEN-PORT ANTENNA CUBE FOR MIMO SYSTEMS

TABLE I MEASUREMENT CONFIGURATIONS

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A. Transmitter Power Constraints As the received power and richness of scattering are quite different at different UE locations, the measured channel response matrices must be appropriately normalized. For the rich scattering required to achieve low correlations for MIMO communications often produces low SNR, which in turn decreases the channel capacity [14], we adopt the MIMO system with vertical 5-dipole at AP and vertical 3-dipole at UE as reference to normalize the channel responses with average transmitted power as discussed in [15]. This normalization considers not only richness of the multipath but also the power gain. Obviously, the can be expressed as in (1)

TABLE II CONFIGURATIONS OF THE STUDIED MIMO SYSTEMS

where , which is different with the average SNR of the measurements, is the assumed average SNR of the referenced MIMO systems with channel response , is the number of the locales and is the number of the measured points in each locale, denotes the number of the channel bands, and are the numbers of transmit and receive antennas of channel responses, respectively, and is the number of the measured frequency bins in the th band. means the average received noise per frequency bin, and is the trace operation. In the following, the assumed average SNR is set to 15 dB in analyzing the channel capacity. B. Channel Capacity of MIMO Systems With Antenna Selections Over Wide Bands

end-fire directions of the referenced dipole array at AP. In each place, channel matrices at 4 points separated by 6.5 cm, i.e., half-wavelength, were measured in order to obtain independent fading, and denoted as , where represents the serial number of the locale and is the serial number of measurement point in the locale place. For each , the responses over the whole WLAN band were measured. As we measured the channel responses after midnight and before dawn, the channels were supposed to be static, so the elements in the channel matrix were measured in sequence and the switching of the was completed by using RF switches. In the measurements of referenced MIMO system with a vertical 5-dipole at AP and a 3-dipole array at UE, the maximum measured S21 is 45 dB, and the average measured S21 is 52 dB. That is, the average SNR of the measurement is about 52 + 90 dB 38 dB with referenced linear dipole arrays, here 90 dB is the S21 noise floor of the proposed measurement system. The measured channel responses are assorted to construct the wideband channel of referenced dipole-array MIMO systems and MIMO systems with antenna cube. The frequency bands are divided following the IEEE 802.11 specifications as shown in Table II. That means, when studying the channel capacity of any MIMO system with specified antennas and places, 14 wideband channels are adopted based on the frequency partition of IEEE 802.11 specifications.

Though prior proposed cubes were demonstrated in full MIMO systems, the transceivers of a full MIMO system using antenna cubes might be too expensive to accommodate in today’s personal wireless communication systems. Antenna selection is a good approach to reduce a system’s cost while maintain its performance. The bulk selection [16], [17] method is adopted as a reference. Bulk selection method is a global optimization method, which assumes there is a direct path between any input port and output port. The channel capacity with equal power emission strategy [18] is adopted to evaluate performance of measured MIMO systems covering the th band. Then channel capacity of wideband systems with bulk antenna selection is (2) denotes the different combination of AP antenna elwhere ements and is the set of the selectable antenna combinations. Assuming there are 15 ports in the AP, each time the total number of combinations is 455 and 3003 when 3 and 5 branches are selected respectively. On the UE side, all available antennas are always used. is the channel capacity of the MIMO systems with selected antennas combination over the th band, and expressed as (3)

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Fig. 9. Configurations of the switching circuits: (a) 15-to-3 global selection circuit; (b) pattern selection circuit; (c) 15-to-5 global selection circuit; (d) polarization selection circuit.

C. Simplified Pattern and Polarization Selection Methods Although antenna selection is capable of reducing the cost of the RF channels while maintaining the performance of the MIMO systems, determinations of the forms of the antenna array and implementations of the RF selection circuits are not trivial [12], [19]–[21]. The existing research activities on antenna selection little involve designs of antenna arrays and selection circuits. The often used or assumed global selection circuits require many RF switches and complicated RF circuits, which are difficult to realize and may introduce inevitable high insertion loss. Two simplified selection circuits with low complexity and cost are presented to reduce the complexity of global selection circuit and maintain a comparable performance, which are pattern and polarization selection circuits. As shown in Fig. 9, global selection methods select the best channels irrespective of the polarizations and antenna types by a complex RF switch matrix. While when pattern selection is applied, each port with the same polarization in each tri-polarization antenna is connected to a 5-to-1 RF switch. The pattern selection generates three output ports. The pattern combinations approaching the most channel capacities are then selected in the performance evaluation. In polarization selection, the three ports in each tri-polarization antenna are connected to a 3-to-1 RF switch. The polarization selection generates five output ports. The proposed antenna selection schemes consist of -to-1 switches while the global selection circuits consist of an -toswitch matrix, here is the number of the selected antennas and is the number of the available receive antennas. The switch matrix is much more complex than -to-1 switches. IV. RESULT COMPARISONS Because the spread of multi-path in elevation direction and polarization rotation are significant in indoor scenarios, the per-

formance of the MIMO systems will depend not only on the number of the antennas used in the base station but also on the radiation pattern, polarization and array structure. The whole spherical coverage characteristic and capability of receiving any polarized impinging wave make the compact antenna cube particularly suitable for indoor communications. We examined the performance of the MIMO systems with the antenna cube and various terminal antennas in different locales and postures as followed. The performance of the selection MIMO systems with antenna cube in AP is compared with that of the referenced full MIMO systems with the often used uniformly spaced vertical dipole arrays. In the following studies, the measured data of all locations illustrated in Fig. 6 is adopted. The number of locations is 10. Four spots are measured at each location. Each measurement includes 14 channels. The total size of the channel samples for all following figures is and in each channel sample, 23 frequency bins are measured with a frequency step of 1 MHz to cover the 22 MHz channel bandwidth. A. Average Normalized Receive Power In wireless communication systems, the performance is affected by the signal to noise ratio. Thus, the capability of collecting more power is quite important to AP antennas. The average normalized receive power of the compact antenna cube and the referenced dipole arrays with various antenna at UE are listed in Table III, which is normalized according to the average receive power on each port of referenced vertical 5-dipole array at AP with vertical 3-dipole array at UE as

(4)

where , and are the numbers of the transmit and the receive antennas of the normalized MIMO channels. In Table III, normalized receive powers over different sets of scenarios are listed. In the column of “All Scenarios”, the locales UE1-10 are considered. In the columns of “LOS Scenarios” and “NLOS Scenarios”, the locales UE2, 5, 8, 10 and UE1, 3, 4, 6, 7, 9 are taken into accounted, respectively. Further, “Broad-sight” (locales UE5, 10) and “End-Fire” scenarios (locales UE2, 8) are compared. As shown, when vertical 3-dipole array is used at UE, the average received power of the antenna cube, which is calculated on each port over all locations, is similar to that of the referenced dipole array. However, in other situations, i.e., horizontal dipole array and dual-polarization antenna are used at the UE, the received power of the reference array at AP deteriorates. The average power of the referenced dipole array over all scenarios is 6.14 and 6.01 dB with horizontal 3-dipole and is 3.14 and 3.00 dB with dual-polarized antenna when and , respectively. While the power of the antenna cube with selections maintains in all circumstances. When LOS and NLOS scenarios are considered separately, the received power on ports of antenna cube with selection is

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TABLE III AVERAGE NORMALIZED RECEIVE POWER OF AP ANTENNAS

Fig. 11. Capacity CCDFs of MIMO systems with cube using 15-to-3 global and vertical and pattern selection circuits and vertical dipoles while 3-dipole array is applied in UE: (a) LOS and NLOS; (b) broad-sight and end-fire scenarios.

Fig. 10. Capacity CCDFs of MIMO systems with cube using 15-to-3 global and vertical and pattern selection circuits and vertical dipoles while 3-dipole array is applied in UE.

mostly larger than that of the referenced 5/3-dipole array. In few situations, the received power of antenna cube is less than that of the referenced dipole array, but the difference is quite small. It also can be drawn that in almost all the situations, the received power of antenna cube with global selection is slightly stronger than that of antenna cube with simplified selection. B. Channel Capacity and Eigenvalues 1) Vertical/Horizontal Three-Dipole Array is Employed as UE Antennas: First, the scenarios that the vertical 3-dipole array is applied as UE antennas are considered. The channel capacity complementary cumulative density functions (CCDFs) of studied MIMO systems are shown in Fig. 10, when is considered, the 50% outage capacity of full MIMO system with antenna cube is 7.2 bits/s/Hz more than that of full MIMO system with dipole array. The selection MIMO systems with antenna cube also perform better than the full MIMO system with dipole array in general, no matter whether global or simplified pattern selection circuit is used. Considering the

50% outage capacity of the systems, the capacity of MIMO systems using global selection is about 2.7 bits/s/Hz more than the full MIMO systems with dipoles as AP antennas, while the difference between the selection MIMO systems with global and pattern selection circuits is less than 0.5 bits/s/Hz. The comparisons between LOS and NLOS scenarios and between the broad-sight and end-fire scenarios (which all have LOS path) are demonstrated in Fig. 11. For the average transmit power normalization is performed with respect both LOS and NLOS scenarios dependently, the MIMO systems in LOS scenarios performs better those in NLOS scenarios for the relative power gain advantage, which is different from the commonly used SNR normalization [15]. As shown in Fig. 11(a), the channel capacity differences between MIMO systems with cube and dipole array at AP are nearly same in LOS and NLOS scenarios when the 50% outage capacity is considered, which are 2.1 and 2.3 bits/s/Hz, respectively. But when the UE antenna is in end-fire direction of the dipole array, as shown in Fig. 11(b), the channel capacity deteriorates because of lower received power which is shown in Table III. When is considered, which is shown in Fig. 12, the 50% outage capacity of full MIMO system with antenna cube is 4.5 bits/s/Hz more than that of full MIMO system with dipole

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Fig. 12. Capacity CCDFs of MIMO systems with cube using 15-to-5 global and verand polarization selection circuits and vertical dipoles while tical 3-dipole array is applied in UE.

Fig. 14. Eigenvalue PDFs of normalized MIMO channels with vertical 3-dipole array at UE and: (a) vertical 5-dipole array at AP; (b) antenna cube using simplified selections at AP; (c) antenna cube using global selection at . AP; (d) full cube at AP, where

Fig. 13. In Fig. 13(a), the 50% outage capacity differences between MIMO systems with cube and dipole array at AP are 1.1 and 0.7 bits/s/Hz for LOS and NLOS scenarios. As shown in Fig. 13(b), it is obvious that the capacity of MIMO system with referenced 5-dipole array is more susceptible to the environment than that of the MIMO system with selected antenna cube. The slops of the capacity curves of MIMO system with dipole array in broad-sight and end-fire scenarios vary considerably, but those of MIMO systems with cube antenna change little. The capacity of MIMO channel with global selected antenna cube is 0.1 and 2.3 bits/s/Hz more than that of MIMO channel with vertical 5-dipole array. The eigenvalue probability density functions (PDFs) of the normalized MIMO channel are studied. The normalization operation is according to as

Fig. 13. Capacity CCDFs of MIMO systems with cube using 15-to-5 global and verand polarization selection circuits and vertical dipoles while tical 3-dipole array is applied in UE: (a) LOS and NLOS; (b) UE in broadsight and endfire of vertical dipoles at AP in LOS scenarios.

array. The capacity of MIMO systems using global selection and polarization selection is 1.9 and 1 bits/s/Hz more than that of the full MIMO systems with vertical 3-dipole array. The comparison between LOS and NLOS scenarios and that between the broad-sight and end-fire scenarios are shown in

(5) The eigenvalue PDFs of MIMO systems with vertical 3-dipole at UE are illustrated in Fig. 14. In most situations, the full MIMO system with antenna cube has three significant eigenvalues with vertical 3-dipole array at UE, which is equal to the number of transmit antennas. When is considered, which is denoted with solid symbols in Fig. 14. For the selection systems, about 50% of the second maximum eigenvalues are larger than 0 dB, while for

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Fig. 16. Eigenvalue PDFs of normalized MIMO channels with dual polarization antenna at UE and: (a) vertical 5-dipole array at AP; (b) antenna cube using simplified selections at AP; (c) antenna cube using global selection at AP; (d) . full cube at AP, where

Fig. 15. Capacity CCDFs of MIMO systems with cube and dual polarization (15-to-3 global and antenna while the number of selected branch is: (a) (15-to-5 global and polarization selection). pattern selection), (b)

the MIMO system with dipole array, only about 20% of the 2nd maximum eigenvalues are larger than 0 dB. Most the minimum eigenvalues of MIMO system with dipole array are less than 10 dB, and are quite less than those of MIMO systems with selections. When is considered, which is denoted with hollow symbols in Fig. 14. The eigenvalue PDFs of MIMO channels with full cube are similar to those of the full MIMO system with for full 15 RF branches are used. The full MIMO systems with antenna cube have three significant eigenvalues in most situations. For the MIMO channels with global and polarization selected antenna cube and vertical 5-dipole array, the differences between the distribution of the first maximum and second maximum eigenvalues are small. The minimum eigenvalues of MIMO channels with antenna cube are mostly larger than 10 dB, but a fairly large number of the minimum eigenvalues of MIMO channels with vertical 5-dipole array are less than 10 dB. This shows the antenna cube is likely to provide more effective subchannels. Secondly, the MIMO systems with horizontal 3-dipole array at UE are considered. In practical communication systems, performance of the communication system often deteriorates because of undesirable factors, such as polarization mismatch and

so on, that is quite common in wireless communications for the UE antennas are often rotated for the randomness of user behaviors. Considering the MIMO system with vertical dipoles at the AP, the performance badly degrades with horizontal dipoles at UE because the polarization mismatch seriously deteriorates the received power as listed in Table III. However, for the MIMO system with the cube, it works both well when either vertical or horizontal dipoles at the UE. This means that the MIMO systems with the antenna cube are more robust. When horizontal 3-dipole is adopted at UE, the 50% outage capacity of global selection MIMO systems with antenna cube is 4.6 and 3.9 bits/s/Hz better than those of the full MIMO systems with vertical 3-dipole and 5-dipole arrays at AP, respectively. 2) Dual Polarization Antenna is Employed as UE Antenna: In these scenarios, dual polarization antenna is employed in UE. As shown in Fig. 15(a), the selection MIMO system with antenna cube performs much better than the full MIMO system with dipole array when , the 50% outage capacity of global selection MIMO system with antenna cube is 2.9 bits/s/Hz more than that of the full MIMO system, and is nearly the same with the capacity of MIMO systems with pattern selection circuits, the 50% outage capacity of full MIMO system with antenna cube is 5.4 bits/s/Hz more than the capacity of the MIMO systems with dipole array, as shown in Fig. 15(a). When , the MIMO systems with simplified polarization selection circuit also perform better than the referenced full MIMO systems. As shown in Fig. 15(b), the 50% outage capacity of the MIMO systems with global and polarization selection is 2.0 and 1.6 bits/s/Hz more than the capacity of

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Fig. 17. Statistics of the selected antennas: (a) numbers of selected faces when

the referenced MIMO system when dual polarization antenna is used in UE. The capacity of the full MIMO systems with cube is 3.6 bits/s/Hz more than that of the MIMO system with referenced vertical 5-dipole array. The eigenvalue PDFs of MIMO systems with dual polarization antenna are illustrated in Fig. 16, where solid and hollow symbols are used to denote situations of and respectively. The eigenvalues of selection MIMO systems with antenna cube at AP are located in higher range than that of MIMO systems with vertical dipole. Furthermore, the second maximum eigenvalues of MIMO systems with vertical 3-dipole array are much less than that with vertical 5-dipole array while the difference between eigenvalues of MIMO systems with antenna cube when and are little. Almost all the second maximum eigenvalues of MIMO systems with vertical 3-dipole array are less than 0 dB while 50% of the second maximum eigenvalues of selection MIMO systems with antenna cube when are large than 0 dB even simplified selection circuit is implied. As above, the antenna cube performs well when linking with different equipment antennas in various scenarios, and satisfies the requirements of MIMO systems especially with antenna selection. It is noted that the capacity of the MIMO systems with antenna cube maintains no matter what UE antennas are adopted. C. Statistics of the Selected Antennas To further reveal the impact of antenna cube on channel capacity of selection MIMO systems, the statistics of the selected antenna in each MIMO channel realizations are shown in Fig. 17. The number of the accounted MIMO channel realizations is 560. Particularly, when pattern or polarization selection circuit is implied, the numbers of the selected specific ports or the faces that the selected antennas lie on are equal because of the constraints of the selection circuits. When , the numbers of faces that the selected antennas lie in are accounted and shown in Fig. 17(a). As shown in Fig. 17(a), the tri-polarization antenna in the #1 (up) face is more likely to be selected for a fairly large part of the transmitted waves are reflected by the ceiling. The numbers of the selected tri-polarization antennas vary little when different UE antennas are used.

; (b) numbers of selected specific antennas when

.

The numbers of the specifically selected antenna in all the faces are accounted and shown in Fig. 17(b) when . The P2 ports have more probability to be selected when vertical 3-dipole array is used as UE antenna for the antennas have vertical polarization radiation patterns and high gain. V. CONCLUSION This study proposes a planar tri-polarization antenna for MIMO systems with antenna selection. The total volume of the antenna cube is 0.76 0.76 0.76 . The designed prototype was fabricated and tested, and measured data validating simulation results were compared. By comparing the channel capacity of MIMO systems between cube and several terminal antennas and the capacity of MIMO systems between dipole array and the same terminal antennas, the validation of the tri-polarization antenna cube for MIMO system with antenna selection is approved. The measurement reveals that the compact tri-polarization antenna cube with the full coverage and polarization diversity is suitable for MIMO systems with antenna selection indoors, and can provide high quality communications in various scenarios with different terminal antennas. REFERENCES [1] B. N. Getu and J. B. Andersen, “The MIMO cube—A compact MIMO antenna,” IEEE Trans. Wirel. Commun., vol. 4, no. 5, pp. 1136–1141, May 2005. [2] B. N. Getu and R. Janaswamy, “The effect of mutual coupling on the capacity of the MIMO cube,” IEEE Antennas Wirel. Propag. Lett., vol. 4, pp. 240–244, 2005. [3] C. Y. Chiu and R. D. Murch, “Experimental results for a MIMO cube,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., 2006, pp. 2533–2536. [4] C. Y. Chiu, J. B. Yan, and R. D. Murch, “24-port and 36-port antenna cubes suitable for MIMO wireless communications,” IEEE Trans. Antennas Propag., vol. 56, no. 4, pp. 1170–1176, 2008. [5] P. N. Fletcher, M. Dean, and A. R. Nix, “Mutual coupling in multielement array antennas and its influence on MIMO channel capacity,” Electron. Lett., vol. 39, pp. 342–344, Feb. 2003. [6] M. R. Andrews, P. P. Mitra, and R. deCarvalho, “Tripling the capacity of wireless communications using electromagnetic polarization,” Nature, vol. 409, no. 1, pp. 316–318, 2001. [7] A. S. Konanur, K. Gosalia, S. H. Krishnamurthy, B. Hughes, and G. Lazzi, “Increasing wireless channel capacity through MIMO systems employing co-located antennas,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 6, pp. 1837–1844, Jun. 2005. [8] K. Itoh, R. Watanabe, and T. Matsumoto, “Slot-monopole antenna system for energy-density reception at UHF,” IEEE Trans. Antennas Propag., vol. 27, no. 8, pp. 485–489, Jul. 1979.

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[9] X. Gao, H. Zhong, Z. Zhang, Z. Feng, and M. F. Iskander, “Low-Profile planar tri-polarization antenna for WLAN communications,” IEEE Antennas Wirel. Propag. Lett., vol. 9, pp. 83–86, 2010. [10] S. Sanayei and A. Nosratinia, “Antenna selection in MIMO systems,” IEEE Commun. Mag., vol. 42, no. 10, pp. 68–73, Oct. 2004. [11] A. Ghrayeb, “A survey on antenna selection for MIMO communication systems,” in Proc. Int. Conf. Inform. Commun. Technol. (ICTTA), 2006, pp. 2104–2109. [12] A. F. Molisch, N. B. Mehta, H. Zhang, P. Almers, and J. Zhang, “Implementation aspects of antenna selection for MIMO systems,” in Proc. Int. Conf. Commun. Network. China (China Com), 2006, pp. 1–7. [13] Y. Li, Z. Zhang, W. Chen, Z. Feng, and M. Iskander, “A dual-polarization slot antenna using a compact CPW feeding structure,” IEEE Antennas Wirel. Propag. Lett., vol. 9, pp. 191–194, 2010. [14] M. Jensen and J. Wallace, “A review of antennas and propagation for MIMO wireless communications,” IEEE Trans. Antennas Propag., vol. 52, no. 11, pp. 2810–2824, Nov. 2004. [15] R. Tian, V. Plicanic, B. K. Lau, and Z. Ying, “A compact six-port dielectric resonator antenna array: MIMO channel measurements and performance analysis,” IEEE Trans. Antennas Propag., vol. 58, no. 4, pp. 1369–1379, Apr. 2010. [16] H. Zhang, A. F. Molisch, and J. Zhang, “Applying antenna selection in WLANs for achieving broadband multimedia communications,” IEEE Trans. Broadcast., vol. 52, no. 4, pp. 475–482, Dec. 2006. [17] H. Zhang and R. U. Nabar, “Transmit antenna selection in MIMOOFDM systems: Bulk versus per-tone selection,” in Proc. IEEE Int. Conf. Commun. (ICC), 2008, pp. 4371–4375. [18] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wirel. Pers. Commun., vol. 6, no. 3, pp. 311–335, Mar. 1998. [19] J. Ahmadi-Shokouh, S. H. Jamali, S. Safavi-Naeini, and G. Z. Rafi, “Switch loss and antenna directivity effects on MIMO antenna selection,” in Proc. Canadian Conf. Elect. Comput. Eng. (CCECE), 2008, pp. 641–646. [20] N. Honma, K. Nishimori, Y. Takatori, A. Ohta, and K. Tsunekawa, “Antenna selection method employing orthogonal polarization and radiation patterns for MIMO antenna,” in Proc. Eur. Conf. Antennas Propag. (EuCAP), 2006, pp. 1–4. [21] Z. Xu, S. Sfar, and R. S. Blum, “Receive antenna selection for closelyspaced antennas with mutual coupling,” IEEE Trans. Wirel. Commun., vol. 9, no. 2, pp. 652–661, Feb. 2010. Jianfeng Zheng received the B.S. and Ph.D. degrees from Tsinghua University, Beijing, China, in 2002 and 2009, respectively. He is currently an Assistant Researcher with the State Key Laboratory on Microwave and Digital Communications, Tsinghua University. His current research interests include spatial temporal signal processing, MIMO channel measurements and antenna arrays for MIMO communications.

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Xu Gao received the B.S. degree from Shandong University, Jinan, China, in 2007, and the M.S. degree from Tsinghua University, Beijing, China, in 2010. He is currently pursuing the Ph.D. degree from the Missouri University of Science and Technology, Rolla. He is currently working with the EMC Lab, Missouri University of Science and Technology. His research interests include antenna design, wave propagation, electromagnetic compatibility, RF design, and computational electromagnetics.

Zhijun Zhang (M’00–SM’04) received the B.S. and M.S. degrees from the University of Electronic Science and Technology of China, Anhui, in 1992 and 1995, respectively, and the Ph.D. degree from Tsinghua University, Beijing, China, in 1999. In 1999, he was a Postdoctoral Fellow with the Department of Electrical Engineering, University of Utah, where he was appointed a Research Assistant Professor in 2001. In May 2002, he was an Assistant Researcher with the University of Hawaii at Manoa, Honolulu. In November 2002, he joined Amphenol T&M Antennas, Vernon Hills, IL, as a Senior Staff Antenna Development Engineer and was then promoted to the position of Antenna Engineer Manager. In 2004, he joined Nokia Inc., San Diego, CA, as a Senior Antenna Design Engineer. In 2006, he joined Apple Inc., Cupertino, CA, as a Senior Antenna Design Engineer and was then promoted to the position of Principal Antenna Engineer. Since August 2007, he has been with Tsinghua University, where he is a Professor with the Department of Electronic Engineering. He is the author of Antenna Design for Mobile Devices (Wiley, 2011). Prof. Zhang is serving as an Associate Editor of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION and the IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS.

Zhenghe Feng (M’00–SM’08) received the B.S. degree in radio and electronics from Tsinghua University, Beijing, China, in 1970. Since 1970, he has been with Tsinghua University, as an Assistant, Lecture, Associate Professor, and Full Professor. His main research areas include numerical techniques and computational electromagnetics, RF and microwave circuits and antenna, wireless communications, smart antenna, and spatial temporal signal processing.

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Printed MIMO-Antenna System Using Neutralization-Line Technique for Wireless USB-Dongle Applications Saou-Wen Su, Member, IEEE, Cheng-Tse Lee, Member, IEEE, and Fa-Shian Chang

Abstract—A printed two-multiple-input multiple-output (MIMO)-antenna system incorporating a neutralization line for antenna port decoupling for wireless USB-dongle applications is proposed. The two monopoles are located on the two opposite corners of the system PCB and spaced apart by a small ground portion, which serves as a layout area for antenna feeding network and connectors for the use of standalone antennas as an optional scheme. It was found that by removing only 1.5 mm long inwards from the top edge in the small ground portion and connecting the two antennas therein with a thin printed line, the antenna port isolation can be effectively improved. The neutralization line in this study occupies very little board space, and the design requires no conventional modification to the ground plane for mitigating mutual coupling. The behavior of the neutralization line was rigorously analyzed, and the MIMO characteristics of the proposed antennas was also studied and tested in the reverberation chamber. Details of the constructed prototype are described and discussed in this paper. Index Terms—2.4 GHz WLAN antennas, multiple-input multiple-output (MIMO) antennas, neutralization line, printed monopole antennas, wireless USB-dongle antennas.

I. INTRODUCTION

M

ULTIPLE-INPUT multiple-output (MIMO) technology using multiple transmit/receive antennas is considered one of the most promising approaches to achieve higher data rate with no additional spectrum required and at the same time, to make use of the indoor multi-path propagation for improving signal quality and reliability. Until quite recently, the IEEE Standard Association has ratified the IEEE 802.11n standard in September 2009 [1]. It can be expected that multiple antennas are demanded accordingly and may be closely packed inside the devices due to limited space left for antennas. Multi-antenna designs that require high decoupling between the antenna ports are essential for the multi-radio, antenna system development. Several methods for improving antenna port isolation have been reported, including incorporating a protruded ground plane between the antennas [2], inserting slits Manuscript received December 23, 2010; revised April 22, 2011; accepted August 16, 2011. Date of publication ; date of current version February 03, 2012. S.-W. Su and C.-T. Lee are with the Network Access Strategic Business Unit, Lite-On Technology Corp., Taipei County 23585, Taiwan (e-mail: stephen. [email protected]). F.-S. Chang is with the Department of Electronics, Cheng Shiu University, Kaohsiung County 83347, Taiwan. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173450

into the ground [3]–[5], arranging antenna shorting portions facing each other [6], [7], manipulating radiation polarization of the antennas [8]–[10] and so on. For the cost- effective concern for USB-dongle applications that the printed antennas are the most favorable designs, none of the above- mentioned techniques for decoupling antenna ports are suited to the requirements of printed antennas and little board space for accommodating decoupling-structure layout. This motivates us to implement another promising technique by incorporating a neutralization line [11], [12] into the printed two-antenna system for USB-dongle applications. A neutralization-line technique allows the signals picked up from one antenna to the other and produces an opposite coupling to the existing one without the presence of neutralization line such that low mutual coupling at certain frequencies is achieved [11]. The proposed design comprises two simple short-circuited monopoles placed on the opposite corners of a FR4 substrate, which can be considered the system PCB of a wireless USB dongle. In between the monopoles is the small ground portion reserved for the feeding network (for example matching circuits), I-PEX connectors for having standalone, coaxial-linefeed antennas as an optional scheme, RF testing connectors for manufacturing test and so on. Therefore, it is important to have this portion as much untouched as possible and to avoid slit cuts or a protruded ground therein. In this paper, the small ground portion of the system ground plane was removed only 1.5 mm long inwards from the top edge to accommodate a thin, printed neutralization line that links to the monopoles relatively close to the antenna feed ports. It was found that by adding the neutralization line in the proposed design, the antenna port isolation can be effectively enhanced, compared with the design with no neutralization line. The antennas are not necessarily targeted on the USB-dongle platform only but also on a wireless module-card solution with the form factor of a USB dongle for possible wireless LCD TV applications. The experimental and simulation results of a constructed prototype are fully presented. II. ANTENNA CONFIGURATION AND DESIGN CONSIDERATION Fig. 1(a) shows the geometry of the proposed two-monopoleantenna system formed on a single-layered FR4 substrate of thickness 1 mm for MIMO applications. The size of the system PCB selected in this study is 30 mm 65 mm, which can be considered the form factor of the PCB for a wireless USB dongle. The two monopoles are printed on the two opposite corners of the PCB [shown on the top portion in Fig. 1(a)] and spaced 14 mm apart with a small ground portion (13 mm 14

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Fig. 2. Photo of a constructed prototype fed by 50-

Fig. 1. (a) Geometry of the two short-circuited monopoles linked by a neutralization line printed on the top portion of a FR4 substrate. (b) Detailed dimensions of the two- monopole-antenna system.

mm) therein between. Each monopole is designed in a clearance area (no grounding layout and electric components 14 therein) of size 8 mm 14.5 mm. The two monopoles are also identical in size and symmetrically placed with respect to the PCB center line [see symmetrical line in Fig. 1(a)]. Accordingly, it is expected that the performance of each monopole should be the same. Notice that the small ground portion is reserved for the antenna feeding network and the I-PEX connectors for the use of the standalone, coaxial-line-feed antennas as an optional scheme. Therefore, it is important to keep this area as much untouched as possible (no slit cut or protruded ground). Detailed design dimensions are given in Fig. 1(b). The preferred dimensions for the prototype were attained by the rigorous parametric studies with the aid of the electromagnetic simulator, Ansoft HFSS [13]. As seen in the figure, monopoles 1 and 2 are fed at ports 1 and 2 and short-circuited to the system ground at points and with an L-shaped strip respectively. Two short, 50- mini-coaxial lines with I-PEX connectors were utilized for feeding the antennas in the experiments (see the photo of a working sample demonstrated in Fig. 2). Notice that the feed gap between the feed point (points and ) and the system ground was fixed to be 1 mm in the study. Both the

mini-coaxial cables.

monopoles are of quart-wavelength resonant structures, and the antenna operating frequencies can be determined by the resonant- path length from the feed point to the open end of the monopole. The input matching of the antenna is easily finetuned by varying the length and the width of the short-circuiting strip from point to for monopole 1 and point to for monopole 2. The two short-circuited monopoles were first designed individually to obtain the optimal, achievable impedance bandwidth for simplicity; the mutual coupling was not considered at this stage. Then the two antennas were connected together by using a neutralization line. This conducting line is of width 0.3 mm and does not take up much available layout space of the system PCB. In this design, the system ground was removed only 1.5 mm long inwards from the substrate’s edge. The antenna port isolation was found to be effectively improved by linking the two highly-coupled monopoles at proper locations near the feed port at point for monopole 1 and point for monopole 2. The locations chosen conform to the studies in [11], which reports that a low impedance area (with minimum voltage but maximum currents) is favorable. The occurrence of the isolation properties is variable with respect to the location of the connecting points and . The studies of this parameter will be elaborated with the aid of Table I in Section III. Finally, both the antenna frequencies are also affected with the incorporation of the line, and each monopole needs fine-tuning to readjust its required frequency band. III. RESULTS AND DISCUSSION A. Reflection Coefficients, Isolation, TARC, and Envelope Correlation A prototype of the proposed antenna as shown in Fig. 2 was first constructed and measured based upon on the design and dimensions thereof described in Fig. 1. Fig. 3 shows the measured reflection coefficients ( for monopole 1 and for monopole 2) and the isolation between the two monopoles, whose simulated counterparts are given in Fig. 4(a). The isolation is only presented by the curves of due to the symmetrical structure of the proposed design.

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TABLE I SIMULATED RESULTS OF THE MONOPOLES AS A FUNCTION OF STUDIED AND ARE, RESPECTIVELY, THE LOWER AND UPPER IN FIG. 3. EDGE FREQUENCIES OF THE 10 dB IMPEDANCE AND THE SAME IS OF THE MAXIMUM FOR BOTH MONOPOLES 1 AND 2; VALUE WITHIN THE BAND OF INTEREST

Fig. 3. Measured reflection coefficients ( for monopole 1 and for between the two monopoles of the proposed monopole 2) and isolation 8 mm. design;

On average, the experimental data agree with the simulation results, which were based on the finite element method (FEM). The measured impedance matching of the two monopoles over the 2.4 GHz band is all below (about VSWR of 2), which meets the demanded bandwidth specification for WLAN operation. The isolation between the antennas is all below about 19 dB. When there is no neutralization line (the reference design, see Fig. 8), the antenna port isolation rapidly deteriorates by about 9 dB as seen in Fig. 4(b), compared with the data in Fig. 4(a). This behavior suggests that the isolation can be effectively improved by incorporating the neutralization line into the design, although the two antenna ports face each other with the same radiation polarization (see Fig. 10). It is noticed that the antenna operating frequencies and the impedance bandwidth thereof are also affected by the use of the neutralization-line technique. Furthermore, various locations of the connecting points and were also analyzed on the monopole frequencies and the in-band isolation ; the results are tabulated in Table I. The antenna frequencies are seen to be less affected compared with the port isolation and can still be within the 2.4 GHz frequency range. However, the dip of the curve shifts from the lower to higher frequencies with an increase in the length . In this case, there exists an optimal location for connecting both the monopoles. Fig. 5 presents the impedance of the isolation studied in Fig. 4. For the reference, the resistance impedance is stable and close to 50 with inductive reactance over the band. This behavior

Fig. 4. Simulated reflection coefficients ( for monopole 1 and for between the two monopoles for (a) the monopole 2) and isolation proposed design and (b) the reference case (with no neutralization line).

resembles an inductor put in between and well matched to the two ports (that’s ports 1 and 2 here) and transfers the signals from port 1 to port 2, resulting poor antenna port isolation. For the proposed design, it is interesting to observe that part of the resistance values is negative [14], which indicates an opposed direction for the current flow in a virtual capacitor (because of negative imaginary part) placed between the ports to replace the two monopoles and the radiation air path. The increase in the currents entering port 1 to the loading between the two ports also results in decreased voltage over the loading. In this case, the coupling field between the antenna ports is weak, leading to good antenna port isolation. To consider the constructive and destructive coupled signals on the combination of each antenna port’s reflected signals, the total active reflection coefficient (TARC) [15]–[17] is also investigated. TARC is defined as the ratio of the square root of total reflected power divided by the square root of total incident (1) power and can be considered the MIMO array radiation efficiency for a multi-port antenna [16]. The calculations can be done by using (1) described in [17], where is the phase angle of port 2 excitation, from which it is straightforward to see that

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Fig. 5. Impedance of isolation between the two monopoles for the proposed and the reference designs studied in Fig. 4.

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Fig. 7. Calculated envelope correlation for the two-monopole-antenna system.

[21]. In addition to the said method, the evaluation of the envelope correlation can be measured in a reverberation chamber [22]. The correlation coefficient is measured, and the envelope correlation is then obtained by (2) (2) B. Current Distribution, Near-Field, and Far-Field Radiation Characteristics

Fig. 6. Calculated TARC for one monopole of the two-monopole antenna system; each curve shows a reflection coefficient for an excitation with constant amplitude but different phase angle of port 2 excitation in steps of 30 degrees for 180 degrees.

TARC accounts for both coupling and random signals combining. Fig. 6 presents the calculated TARC from the scatteringmatrix elements of , , , obtained in Fig. 4(a) for monopole 1 with randomly phased excitation of monopole 2 with a set of seven excitation vectors. The curves retain the original characteristics of the reflection coefficient of a single antenna, but the impedance bandwidth is changed due to the effects of the mutual coupling and the incident waves with random phases. Interesting to notice that TARC becomes worst when the phase is equal to 180 (out- of-phase incident signals upon monopole 2 with respect to monopole 1). The average TARC in Fig. 6 shows that the in-band impedance is all below 10 dB and the worst case calculated TARC is smaller than 7.3 dB over the band. Fig. 7 plots the calculated envelope correlation between the two monopoles. The correlation was determined by the parameters in (11) reported in [18] for sufficiently accurate results in many practical cases [19]. However, it should be noticed that the equation is unsuitable for the case of zero mutual coupling . The magnitude and phase of the parameters were collected from the simulation data in Fig. 4(a). A brief description of the calculation was discussed in [20]. From the results, the values remain under 0.006 in the 2.4 GHz band and are much smaller than 0.5 at the mobile station (the user end)

The excited surface-current distributions of the design with (the proposed) and without (the reference) the neutralization line are studied in Fig. 8 to understand the behavior of the neutralization line in relation to the two monopoles. The currentmagnitude scale is kept the same among all the cases. First, the current distributions on the system ground plane and the strength thereof are similar between the proposed and the reference. This behavior is different from the finding in [23], which indicates the isolation between the antennas is related to the surface currents on the ground. Instead, the mutual coupling in this study is mitigated by introducing the counter-phased currents against the excited antenna [11]. For example, when monopole 1 is excited (port 1 excitation) with the currents entering the antenna, the current vector on the two-third of the neutralization line closer to monopole 2 is in the direction toward monopole 1. In this case, the surface currents are out of phase with a null located closer to monopole 1 on the line, such that the conductive currents are opposed to the excited antenna. In addition, it can be seen that the currents enter the two monopoles in the proposed (see currents from points to or to ) but in opposite directions in the reference (currents entering port 2 from monopole 2). It means that there exists an close path, including monopoles 1, 2, and the air between the open ends of the two monopoles, from port 1 to port 2, and the signal currents entering port 2 are against those entering port 1 and out of phase between the two ports for the proposed. Quite the contrary, for the reference, the signals currents enter port 1 but leave port 2 from monopole 2, and the currents even enter the system ground through the shorting strip. These can explain poor isolation for the reference and better antenna port isolation for the proposed. Second, for the reference, although the current-distributions compared with the proposed are not much different on the system ground and identical on the monopole from point

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Fig. 8. Simulated surface-current distributions at 2442 MHz for the proposed and the reference designs with port 1 and port 2 excitation, respectively.

and to the open end, the antenna isolation is poor because without any means of coupling cancellation. Also, the currents leave monopole 1 and enter monopole 2, respectively, at each open end of the monopole. This suggests that the corresponding antenna could receive the radiating signals of the excited antenna through the near-field radiation in this design. Therefore, to redirect the maximum near-field strength of the excited antenna away from the port of the corresponding antenna should facilitate port-to-port decoupling in a two-antenna system. Fig. 9 presents the simulated reactive near-field radiation patterns for monopole 1 excited at 2442 MHz for the proposed and the reference designs. The radius with port 1 or the gap source in the simulation as the center was set 14 and 22 mm, which are the effective range that the near field of the excited antenna (monopole 1) affects the corresponding one (monopole 2). The radius, 14 mm, is the same length as that of the small ground portion between the monopoles; in this case, the range is of the port-to-port distance. Therefore, the radiation in Fig. 9(a) represents that when monopole 1 is operating, the coverage reaches only to port 2 but not monopole 2 included. For the radius of 22 mm in Fig. 9(b), the range counts from port 1 to the right edge of monopole 2. Compared with the reference, which shows the large field strength aiming at port 2, the maximum strength of the reactive near field in Fig. 9(a) is not in the direction of port 2 but pointing to the portion of the neutralization line with the maximum currents seen in Fig. 8. This characteristic indicates that the large currents on the neutralization line can draw the near field in the case of the port-to-port radius and redirect the field away from the receiving antenna port, which in turn results in better port isolation. However, if the range of the reactive near field exceeds the port-to-port distance, the near-field radiation behaves similarly between the proposed and the reference as can be seen in Fig. 9(b). This phenomenon is expected because the current distributions on monopoles 1 and 2 from point and to the open end are identical, the reactive near field excited by monopole 1 can reach the open end of monopole 2 over the air, such that the currents leave the open end of monopole 1 and enter the open end of monopole 2. The reactive near fields with other radius values larger than port-to-port range of 14 mm but smaller than one wavelength (range criterion for reactive near

Fig. 9. Simulated reactive near-filed radiation patterns at 2442 MHz for the proposed and the reference designs with the radius of (a) 14 mm and (b) 22 mm with respect to port 1 (monopole 1) excitation.

field) at 2442 MHz were also examined. The results showed similar patterns for both the proposed and the reference designs. The over-the-air (OTA) performance of the antenna in free space was studied. Fig. 10 shows the far-field, 2-D radiation patterns at 2442 MHz, the center frequency of the 2.4 GHz band, in and fields for monopoles 1 and 2. The patterns were normalized with respect to the maximum field strength among three major planes: the – , – , and – cuts. The omnidirectional radiation patterns in this design lie in the – and – planes, and the radiation for ports 1 and 2 tends to cover the complementary space region (see – cuts). The polarization for the two monopoles was observed the same. Fig. 11 presents the simulated, far-field 3-D radiation patterns of the antennas studied in Fig. 10; the measured counterparts are given in Fig. 12. The measurement was made by the ETS-Lindgren OTA test system using the great-circle method in a CTIA authorized test laboratory [24]. Overall, the measured results are similar to the simulation. It can be seen that the null radiation is located in the opposite half-spaces in the – planes. Other in-band frequencies were also measured, and no inconsistency on the patterns was noticed. Fig. 13 shows the peak antenna gain and the radiation efficiency against frequency for the two monopoles. Again, because the two antennas are identical and symmetrically placed with respect to the PCB center, the gain and the radiation efficiency are about the same. The peak gain in the 2.4 GHz band for the two antennas is at a constant level of about 2.1 dBi, and the radiation efficiency is larger than about 70%. The gain measurement here takes account of the antenna mismatching and is the “realized gain” [25]. The radiation efficiency was obtained

SU et al.: PRINTED MIMO-ANTENNA SYSTEM USING NEUTRALIZATION-LINE TECHNIQUE

Fig. 10. Simulated 2-D radiation patterns at 2442 MHz for (a) monopole 1 and (b) monopole 2 studied in Fig. 3.

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Fig. 12. Measured 3-D radiation patterns (including the – and – cuts) at 2442 MHz for (a) monopole 1 and (b) monopole 2 studied in Fig. 3.

Fig. 13. Measured antenna gain and radiation efficiency for monopoles 1 and 2 studied in Fig. 12. Fig. 11. Simulated 3-D radiation patterns at 2442 MHz for monopole 1 (port 1 excitation) and monopole 2 (port 2 excitation) studied in Fig. 3.

by calculating the total radiated power of the antenna under test (AUT) over the 3-D spherical radiation first and then dividing

that total amount by the input power of 0 dBm (default value) given to the AUT in the test laboratory. Finally, to find out the antenna diversity gain, the proposed design was tested in the Bluetest reverberation chamber [22],

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The proposed design is also expected to be applied to wireless module-card solution in the form factor of a USB dongle. REFERENCES

Fig. 14. Cumulative probability distribution function of the two monopoles in the reverberation chamber based on 3016 measured power samples for each monopole (branch).

which emulates a rich scattering and fading environment following a Rayleigh distribution to represent a real MIMO environment. The of the two monopoles were measured simultaneously by connecting each antenna (denoted as one branch) to a four-port vector network analyzer. The subscript “1” and “ ” of means port 1 connecting to the three transmitting monopoles placed perpendicular to each other for three polarization and port j connecting to each corresponding antenna in the test (see Fig. 12, [26, Fig. 10]). The center frequency was set at 2442 MHz with used, measured frequencies ranging from 2440 to 2444 MHz for sampling. Fig. 14 plots the cumulative distribution function (CDF) of the measured power-transmission samples for the two branches (monopoles 1 and 2) against the relative received power recorded. At a cumulative probability level of 1% (that’s, the sufficient quality 99% of the time), the difference between the CDF of selection combining and the best CDF between the two monopoles represents the apparent diversity gain [26]. The apparent diversity gain was observed about 9.8 dB in the test. IV. CONCLUSION A printed, two-monopole-antenna system decoupled by using the neutralization-line technique has been demonstrated to attain good antenna port isolation, and the constructed prototype has been successfully constructed and tested. Each antenna is of the same size and occupies a clearance layout area of 8 mm 14.5 mm on the two opposite corners of the system PCB with a small ground portion between the antennas. The neutralization line in this design does not occupy much board space of the system ground plane and only takes 1.5 mm long inwards from the PCB edge in the small ground portion. In this case, the antenna feeding network and the I-PEX connectors can be all placed on that small ground portion for practical applications. The results showed that the obtained antenna port isolation is less than about 19 dB and is better than that of the reference case with no neutralization line by about 9 dB. The envelope correlation and the TARC were also studied and derived from the parameters. The radiation patterns of the two monopoles cover the complementary space regions in general, and the antenna yields peak gain of about 2.1 dBi with radiation efficiency exceeding about 70%. The impedance of the isolation, the surface currents, and the near-fields were analyzed in detail for the effects of the neutralization line used.

[1] Wireless LAN specification to provide significantly improved data throughput and range, The IEEE Standard Association [Online]. Available: http://standards.ieee.org/announcements/ieee802. 11n_2009amend-ment_ratified.html [2] T. Y. Wu, S. T. Fang, and K. L. Wong, “Printed diversity monopole antenna for WLAN operation,” Electron. Lett., vol. 38, pp. 1625–1626, Dec. 2002. [3] T. Ohishi, N. Oodachi, S. Sekine, and H. Shoki, “A method to improve the correlation coefficient and the mutual coupling for diversity antenna,” in IEEE Antennas Propag. Soc. Int. Symp. Dig., 2005, pp. 507–510. [4] G. A. Mavridis, J. N. Sahalos, and M. T. Chryssomallis, “Spatial diversity two-branch antenna for wireless devices,” Electron. Lett., vol. 42, pp. 266–268, Mar. 2006. [5] C. Y. Chiu, C. H. Cheng, R. D. Murch, and C. R. Rowell, “Reduction of mutual coupling between closely-packed antenna elements,” IEEE Trans. Antennas Propag., vol. 55, no. 6, pp. 1732–1738, Jun. 2007. [6] K. L. Wong and J. H. Chou, “Integrated 2.4- and 5-GHz WLAN antennas with two isolated feeds for dual-module applications,” Micro. Opt. Technol. Lett., vol. 47, pp. 263–265, Nov. 2005. [7] S. W. Su, J. H. Chou, and T. Y. Wu, “Internal broadband diversity dipole antenna,” Microw. Opt. Technol. Lett., vol. 49, pp. 810–812, Apr. 2007. [8] Y. Ge, K. P. Esselle, and T. S. Bird, “Compact diversity antenna for wireless devices,” Electron. Lett., vol. 41, pp. 52–53, Jan. 2005. [9] S. W. Su, J. H. Chou, and Y. T. Liu, “Realization of dual-dipole-antenna system for concurrent dual-radio operation using polarization diversity,” Micro. Opt. Technol. Lett., vol. 51, pp. 1725–1729, Jul. 2009. [10] S. W. Su, “A three-in-one diversity antenna system for 5 GHz WLAN applications,” Micro. Opt. Technol. Lett., vol. 51, pp. 2477–2481, Oct. 2009. [11] A. Diallo, C. Luxey, P. L. Thuc, R. Staraj, and G. Kossiavas, “Study and reduction of the mutual coupling between two mobile phone PIFAs operating in the DCS1800 and UMTS bands,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3063–3074, Nov. 2006. [12] A. Diallo, C. Luxey, P. L. Thuc, R. Staraj, and G. Kossiavas, “Enhanced two-antenna structures for universal mobile telecommunications system diversity terminals,” IET Microw. Antennas Propag., vol. 2, pp. 93–101, 2008. [13] Ansoft Corp., Pittsburgh, PA, “HFSS,” [Online]. Available: http://www.ansoft.com/products/hf/hfss [14] Wikipedia, the Free Encyclopedia, “Negative Resistance,” [Online]. Available: http://en.wikipedia.org/wiki/Negative_resistance [15] M. Manteghi and Y. Rahmat-Samii, “Multiport characteristics of a wide-band cavity backed annular patch antenna for multipolarization operations,” IEEE Trans. Antennas Propag., vol. 53, no. 1, pp. 466–474, Jan. 2005. [16] D. W. Browne, M. Manteghi, M. P. Fitz, and Y. Rahmat-Samii, “Experiments with compact antenna arrays for MIMO radio communications,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3239–3250, Nov. 2006. [17] S. H. Chae, S. K. Oh, and S. O. Park, “Analysis of mutual coupling, correlations, and TARC in WiBro MIMO array antenna,” IEEE Antennas Wirel. Propag., vol. 6, pp. 122–125, 2007. [18] S. Blanch, J. Romeu, and I. Corbella, “Exact representation of antenna system diversity performance from input parameter description,” Electron. Lett., vol. 39, pp. 705–707, May 2003. [19] V. Plicanic, Z. Ying, T. Bolin, G. Kristensson, and A. Derneryd, “Antenna diversity evaluation for mobile terminals,” in Proc. Euro. Conf. Antennas Propag., 2006, pp. 1–3. [20] S. W. Su, “High-gain dual-loop antennas for MIMO access points in the the 2.4/5.2/5.8 GHz bands,” IEEE Trans. Antennas Propag., vol. 58, no. 7, pp. 2414–2419, Jul. 2010. [21] R. G. Vaughan and J. B. Andersen, “Antenna diversity in mobile communications,” IEEE Trans. Veh. Technol., vol. 36, no. 11, pp. 149–172, Nov. 1987. [22] Bluetest, Gothenburg, Sweden, “Reverberation test systems,” [Online]. Available: http://www.bluetest.se/products/reverberation-test-systems [23] K. L. Wong, J. H. Chou, S. W. Su, and C. M. Su, “Isolation between GSM/DCS and WLAN antennas in a PDA phone,” Micro. Opt. Technol. Lett., vol. 45, pp. 347–352, May 2005.

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[24] CTIA, the Wireless Association, Washington, DC, “CTIA Authorized Test Laboratory,” [Online]. Available: http://www.ctia.org/business_resources/certification/test_labs/ [25] J. L. Volakis, Antenna Engineering Handbook, 4th ed. New York: McGraw-Hill, 2007, ch. 6, pp. 16–19. [26] B. Furht and S. A. Ahson, Long Term Evolution: 3GPP LTE Radio and Cellular Technology. Boca Raton, FL: CRC Press, 2009, ch. 12, pp. 441–443.

Saou-Wen Su (S’05–M’08) was born in Kaohsiung, Taiwan, on November 11, 1977. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from National Sun Yat-Sen University, Kaohsiung, Taiwan, in 2001, 2003, and 2006, respectively. Since April 2006, he was with the Technology Research and Development Center, Lite-On Technology Corporation, Taipei, Taiwan, where he is currently working with the Network Access Strategic Business Unit. He built up the first RF Antenna Design Team, Lite-On Technology Corporation and contributed numerous cutting-edge designs to the company’s ODM projects, including enterprise/SMB access point, router, Bluetooth headset/car kit, home entertainment device, media box, RF module, etc. Many customized and standard antenna designs were successfully mass produced. Currently, he has published over 80 refereed SCI journal papers and numerous international conference articles. He holds 25 U.S. and 26 Taiwan patents and many patents pending. His expertise is in the industrial RF antenna designs for wireless AP/router, Bluetooth, WLAN, and MIMO applications, and previous researches prior to Lite-On Technology Corporation included mobile-phone and wideband antenna designs. Dr. Su was a recipient of a one-year full-time School Study Exchange Program Scholarship to The University of Auckland, New Zealand from the Asian 2000 Foundation in 1998.

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Cheng-Tse Lee (S’08–M’10) was born in Yilan, Taiwan, in 1983. He received the B.S. degree in electronic engineering from National Changhua University of Education, Changhua, Taiwan, and the M.S. and Ph.D. degrees in electrical engineering from National Sun Yat-Sen University, Kaohsiung, Taiwan, in 2005, 2007, and 2010, respectively. He is currently with the Network Access Strategic Business Unit, Lite-On Technology Corporation, Taipei, Taiwan. His main research interests include antenna designs for wireless communications, especially for the planar antennas for mobile phone, laptop computer, and also in microwave and RF circuit design. His expertise is in the industrial antenna designs for WWAN, WLAN, Bluetooth and MIMO applications.

Fa-Shian Chang was born in Taoyuan, Taiwan, on April 21, 1968. He received the B.S. degree in physics from Chinese Military Academy, Kaohsiung, Taiwan, the M.S. degree in applied physics from Chung Cheng Institute of Technology, National Defense University, Tauyuan, Taiwan, and the Ph.D. degree in electrical engineering from National Sun Yat-Sen University, Kaohsiung, Taiwan, in 1990, 1995, and 2002, respectively. Since November 1990, he has served in the military at Chinese Military Academy, and became an Assistant Professor with the Department of Electrical Engineering in 2005. He built up the Advanced Technology Laboratory at Chinese Military Academy and did several government-grant projects in the fields of base station antennas, simulation system, and unman ground vehicle. Many of the designs were successfully produced. After retiring from the colonel position, he taught at the Department of Electronics, Cheng Shiu University, Kaohsiung, Taiwan, as an Assistant Professor and was in charge of the Intelligent Vehicle Development Laboratory. He has published over 25 refereed SCI journal papers and many international conference articles. He holds 4 U.S. and 21 Taiwan patents and many patents pending. His expertise is in the antenna designs for remote control robot, WLAN, and MIMO applications.

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Simple and Efficient Decoupling of Compact Arrays With Parasitic Scatterers Buon Kiong Lau, Senior Member, IEEE, and Jørgen Bach Andersen, Life Fellow, IEEE

Abstract—Compact arrays such as multiple antennas on a mobile terminal suffer from low efficiency and high correlation between antenna signals. In the present paper, a simple and rigorous procedure for decoupling two closely coupled antennas with a parasitic scatterer is proposed. The parasitic scatterer, which can be an additional antenna, acts as a shield between two active antenna elements. In contrast to previous studies involving the use of parasitic scatterer for decoupling antennas, we demonstrate using antenna impedances the underlying decoupling mechanism for two arbitrary antennas. By a proper choice of parameters, perfect matching and decoupling can be obtained for a given antenna spacing without extending the overall area used, and without introducing additional decoupling networks. The price to pay is a reduction of bandwidth relative to that of widely spaced antennas, which is the case for other decoupling methods as well. Simulation and experimental results are used to substantiate the effectiveness of the proposed design approach on a two-monopole array with an antenna spacing of 0.1 wavelength. Finally, several practical considerations of the proposal are also presented, including the extension of the approach for more than two active antennas and its implementation in mobile terminals. Index Terms—Antenna array mutual coupling, impedance matching, parasitic antennas.

C

I. INTRODUCTION

ONVENTIONALLY, antenna arrays were used in radar installations and satellite communications. In these applications, it is typical to separate adjacent antenna elements by one half of a wavelength , in order to maximize array resolution without the problem of ambiguity [3]. The same conclusions apply to the more recent application of antenna arrays at base stations in wireless communications (see e.g., [4]). However, the overall size of the array structure has become a subject of current interest, following the widespread adoption of multiple-input multiple-output (MIMO) technology in existing and future wireless communications standards [5]. One reason for this is that the implementation of multiple antennas in compact user terminals involves challenging design tradeoffs [6]. For example, even though techniques exist to mitigate muManuscript received June 13, 2010; revised December 15, 2010; accepted January 21, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. This work was supported by VINNOVA under grant 200800970 and Vetenskapsrådet under grant 2006-3012. This paper was presented in part at the International Workshop on Antenna Technology, Santa Monica, CA, Mar 2–4, 2009 [1] and also in part as a patent application [2]. B. K. Lau is with the Department of Electrical and Information Technology, Lund University, Sweden (e-mail: [email protected]). J. B. Andersen is with the Antennas, Propagation and Radio Networking (APNET) Section, Department of Electronic Systems, Faculty of Engineering and Science, Aalborg University, Denmark (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173440

tual coupling and correlation among closely spaced antennas [6], the achievable bandwidth is reduced when compared to widely spaced antennas [7]. Nevertheless, antenna decoupling techniques can be used to facilitate a smaller antenna separation for a given set of performance requirements. A. Existing Decoupling Techniques One well-studied technique to decouple closely spaced antennas is to apply the so-called multiport conjugate (MC) match through introducing a separate impedance matching network [6]–[15]. The MC match has been successfully demonstrated for monopoles [8], [10], [11], [13], [14], dipoles [7], [9], patch antennas [12] and planar inverted F antennas (PIFAs) [15]. Two drawbacks with implementing an additional network to achieve decoupling are that ohmic losses are expected from the decoupling network [14] and that the decoupling network can increase the overall footprint of the multiple antenna system. Other decoupling techniques, which are specific to antennas on a common ground plane, include ground plane modifications [16], [17] and use of neutralization line [18], [19]. More recently, the use of a parasitic element has been proposed as an attractive alternative to decouple two closely spaced antennas [20]–[23]. Akin to the MC match, it can decouple different types of antennas, including dipoles [20], [23], monopoles [21], [24], PIFAs [20], [24] and ultrawideband (UWB) antennas [25]. In fact, the use of parasitic elements in an antenna system is not new. Their previous applications, which are unrelated to decoupling of multiple antennas, include: • changing of antenna patterns [26]–[30]; • limiting current flow of antenna on a small ground plane [31]; • enhancing bandwidth of the antenna structure [32]–[35]; • adding a resonant frequency band [36]; • increasing the reflection phase range of reflectarrays to beyond 360 [37]. One common feature in the existing literature on parasitic decoupling is that the design procedure minimizes the coupling coefficient in a best effort manner through sweeping the parameters of the parasitic element. As such, they are unlike the MC match, which generates perfect decoupling at the desired frequency for the given self and mutual impedances of the closely coupled antennas. Another commonality of existing parasitic decoupling literature, with the exception of [24], is that the structure of the parasitic element does not resemble that of the closely coupled antennas. For example, [20] proposes a H-shape structure and a meander T-shape structure for decoupling dipoles and PIFAs, respectively, and a parameter sweep is employed to design these structures.

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LAU AND ANDERSEN: SIMPLE AND EFFICIENT DECOUPLING OF COMPACT ARRAYS WITH PARASITIC SCATTERERS

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B. Proposed Parasitic Decoupling Technique In this paper, we propose a simple and efficient parasitic decoupling technique, which can perfectly decouple two arbitrarily spaced antennas using a reactively loaded parasitic antenna in between them. It will be shown that our approach gives similar result as a MC matching network, but in a much simpler realization while maintaining the overall size of the antenna system. The proposed design procedure is simple and rigorous, in that the objective is to tune the dimensions of both the active and parasitic antennas in order to satisfy a criterion derived from antenna impedances. The criterion provides perfect decoupling of the active antennas through the use of a purely reactive load at the parasitic antenna. The reactive load ensures lossless decoupling in the case of ideal elements. Experimental results also show that the proposed technique gives significantly better measured efficiency than the MC match for two monopoles of 0.1 spacing [13]. Whereas [24] shows the possibility to decouple two active antennas by placing a reactively loaded parasitic antenna in between them, it relies on numerical optimization of only the reactive load. No explicit information is provided on the underlying principle and mechanism, apart from the observation that loading the parasitic antenna with different reactive loads changes the gain patterns and coupling between the active antennas. In this paper, we show that tuning the active and parasitic antennas by changing their dimensions is necessary for achieving perfect decoupling at the center frequency. The drawback of using any of the aforementioned techniques for coupling compensation is the narrow bandwidth of the resulting antenna system, but this is unavoidable for antenna systems with small antenna spacing [6]. Another consequence of these approaches is a change of radiation pattern, but this should only pose a minor problem in a rich scattering environment [38], and in fact it is angle diversity which facilitates the decorrelation of the signals. A simpler solution with optimum uncoupled port matching [39]–[41] is also a possibility, but the efficiency is reduced compared with decoupling techniques. The use of parasitic scatterer or reflector to increase isolation of UWB antennas (see [25] and references therein) has also been proposed. It is expected that a similar approach can be devised to enhance the bandwidth of decoupled narrowband antennas by generating multiple resonances in the parasitic element. For the purpose of demonstrating the effectiveness of our parasitic decoupling concept and giving insight into its operation, we use electrical dipoles or monopoles as generic examples in this paper. However, the basic principle will work for any antenna, since the method only relies on antenna impedances. The paper is organized as follows: Section II introduces the theoretical derivation of parasitic decoupling and the design procedure, which is illustrated using the simple case of two closely coupled dipoles. Section III shows the design approach for monopole antennas in full wave simulations, and the results are also verified in an experiment. Insights and practical issues relating to the technique are discussed in Section IV. Section V concludes the paper.

Fig. 1. A decoupling setup for a black box containing an arbitrary two-antenna structure (ports 1 and 3) and a parasitic scatterer (port 2). Port 2 is terminated with an impedance load, whereas each of ports 1 and 3 is matched to a 50 feed cable.

II. THEORY OF DECOUPLING WITH A PARASITIC SCATTERER A. Derivation of Decoupling Procedure The theory of decoupling two arbitrary active antennas with a parasitic scatterer can be illustrated with the setup in Fig. 1. The “black box” in the setup consists of two active antennas (ports 1 and 3) and a parasitic scatterer (port 2) that acts as a shield between the active antennas. The 3-port black box (or network) of multiple antennas is also intended to highlight the fact that the closely coupled antenna and scatterer cannot be considered as separate structures in general, e.g., they may share a common ground. The parasitic scatterer is terminated by the load impedance and the matching circuits (or matching network) connected to antennas 1 and 3 transform the antenna input impedance to the impedance of the feed cable (typically 50 ). The self and mutual impedances of the three-port array at the center frequency ( , being the speed of light in vacuum) are represented by and , respectively, where , , 2, 3. We begin with the voltage and current relationship of the setup (1) , where and are the voltage or in matrix notation and current across the th antenna port. Moreover, due to reciprocity, , and . The termination condition for the parasitic scatterer implies that , which upon substitution into (1) and rearrangement gives the voltage and current relationships across the ports of the active antennas (2) where (3) (4) (5)

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To perfectly decouple the active antennas, we require that , or equivalently

(6) Treating the real and imaginary parts of (6) separately, and setting the load resistance to zero which will ideally circumvent any ohmic loss in the loaded scatterer (7) (8)

Fig. 2. A decoupling setup with the dipole 2 acting as a parasitic scatterer for the active dipoles 1 and 3. The parasitic scatterer is terminated with an impedance load.

where and . Based on the above derivation, the design procedure for decoupling can be formulated into the following steps: 1) For a given closely coupled two-antenna array, insert a third antenna between them as the parasitic scatterer. 2) Tune the three antennas so that criterion (7) is satisfied. 3) Calculate the reactance load for the parasitic scatterer using (8). 4) Calculate the new input impedances of the active antennas and using (3) and (5), respectively. 5) Calculate the required matching circuits to transform and to 50 . B. Illustrative Example of Design Procedure Since the above derivation is purely based on antenna impedances, the two antennas and the parasitic scatterer can be arbitrary and need not be of the same type. However, the commonly used reference of dipole antennas are used to demonstrate the decoupling procedure in the following numerical example. The setup is given in Fig. 2, which is identical to Fig. 1, except that the antennas are now explicitly shown. The center frequency is 900 MHz and the diameter of the dipoles is 2 mm. For simplicity, the dipole lengths are assumed to be identical , such that (i.e., valid for the thin dipoles used here). In general, allowing for different lengths will increase the flexibility of the design method. The method-of-moments (MoM) Matlab scripts from [42] are used to generate the antenna impedances. The spacing between the two active dipoles is set at . For this example, the criterion (7) can be achieved by adjusting the identical length of the dipole antennas . As illustrated in Fig. 3(a), two solutions satisfy this criterion, i.e., and the corresponding load reactances in . Therefore, the proposed Fig. 3(b) are procedure can in theory achieve perfect and lossless decoupling, i.e., the scattering (or S) parameters , by ensuring that both conditions (7) and (8) are fulfilled. The reactive load at the parasitic element may be realized by either lumped (e.g., inductor) or distributed (e.g., open-circuited transmission line) elements. In this example, lossless inductors are used.

Fig. 3. Load (a) resistance and (b) reactance of the parasitic scatterer for perfect decoupling versus the length of the dipole antennas.

In general, the identical input impedance of dipoles 1 and 3 is not equal to the reference impedance of 50 when the load reactance of antenna 2 is set to one of the two values . It follows from (3) and (6) that (9) which in this case reduces to (10) . due to the symmetry The expression (10) implies that at the center frequency, the input impedance of the active antennas decreases correspondingly when the spacing is reduced, due to the self and mutual impedances approaching each other. Therefore, if becomes small, the required impedance transformation ratio to achieve 50 is high. For this example of , the input impedance of each of the two decoupled active port are as low as and , respectively, for the two . This complicates the solutions with matching and gives narrowband results. However, it is possible

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Fig. 5. Monopole uniform linear array of three elements, with the coordinate system used in the radiation pattern measurement.

to use a more sophisticated matching network (such as a Chebyshev design) to enhance the bandwidth of by more than a factor of two, if required, using a similar approach as for matching single antennas [43]. The impedance matching circuit needed to transform the impedance of each of the two decoupled active antennas (i.e., and ) to 50 is realized here with transmission lines and a single open-circuited stub [44], although lumped elements [44] may be more attractive for circuit miniaturization, especially at lower frequencies. Note that similar uncoupled matching circuits are required for any realization of MC match, except that in the present case the decoupling function of the decoupler line [10] or the rat-race hybrid 180 coupler [11] in the overall MC matching circuit is provided by the parasitic scatterer. The scattering parameters of the decoupled active antennas using either of the two reactance load solutions are shown in Fig. 4, where and are the scattering parameters of matching the active antennas after the decoupling and 50 steps. Lossless inductors are used in the MoM simulation to provide the required reactance load at the parasitic scatterer. As expected, perfect decoupling and matching is achieved at the center frequency for either of the two solutions. However, the solution with the shorter dipoles gives a more narrowband behavior in , as can be expected from the higher reactance load needed. As a reference case, the scattering parameters of two half-wavelength dipoles that are individually conjugate matched with their self-impedances (i.e., self impedance match) are also shown. In this case, the antenna spacing of 0.1 is kept and no parasitic scatterer is used. Comparing the decoupling case with the reference case, it is clear that the decoupling approach gives very good matching performance, albeit for a relatively small bandwidth. As another comparison, the scattering parameters for a realization of MC match based on hybrid 180 coupler [11], [13] are also provided in Fig. 4. Using this realization, the output ports contain the odd and even modes. The isolation between the odd

and even modes has a large bandwidth and thus not shown here. As in the reference case, the antenna spacing is 0.1 and no parasitic scatterer is used. It is observed that the odd mode of the MC match, which has a smaller bandwidth than the even mode, has been found to yield similar bandwidth performance to the solution of the parasitic decoupling approach. III. SIMULATION AND EXPERIMENTAL VERIFICATION In this section, we present simulation and experimental results of the proposed decoupling approach at 900 MHz for the monopole antenna setup shown in Fig. 5. The same monopole array structure as in [40] is used, except that here we use three monopoles, instead of only two. Monopole 2 is the parasitic scatterer, whereas monopoles 1 and 3 are the active elements. Monopole 3 is located at the center of the ground plane, whereas monopoles 1 and 2 are separated by 0.1 and 0.05 from monopole 3 along the negative -axis, respectively (i.e., ). The ground plane of the monopole has the surface dimensions of 330 mm 250 mm, and it is made from FR4 material of thickness 1.55 mm, with a thin copper coating on the . The dielectric constant and loss underside of thickness 35 tangent of the FR4 material at 900 MHz is 4.4 and 0.02, respectively. The copper-coated FR4 ground plane is used due to it being relatively lightweight and more rigid than pure copper ground plane of comparable thickness. The monopole conductors are made from cylindrical copper wires of 2 mm in diameter. Each of the two matching circuits, which is connected to the feeding end of the copper conductor, is printed on a PTFE printed circuit board (PCB) as transmission lines and open-circuited stubs. The PTFE PCB has a thickness of 0.8 mm and a . At 900 MHz, The PTFE material has a copper layer of 35 dielectric constant of 2.53 and a loss tangent of 0.0015. The design procedure listed in Section II-A is applied to the simulation model of the monopole array setup. The simulation results of the monopole setup are obtained using the time-domain solver of CST Microwave Studio. For convenience of tuning, we apply distributed elements for both the reactive load at the parasitic element and the matching circuits at the active antennas. In particular, an open-circuited transmission line on a PCB is used as the reactive load and the matching circuits consist of transmission lines and single open-circuited stubs. These circuits are incorporated into the antenna simulation

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Fig. 6. Simulated and measured scattering parameters for active monopole antennas 1 and 3.

through circuit co-simulation in CST Design Studio. For the experimental verification, the scattering parameters of the fabricated monopole array (with the corresponding distributed decoupling and matching circuits attached) are measured with a two-port vector network analyzer and the radiation patterns are measured in a Satimo Stargate-64 measurement facility. As in the case of dipoles, two reactance load solutions can be found for perfect decoupling. However, we focus on the solution giving the larger bandwidth. The scattering parameters of the decoupled (and matched) active monopoles from simulation and measurement are given in Fig. 6. As can be seen, the simulation and measurement results are in good agreement with each other. Due to higher ohmic losses in practice than in simulation, the bandwidths of the measured cases are slightly larger than the simulated ones. Practical tuning likewise limits the exact reproduction of the isolation parameter. The simulated and measured radiation patterns of the decoupled active elements are shown in Fig. 7. Again, the simulated and measured results are in good agreement. It is noted component of the plane in that the simulated Fig. 7(e) and (f) is not visible, since it is not within the given range of pattern magnitudes. In addition, the simulated patterns of the two active elements exhibit non-exact mirror symmetry, and this is because the center of the array is slightly displaced (i.e., by 0.05 ) from the center of the ground plane. As can be expected from the linearly polarized monopoles, the component is dominant in the radiation patterns. Both and planes reveal that the maximum gains of the two patterns point away from each other, towards the array endfires ( or 270 ), at a elevated angle of . The directivity of the patterns is about 7.5 dBi, which is significantly higher than that of a single monopole. This confirms that angle diversity is strongly utilized in this setup. The simulated and measured pattern correlation, assuming a 3D uniform angular power spectrum (APS), is around 0.05 and 0.02, respectively. In the ideal case of a lossless setup, perfect decoupling and matching in the 3D uniform APS will lead to zero pattern correlation [7], [45]. The slight discrepancies between the theoretical zero correlation and the small correlation values in the

simulated and measured cases are attributed to the presence of some losses and that it is difficult to practically obtain zero correlation. The tolerance of efficiency measurement in the Satimo facility at 900 MHz is specified to be 0.5 dB. The simulated efficiencies of the parasitic decoupled monopoles are close to 100%, whereas the measured efficiencies are about 70% (-1.5 dB). The discrepancy is primarily the result of imperfect fabrication of the antenna structure and the matching circuits, where the design of the experimental setup emphasizes flexibility rather than precise construction (e.g., monopoles of different antenna spacing can be easily achieved on the same ground plane). As a reference, the measured efficiency of a single monopole on the same ground plane is about 80% (-1.0 dB), which is within the tolerance range of the decoupled monopoles’ efficiencies. for In contrast, for the same antenna spacing of the two-monopole setup which applies the MC match based on hybrid 180 coupler, the measured even and odd mode efficiencies at the center frequency are 75% and under 30%, respectively [13]. These efficiency values are for matching the

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For three-element arrays of non-triangular arrangements, the inherent asymmetry in the array structure introduces different levels of coupling between different pairs of antennas, which complicates the design of parasitic scatterer(s) for perfect decoupling. However, the performance of multiple antenna systems is usually limited by pair(s) of antennas with the smallest antenna separation distance, such as for the case of uniform linear arrays of three or more elements. Therefore, decoupling the antenna pairs with the most severe coupling level can provide an approximate solution. B. Application in Compact Terminals

Fig. 8. Simulated scattering parameters for the UTA, with and without the reand actively loaded parasitic scatterer. Due to symmetry , due to reciprocity.

even and odd mode outputs of the hybrid coupler with transmission lines and single open-circuited stubs (i.e., the narrowband matching solution). Recall that similar matching elements are used to match the parasitic decoupled monopole ports. Comparing the achieved measured efficiency with parasitic decoupling and MC match, the parasitic decoupling approach is superior in terms of both average efficiency and balance of branch power. IV. FURTHER INSIGHTS AND PRACTICAL ASPECTS A. Number of Antennas For future systems, it is most realistic to first consider arrays with only two elements, though an extension of our proposed decoupling technique to the use of more elements is possible. The technique will work for the case of three parallel dipoles (dipoles 1 to 3) in a uniform triangular array (UTA) arrangement, where one parasitic scatterer (dipole 4) in their centroid is able to decouple the triangular array for any separation distance between the active antennas. Applying the same approach from Section II-A in deriving (6) for decoupling two active antennas, and assuming that the active dipoles are identical, the corresponding expression for this three-dipole case is given by . For dipoles with a diameter of 2 mm and antenna spacing of among the active dipoles, the scattering parameters as calculated using the MoM scripts from [42] for two UTA cases (i.e., with and without a parasitic dipole at the centroid) are illustrated in Fig. 8. As before, the self-impedance match and half-wavelength dipoles are used for the reference case without the parasitic dipole. As can be seen, perfect decoupling is achieved at the center frequency when the reactively loaded parasitic dipole is applied, whereas the no-parasitic case has a high coupling coefficient of between a given antenna and each of its two adjacent antennas. Nonetheless, as in the case of two-element arrays, decreasing the separation distance will result in a smaller bandwidth for the decoupled antennas. The reason that the decoupling technique applies directly to the UTA case is that the symmetry of the array structure ensures that the coupling between any (active) antenna pair is equal.

One important application of decoupling techniques is in achieving good performance for mobile terminals with closely spaced antennas [6],[16]–[19]. Limited available space, multiple-band operation and the need for co-existence with other device components complicate the decoupling task significantly. Preliminary simulation results confirm that the proposed parasitic decoupling technique can perfectly decouple dual-PIFA and dual-monopole antennas at 900 MHz for a 40 mm 100 mm ground plane, where the two active and one parasitic antennas are placed at the two short edges and the center of the ground plane, respectively. The parasitic antenna is a PIFA in both cases. C. MIMO Performance It is known that a lossless decoupled and well matched receive array is optimum not only from the viewpoint of maximum power transfer from the antennas to the loads [9], it also facilitates zero correlation in the uniform 3D APS [7], [45]. In fact, the decoupled array is likewise superior in received power and correlation performance to coupled array in other propagation environments [41]. Since MIMO performance measured in terms of either capacity or diversity gain is a function of correlation, branch power imbalance and available power, arrays which are decoupled by any (lossless) method will in general result in a better MIMO performance as well (see e.g., [6], [9],[46]). As an example, we consider the MIMO capacity for the lossless dipoles in Section II at the center frequency. For a MIMO channel , the instantaneous channel capacity with equal transmit power allocation can be expressed as [47] (11) is the identity where is the reference SNR and matrix. Since the interest here is in antenna design, the reference propagation environment of independent and identically is assumed, i.e., distributed (IID) Rayleigh fading channel are zero mean circularly symmetric complex the entries of Gaussian random variables. Without loss of generality, the case of receive antennas is examined. Then, the MIMO channel is given by (12) where is the receive correlation matrix, which fully represents the effects of the antennas on the channel, i.e., it characterizes

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Fig. 9. Contour plot of the simulated total electric field (in dB) 5 mm above the ground plane when active monopole antenna 1 is removed. The center of the ground plane is at the origin and the coordinate system is shown in Fig. 5. The field is shown for only the center region of the ground plane.

the efficiency, efficiency imbalance and correlation among the receive antennas. In particular, (13) where is a normalized correlation matrix whose diagonal elements are 1 and the th element denotes the complex correlation coefficient between the 3D radiation patterns of the th and th antenna ports. denotes a diagonal matrix given by (14) where is the total efficiency of the th antenna. The correlation between the active antennas that has been decoupled with parasitic scatterer and matched to 50 is zero and the total efficiency of each antenna is 100%. This means that and the MIMO capacity is the same as that of the IID and 10,000 Monte Carlo reRayleigh channel. For alizations of the , the ergodic capacity is 11.3 bits per second per Hertz (bits/s/Hz). In comparison, the correlation and total efficiency of the reference case with self-impedance match are 0.55 and 58% (-2.4 dB), respectively. This translates to an ergodic capacity of 9.4 bits/s/Hz. Thus, the proposed decoupling procedure gives an overall gain in capacity of 2 bits/s/Hz. On the other hand, as also pointed out in Section II, the bandwidth of the decoupled array can be significantly smaller than that of a widely spaced array, depending on the antenna spacing [7]. This implies that at a very small antenna separation, the benefit of decoupling will be small, if the operating bandwidth significantly exceeds the achieved antenna bandwidth. D. Shielded Zone As can be seen in the pattern plots in Fig. 7, the shielding effect of the parasitic antenna ensures that the radiation of the active antennas is directed away from each other. However, the

shielding effect is not only limited to far-field beamforming between the excited antenna and the parasitic element. Indeed, since decoupling is a near-field phenomenon, one can expect that there is a quiet zone within the shielded region, as can be seen in the simulated total electric field distribution along the center region of the large ground plane in Fig. 9. In Fig. 9, active monopole antenna 1 is removed and the total electric field is taken at a height of 5 mm above the ground plane. As can be observed, the field at the former location of antenna 1 is over 10 dB lower than the value in the immediate vicinity of the excited antenna 3. Moreover, due to the decoupling phenomenon, removing one of the two active antennas will only marginally affect the impedance and radiation characteristics of the other active antenna. This is confirmed in both simulations and measurements, i.e., the remaining active antenna gives similar reflection coefficient and radiation pattern as those shown in Figs. 6 and 7, respectively. V. CONCLUSIONS This paper takes up the task of decoupling closely coupled antennas with parasitic scatterers. The main intention is to provide the theoretical insights into the approach, which can be applied to two arbitrary coupled antennas for an arbitrary spacing. Example applications on reference antenna arrays of closely spaced dipoles or monopoles illustrate the procedure and its effectiveness. Preliminary results confirm that the approach extends readily into more practical antenna elements, such as those used in mobile terminals. However, the ability of the parasitic scatterer approach to support multi-band operation and its robustness to user effects are interesting subjects for future studies. ACKNOWLEDGMENT The authors would like to thank L. Hedenstjärna of the Department of Electrical and Information Technology, Lund University, for fabricating the antennas and matching circuits. REFERENCES [1] B. K. Lau and J. B. Andersen, “Unleashing multiple antenna systems in compact terminal devices,” presented at the Int. Workshop Antenna Technol. (IWAT2009), Santa Monica, CA, Mar. 2–4, 2009. [2] B. K. Lau and J. B. Andersen, “Antenna System and Method of Providing an Antenna System,” Swedish Patent Application (No. 0702307-0), Oct. 2007. [3] H. Krim and M. Viberg, “Two decades of array signal processing research: The parametric approach,” IEEE Signal Process. Mag., vol. 13, no. 4, pp. 67–94, Jul. 1996. [4] S. Andersson, B. Hagerman, H. Dam, U. Forssén, J. Karlsson, F. Kronestedt, S. Mazur, and K. J. Molnar, “Adaptive antennas for GSM and TDMA systems,” IEEE Personal Commun. Mag., vol. 6, no. 3, pp. 74–86, Jun. 1999. [5] E. Dahlman, S. Parkvall, and J. Sköld, 3G Evolution: HSPA and LTE for Mobile Broadband. London: Academic Press, 2008, pp. 267–298. [6] B. K. Lau, “Multiple antenna terminals,” in MIMO: From Theory to Implementation, C. Oestges, A. Sibille, and A. Zanella, Eds. San Diego: Academic Press, 2011. [7] B. K. Lau, J. B. Andersen, G. Kristensson, and A. F. Molisch, “Impact of matching network on bandwidth of compact antenna arrays,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3225–3238, Nov. 2006. [8] J. B. Andersen and H. H. Rasmussen, “Decoupling and descattering networks for antennas,” IEEE Trans. Antennas Propag., vol. AP-24, no. 6, pp. 841–846, Nov. 1976.

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[9] J. W. Wallace and M. A. Jensen, “Mutual coupling in MIMO wireless systems: A rigorous network theory analysis,” IEEE Trans. Wireless Commun., vol. 3, no. 4, pp. 1317–1325, Jul. 2004. [10] S. Dossche, S. Blanch, and J. Romeu, “Optimum antenna matching to minimise signal correlation on a two-port antenna diversity system,” Elect. Lett., vol. 40, no. 19, pp. 1164–1165, Sep. 2004. [11] S. Dossche, S. Blanch, and J. Romeu, “Decorrelation of a closely spaced four element antenna array,” in Proc. IEEE Antenna Propag. Soc. Int. Symp., Washington, DC, Jul. 3–8, 2005, vol. 1B, pp. 803–806. [12] S. Dossche, J. Rodriguez, L. Jofre, S. Blanch, and J. Romeu, “Decoupling of a two-element switched dual band patch antenna for optimum MIMO capacity,” in Proc. IEEE Antenna Propag. Soc. Int. Symp., Albuquerque, NM, Jul. 2006, pp. 325–328. [13] C. Volmer, M. Sengul, J. Weber, R. Stephan, and M. A. Hein, “Broadband decoupling and matching of a superdirective two-port antenna array,” IEEE Antennas Wireless Propag. Lett., vol. 7, pp. 613–616, 2008. [14] C. Volmer, J. Weber, R. Stephan, K. Blau, and M. A. Hein, “An eigenanalysis of compact antenna arrays and its application to port decoupling,” IEEE Trans. Antennas Propag., vol. 56, no. 2, pp. 360–370, Feb. 2008. [15] C. Volmer, J. Weber, R. Stephan, and M. A. Hein, “Mutual coupling in multi-antenna systems: Figures-of-merit and practical verification,” presented at the Eur. Conf. Antennas Propag. (EUCAP2006), Berlin, Germany, Mar. 23–27, 2009. [16] C. Y. Chiu, C. H. Cheng, R. D. Murch, and C. R. Rowell, “Reduction of mutual coupling between closely-packed antenna elements,” IEEE Trans. Antennas Propag., vol. 55, no. 6, pp. 1732–1738, Jun. 2007. [17] Y. Gao, X. Chen, Z. Ying, and C. Parini, “Design and performance investigation of a dual-element PIFA array at 2.5 GHz for MIMO terminal,” IEEE Trans. Antennas Propag., vol. 55, no. 12, pp. 3433–3441, Dec. 2007. [18] A. Diallo, C. Luxey, P. L. Thuc, R. Staraj, and G. Kossiavas, “Enhanced two-antenna structures for universal mobile telecommunications system diversity terminals,” IET Proc. Microw. Antennas Propag., vol. 2, no. 1, pp. 93–101, Feb. 2008. [19] C. Diallo, A. Luxey, R. Le Thuc, P. Staraj, and G. Kossiavas, “Diversity performance of multiantenna systems for UMTS cellular phones in different propagation environments,” Int. J. Antennas Propag., 2008. [20] A. C. K. Mak, C. R. Rowell, and R. D. Murch, “Isolation enhancement between two closely packed antennas,” IEEE Trans. Antennas Propag., vol. 56, no. 11, pp. 3411–3419, Nov. 2008. [21] P. J. Ferrer, J. M. Gonzalez-Arbesu, and J. Romeu, “Decorrelation of two closely spaced antennas with a metamaterial AMC surface,” Microw. Opt. Technol. Lett., vol. 50, no. 5, pp. 1414–1417, May 2008. [22] S. Hong, K. Chung, J. Lee, S. Jung, S. Lee, and J. Choi, “Design of a diversity antenna with stubs for UWB applications,” Microw. Opt. Technol. Lett., vol. 50, no. 5, pp. 1352–1356, May 2008. [23] A. Abe, N. Michishita, Y. Yamada, J. Muramatsu, T. Watanabe, and K. Sato, “Mutual coupling reduction between two dipole antennas with parasitic elements composed of composite right-/left-handed transmission lines,” presented at the Int. Workshop Antenna Technol. (IWAT2009), Santa Monica, CA, Mar. 2009. [24] T. Michalski, V. Wienstroer, and R. Kronberger, “Beam forming capabilities of smart antennas on mobile terminal,” presented at the Eur. Conf. Antennas Propag. (EUCAP2009), Berlin, Germany, Mar. 23–27, 2009. [25] S. Zhang, Z. Ying, J. Xiong, and S. He, “Ultrawideband MIMO/diversity antennas with a tree-like structure to enhance wideband isolation,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 1279–1282, 2009. [26] R. F. Harrington, “Reactively controlled directive arrays,” IEEE Trans. Antennas Propag., vol. 26, no. 3, pp. 390–395, May 1978. [27] R. M. T. Milne, “A small adaptive array antenna for mobile communications,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., Vancouver, Canada, Jun. 17–21, 1985, pp. 797–800. [28] N. L. Scott, M. O. Leonard-Taylor, and R. G. Vaughan, “Diversity gain from a single-port adaptive antenna using switched parasitic elements illustrated with a wire and monopole prototype,” IEEE Trans. Antennas Propag., vol. 47, no. 6, pp. 1066–1070, Jun. 1999. [29] R. Schlub, D. V. Thiel, J. W. Lu, and S. G. O’Keefe, “Dual-band sixelement switched parasitic array for smart antenna cellular communications systems,” Elect. Lett., vol. 36, no. 16, pp. 1342–1343, Aug. 2000. [30] P. Jarmuszewski, Y. Qi, and A. D. Stevenson, “Antenna With NearField Radiation Control,” Canadian patent No. 2, 414, 124 A1, Sep. 12, 2004.

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[31] K. Sato and T. Amano, “Improvements of impedance and radiation performances with a parasitic element for mobile phone,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., San Diego, CA, Jul. 5–11, 2008. [32] H. Nakano, R. Suzuki, and J. Yamauchi, “Low-profile inverted-f antenna with parasitic elements on an infinite ground plane,” IEE Proc. Microw. Antennas Propag., vol. 145, no. 4, pp. 321–325, Aug. 1998. [33] T. H. Tsai, H. T. Peng, and K. Shih, “Built-in Multi-Band Mobile Phone Antenna Assembly With Coplanar Patch Antenna and Loop Antenna,” U.S. Patent Application Pub. No. 2004/0100410 A1, May 27, 2004. [34] G. Johnson and B. Newman, “Single or Dual Band Parasitic Antenna Assembly,” U.S. Patent No. 6, 456, 249 B1, Sep. 24, 2002. [35] K. Q. da Costa, V. A. Dmitriev, and M. N. Kawakatsu, “Enlarging the impedance matching bandwidth of wire and planar antennas using loop parasitic elements,” presented at the Int. Workshop Antenna Technol. (IWAT2009), Santa Monica, CA, Mar. 2009. [36] J. C. Posluszny and R. C. Posluszny, “Parasitically Coupled Folded Dipole Multi-Band Antenna,” U.S. Application Pub. No. 2006/0061515 A1, Mar. 23, 2006. [37] L. Li, Q. Chen, Q. Yuan, K. Sawaya, T. Maruyama, T. Furuno, and S. Uebayashi, “Novel broadband planar reflectarray with parasitic dipoles for wireless communication applications,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 881–885, 2009. [38] J. B. Andersen, J. O. Nielsen, G. F. Pedersen, G. Bauch, and M. Herdin, “Room electromagnetics,” IEEE Antennas Propag. Mag., vol. 49, no. 2, pp. 27–33, Apr. 2007. [39] J. B. Andersen and B. K. Lau, “On closely coupled dipoles in a random field,” IEEE Antennas Wireless Propag. Lett., vol. 5, pp. 73–75, 2006. [40] Y. Fei, Y. Fan, B. K. Lau, and J. S. Thompson, “Optimal single-port matching impedance for capacity maximization in compact MIMO arrays,” IEEE Trans. Antennas Propag., vol. 56, no. 11, pp. 3566–3575, Nov. 2008. [41] M. A. Jensen and B. K. Lau, “Uncoupled matching for active and passive impedances of coupled arrays in MIMO systems,” IEEE Trans. Antennas Propag., vol. 58, no. 10, pp. 3336–3343, Oct. 2010. [42] S. M. Makarov, Antenna and EM Modeling With MATLAB. New York: John Wiley and Sons, 2002. [43] R. Vaughan and J. A. Bach, Channels, Propagation And Antennas for Mobile Communications. London: The IEE, 2003, pp. 511–511. [44] D. M. Pozar, Microwave Engineering, 3rd ed. Hoboken, NJ: Wiley, 2005. [45] S. Blanch, J. Romeu, and I. Corbella, “Exact representation of antenna system diversity performance from input parameter description,” Elect. Lett., vol. 39, no. 9, pp. 705–707, May 2003. [46] J. W. Wallace and M. A. Jensen, “Termination-dependent diversity performance of coupled antennas: Network theory analysis,” IEEE Trans. Antennas Propag., vol. 52, no. 1, pp. 98–105, Jan. 2004. [47] A. Paulraj, R. Nabar, and D. Gore, Introduction to Space-Time Wireless Communications. Cambridge: Cambridge University Press, 2003.

Buon Kiong Lau (S’00–M’03–SM’07) received the B.E. degree (with honors) from the University of Western Australia, Perth, Australia and the Ph.D. degree from Curtin University of Technology, Perth, in 1998 and 2003, respectively, both in electrical engineering. During 2000 to 2001, he worked as a Research Engineer with Ericsson Research, Kista, Sweden. From 2003 to 2004, he was a Guest Research Fellow at the Department of Signal Processing, Blekinge Institute of Technology, Sweden. Since 2004, he has been at the Department of Electrical and Information Technology, Lund University, where he is now an Associate Professor. He has been a Visiting Researcher at the Department of Applied Mathematics, Hong Kong Polytechnic University, China, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, and Takada Laboratory, Tokyo Institute of Technology, Japan. His primary research interests are in various aspects of multiple antenna systems, particularly the interplay between antennas, propagation channels and signal processing. Dr. Lau is an Associate Editor for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION and a Guest Editor of the 2012 Special Issue on MIMO Technology for the same journal. From 2007 to 2010, he was a Co-Chair of Subworking Group 2.2 on “Compact Antenna Systems for Terminals” (CAST) within EU COST Action 2100. Since 2011, he is a Swedish national delegate and the Chair of Subworking Group 1.1 on “Antenna System Aspects” within COST IC1004.

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Jørgen Bach Andersen (M’68–SM’78–F’92– LF’02) received the M.Sc. and Dr.Techn. degrees from the Technical University of Denmark (DTU), Lyngby, Denmark, in 1961 and 1971, respectively. In 2003 he was awarded an honorary degree from Lund University, Sweden. From 1961 to 1973, he was with the Electromagnetics Institute, DTU and since 1973 he has been with Aalborg University, Aalborg, Denmark, where he is now a Professor Emeritus and Consultant. He was head of a research center, Center for Personal Communications, CPK, from 1993–2003. He has been a Visiting Professor in Tucson, Arizona, Christchurch, New Zealand, Vienna, Austria, and Lund,

Sweden. He has published widely on antennas, radio wave propagation, and communications, and has also worked on biological effects of electromagnetic systems. He has coauthored a book, Channels, Propagation and Antennas for Mobile Communications (IEE, 2003). He was on the management committee for COST 231 and 259, a collaborative European program on mobile communications. Professor Andersen is a former Vice President of the International Union of Radio Science (URSI) from which he was awarded the John Howard Dellinger Gold Medal in 2005. He is Associate Editor of Antennas and Wireless Propagation Letters and Co-Editor the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION Special Issue on Multiple-Input Multiple-Output (MIMO) Technology.

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Reducing Mutual Coupling of MIMO Antennas With Parasitic Elements for Mobile Terminals Zhengyi Li, Zhengwei Du, Masaharu Takahashi, Senior Member, IEEE, Kazuyuki Saito, Member, IEEE, and Koichi Ito, Fellow, IEEE

Abstract—Mutual coupling is a critical problem in the design of MIMO antennas because it deteriorates the performance of MIMO systems, which not only affects the antenna efficiency but also influences the correlation. Therefore, in this paper, using parasitic elements to reduce mutual coupling is studied. By adding parasitic elements a double-coupling path is introduced and it can create a reverse coupling to reduce mutual coupling. As an example, a dual-slot-element antenna with parasitic monopoles for mobile terminals is described. The discussion on channel capacity shows that the antenna can be considered as a good candidate for MIMO systems. Furthermore, based on the study of current distributions, it is concluded that the technique is sensitive to relative positions between parasitic elements, and relative positions between active element and parasitic element. Finally, we also extend the technique to a tri-element antenna. Index Terms—Channel capacity, current distribution, MIMO antennas, mutual coupling, parasitic elements.

I. INTRODUCTION

M

ULTIPLE-INPUT MULTIPLE-OUTPUT (MIMO) technology has been proposed for several years, which significantly improves the performance of wireless communication systems [1]–[3]. In these systems, antennas play an important role, since antenna’s features are inherently included in the communication channel between the transmitter and the receiver. Especially, mutual coupling between antenna elements not only affects the antenna efficiency but also influences the correlation. At the base station, low mutual coupling is easy to be realized where element separations are always many wavelengths. However, for mobile terminals, acquiring low mutual coupling will be difficult owing to limited volume. At present, several antenna designs have been proposed to reduce mutual coupling for mobile terminals. In [4]–[6], slot technique was presented to achieve low mutual coupling. The slot technique is explained as a slow wave structure, which Manuscript received May 31, 2010; revised May 27, 2011, September 16, 2011; accepted September 23, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. This work was supported in part by the National Basic Research Program of China under Grant 2009CB320205, in part by the National Natural Science Foundation of China under Grant 60971005, and in part by the Tsinghua-QUALCOMM Associated Research Plan. Z. Li, M. Takahashi, and K. Saito are with the Research Center for Frontier Medical Engineering, Chiba University, Chiba 263-8522, Japan (e-mail: zhy.li. [email protected]; [email protected]; [email protected]. jp). Z. Du is with the State Key Laboratory on Microwave and Digital Communications, Tsinghua National Laboratory for Information Science and Technology, Department of Electronic Engineering, Tsinghua University, Beijing 100084, China (e-mail: [email protected]). K. Ito is with the Graduate School of Engineering, Chiba University, Chiba 263-8522, Japan (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2011.2173432

can decrease the wavelength of the signal and thus increase the separation between antenna elements [4]. Besides, a protruding T-shaped stub in the ground plane was used to improve the mutual coupling between antenna elements [7], [8]. Similarly, a T-shaped and dual-inverted-L-shaped ground branch was added to acquire low mutual coupling [9]–[11]. Then, in [12], the ground branch technique was analyzed, and by adding a ground branch, a dual-element Inverted-F antenna with low mutual coupling was proposed. That study demonstrated that the technique creates an additional coupling path to cancel out the original coupling. In addition, neutralization technique was proposed, which is adding a neutralization line between the feeding strips or the shorting strips of the PIFAs [13]–[15]. As the similar neutralizing principle, lumped circuits or neutralization lines were applied between planar monopoles [16], [17]. Considering all these studies, most of them have a common idea, which is adopting some structure to create reverse coupling to reduce mutual coupling. According to this common idea, we propose using parasitic elements to reduce mutual coupling. Parasitic elements create reverse coupling to reduce mutual coupling. The principle of this technique is introduced in Section II. In Section III, as an implementation, a dual-slot-element antenna with parasitic monopoles is described. Compared to the dual-element Inverted-F antenna in [12] operating at 2.4 GHz WLAN band (2400–2480 MHz), the dual-slot-element antenna is designed for the UMTS band (1920–2170 MHz), which will face the problems of working at lower frequency and wider bandwidth. By using a set of parasitic elements (two parasitic monopoles), its bandwidth can cover the UMTS band with low mutual dB). Since its diversity performance has coupling ( been presented in our previous work [18], in this paper we mainly focus on its MIMO performance by studying channel capacity. Then, in Section IV, in order to deeply understand the technique, the current distributions are validated and studied. Furthermore, we extend the technique to a tri-element antenna in Section V. Finally, in Section VI, some important conclusions are drawn. II. PRINCIPLE OF REDUCING MUTUAL COUPLING A simplified model of reducing mutual coupling is illustrated in Fig. 1. At first, there are two close antenna elements in a mobile terminal as shown in Fig. 1(a). Element 1 is excited by a current of . In the meanwhile, owing to small separation, a is coupled on element 2, in which represents current of coupling coefficient. Then, as given in Fig. 1(b), we add some parasitic elements between the two antenna elements. As a result, there are two coupling paths: one is the original coupling ; the other is the double-coupling path, in which the path

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Fig. 1. Simplified model of reducing mutual coupling: (a) two close antenna elements; (b) two close antenna elements with parasitic elements.

Fig. 2. Geometry of the dual-slot-element antenna with dimensions in mm (top layer in black color and bottom layer in grey color).

current is firstly coupled from element 1 to parasitic elements and secondly coupled from parasitic elements to element 2. It should be noted that the number of parasitic elements is not specified. Therefore, the coupling currents on parasitic elements are given by (1) where N is the number of parasitic elements, and are the corresponding coupling coefficients. Considering the overall performance, an average coupling coefficient is used . Thus, the to represent the coupling coefficients . Beaverage equivalent coupling current is expressed by is coupled cause of the symmetric structure, a current of on element 2 by the double-coupling path. If we change the two coupling coefficients ( and ) by properly designing the antenna configuration, the mutual coupling may be close to zero, which is expressed by (2) It means that parasitic elements can create reverse coupling to reduce mutual coupling. III. DUAL-SLOT-ELEMENT ANTENNA Based on the principle of reducing mutual coupling in Section II, a dual-slot-element antenna with parasitic monopoles is presented in this section. A. Antenna Configuration and Scattering Parameters The antenna is printed on a FR4 substrate board (95 mm 60 mm), which has a thickness of 0.8 mm and a relative permittivity of 4.4. As shown in Fig. 2, the antenna includes two symmetric slot elements, and each slot element is fed by a 50- microstrip

Fig. 3. Simulated scattering parameters (“PM” means parasitic monopoles).

line with one via-grounded end. On the bottom layer of the substrate, the ground plane (75 mm 60 mm) is printed. In order to reduce mutual coupling, two parasitic monopoles are added. The metal strips of the parasitic monopoles were chosen to be of the same width of 1.5 mm as the feeding lines to simplify the design. For each parasitic monopole, one rectangular portion is added at the corner to adjust matching. The length of each slot element is 25.3 mm and the total length of each parasitic monopole from the point “O” to “A” is about 26 mm, both implying a quarter-wavelength mode. The simulated scattering parameters are plotted in Fig. 3, and as a comparison, the simulated performance without the two parasitic monopoles is added in Fig. 3, both of which are simulated by High Frequency Structure Simulator (HFSS) [19]. It is found that by adding the two parasitic monopoles the mutual decreases from coupling is greatly improved, in which dB to dB. Meanwhile, the operation band shifts a little to lower frequency and the bandwidth increases somewhat.

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Fig. 5. Measured radiation patterns in

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plane.

Fig. 4. Measured scattering parameters.

Based on the simulation, a prototype antenna is fabricated. Its measured scattering parameters are shown in Fig. 4. Due to is almost the same as the symmetric structure, the measured , and is thus not plotted in the figure for brevity. From Fig. 4, the two slot elements are well matched in the whole UMTS band dB criterion is (1920–2170 MHz) where the satisfied. In the meanwhile, across the band low mutual coupling dB) is acquired. ( B. Channel Capacity In MIMO systems, usually, channel capacity is adopted to evaluate system performance. When the transmitter does not know the channel conditions, the power is equally divided to each transmit antenna element and the channel capacity is given by (3) is the number of receive antenna elements, is where the number of transmit antenna elements, is the identity matrix, is the average received signal-to-noise ratio is the normalized channel ma(SNR), denotes the conjugate transpose [2]. trix, and are correlated because of propagaIn fact, the entries of tion environment and antenna elements. Therefore, one popular simplified model, the “Kronecker” model, is used to calculate , which separates the correlation into two independent components [20], [21] (4) where is the receive correlation matrix, is the transmit correlation matrix, and is a random matrix with independently deidentical distributed complex Gaussian entries, and notes the matrix square root. The th entry of is calculated by

(5)

where and represent the field patterns of antenna represents incoming wave, deelement and , and notes the conjugate operation, and represents expectation [21]. The mobile wireless environment defined in [22] has a series of reasonable assumptions: the fading envelope being Rayleigh distributed, the incoming wave arriving in horizontal plane only, the incoming wave’s orthogonal polarizations being uncorrelated, the individual polarizations being spatially uncorrelated, and finally the time-averaged power density per steradian being constant. Based on these approximations and the derivation in can be written as Appendix A,

(6) where is the cross-polarization discrimination (XPD) of the incoming wave. In this paper, is assumed to be 0 dB, which is the average value in an urban fading environment [22], [23]. Therefore, we can calculate the channel capacity and its cumulative distribution function (CDF) by using the measured radiation plane, which are shown in Fig. 5. These radiapatterns in tion patterns were measured at 2.1 GHz in an anechoic chamber with one port excited and the other terminated to a 50- load. As in Table I, four kinds of system parameters are studied, “2 2 MIMO a”, “2 2 MIMO b”, “2 2 MIMO c”, and SISO is uncor(single-input single-output). In “2 2 MIMO a”, and are equal to identity matrix. In related, and thus, “2 2 MIMO b”, the dual-slot-element antenna is equipped is equal to . In both in the transmitter and receiver so “2 2 MIMO c”, the dual-slot-element antenna is also equipped both in the transmitter and receiver but the correlated matrix is calculated only with the magnitude of radiation patterns (assuming a constant phase over all angles for both antenna elements). Fig. 6 shows the CDFs of channel capacity in the four conditions. Based on the results, firstly, it is found that the MIMO performance with the dual-slot-element antenna is promising since the CDF curve is very close to the uncorrelated one. Secondly, relatively large distance between the

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Fig. 6. CDFs of channel capacity in the four conditions (“2

2 MIMO a”, “2

2 MIMO b”, “2

2 MIMO c”, and SISO).

TABLE I FOUR KINDS OF SYSTEM PARAMETERS

Fig. 7. Channel capacities in Bluetest Reverberation chamber (“3 a”, “3 2 MIMO b”, and “3 1 MISO”).

CDF curves of “2 2 MIMO b” and “2 2 MIMO c” means that the decorrelation of phases contributes more to system performance compared to that of magnitude, which is similar to the conclusion in [24]. Thirdly, even if we remove the effect of phases and only adopt the magnitude of radiation patterns, the system performance is still much better than that of SISO. Besides, we also evaluated the antenna in Bluetest Reverberation chamber [25]. In the chamber, three perpendicular antenna elements are equipped in the transmitter to generate isotropic environment, and the dual-slot-element antenna is equipped in the receiver. Therefore, a 3 2 MIMO system was setup. Fig. 7 shows the average channel capacities (marked as “3 2 MIMO b”), in which 2100 channel realizations were measured (100 stirrer positions 21 frequency points centered at 2.1 GHz). As a comparison, two other systems’ channel capacities are also plotted: “3 2 MIMO a” ( is uncorrelated) and “3 1 MISO”. It is found that the channel capacity of “3 2 MIMO

2 MIMO

b” is much higher than that of “3 1 MISO” though it is a little lower than that of uncorrelated channel (“3 2 MIMO a”). In addition, the average radiation efficiency was also measured in Bluetest Reverberation chamber, which is 80% and 77% for element 1 and element 2, respectively. According to the calculated channel capacity by using radiation patterns and measured channel capacity in Bluetest Reverberation chamber, our antenna can be considered as a good candidate for MIMO systems. IV. CURRENT DISTRIBUTION VALIDATION AND STUDY In Sections II and III, we adopted parasitic elements to reduce mutual coupling and implemented the technique in a dual-slotelement antenna. Therefore, in order to further understand the technique, the current distributions are validated and studied. A. Current Magnitude Distributions The performance of reducing mutual coupling can also be validated with surface current magnitude distributions. Fig. 8(a)

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as in Fig. 11, based on the definition of scattering parameters, can be expressed the source current and coupling current by (7) (8) where represents characteristic impedance and is equal to 50- in general. Thus, the coupling coefficient is given by (9) If we check the current distribution on dipole 1, it is the sum of the source current and the reflected current, which is (10) Fig. 8. The current magnitude distributions on the dual-slot-element antenna (a) with the two parasitic monopoles and (b) without the two parasitic monopoles (light color means large current density).

Within antenna’s operation band, is relatively small, so (7) is close to (10) and a approximate value of (the coupling coefficient between current distributions on dipole 2 and dipole 1) is given by (11)

Fig. 9. The current vector distributions on the dual-slot-element antenna without the two parasitic monopoles.

shows the current magnitude distributions at 2.1 GHz, in which slot element 1 (the left slot element) is excited and slot element 2 (the right slot element) is terminated to a 50- load. As a comparison, the current magnitude distributions without the two parasitic monopoles are plotted in Fig. 8(b). From the figure, it can be observed that the current distributions on the slot element 2 decrease dramatically by adding the two parasitic monopoles. B. Current Vector Distributions Firstly, the surface current vector distributions on the dualslot-element antenna without the two parasitic monopoles at 2.1 GHz are shown in Fig. 9, in which slot element 1 is excited and slot element 2 is terminated to a 50- load. From the current on slot eldistributions, it is found that the coupling current ement 2 is out-of-phase with on slot element 1 (the current on the right edge of slot element 1 is out-of-phase with the current on the right edge of slot element 2). However, the currents on two antenna elements will not always satisfy the out-of-phase condition, when we change the distance between the two antenna elements. As a simplified example, the coupling coefficient of two halfwavelength dipoles is examined. It is found that the currents on the two dipoles are in-phase in some separations while out-ofphase in other separations, which is illustrated in Fig. 10. In fact,

The calculated magnitude and phase of coupling coefficient by using (9) and (11) are plotted in Fig. 12. When the distance between the two dipoles increases (within half-wavelength) the magnitude of coupling coefficient would decrease sharply to below 0.2. Beyond half-wavelength, the magnitude changes very little. For the phase, the change is near linear, including the in-phase (zero degree) and out-of-phase (180 degree and degree). It should be noted that, the coupling coefficient depends on antenna type, radiation patterns, and polarization, though the trend of it is similar. For example, for the dual-slot-element antenna without parasitic monopoles in Fig. 9, by using (11), the magnitude and phase of are 0.41 and 43 degree, respectively. They are so different from the results of two half-wavelength dipoles in Fig. 12. With the same magnitude the distance should be about 0.2 wavelength, while it should be about 0.6 wavelength with the same phase. Secondly, the surface current vector distributions on the dual-slot-element antenna with the two parasitic monopoles at 2.1 GHz are illustrated in Fig. 13. By adding the two parasitic monopoles, there are two coupling paths. One is the original is coupled on slot element 2 coupling path, by which (black solid line with arrow). The other is double-coupling path, in which the current is firstly coupled from slot element 1 to parasitic monopoles (white solid line with arrow), and secondly coupled from parasitic monopoles to slot element is generated on slot element 2 (black 2, and as a result dotted line with arrow). It is found that the current on the left parasitic monopole is in-phase with the current on the right edge of slot element 1, and the current on the right parasitic monopole is out-of-phase with the current on the left parasitic monopole. Therefore, on slot element 2, the double-coupling will be approximately 180 degree out-of-phase current , leading to low mutual with the original coupling current coupling. It should be noted that if we change the distance between the parasitic monopoles or the distance between one

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Fig. 10. Illustration of currents on two half-wavelength dipoles.

Fig. 11. Definition of scattering parameters.

Fig. 12. Calculated (a) magnitude and (b) phase of coupling coefficient two half-wavelength dipoles.

on

slot element and one parasitic monopole these phase relationships will change, which is similar to the discussion about two half-wavelength dipoles. Thus, the performance of reducing mutual coupling will change. For example, we change the two parasitic monopoles’ horizontal positions defined by parameter with no other parameters changing, as in Fig. 14. The simulated mutual couplings with different values of parameter are given in Fig. 14. When the value of parameter is chosen to be 3 mm the performance of reducing mutual coupling degrades by about 5–8 dB, compared to that of our antenna ( is equal to 27 mm). Consequently, this technique, using parasitic elements to reduce mutual coupling, is sensitive to relative positions between parasitic elements, and relative positions between active element and parasitic element.

Fig. 13. The current vector distributions on the dual-slot-element antenna with the two parasitic monopoles. (At first, the current vector distributions were generated by the simulator. Then, we focused on the part of slot elements and parasitic monopoles, and simplified the distributions to get a better illustration. However, the current is very small on the right slot element since the mutual coupling is greatly reduced. Therefore, two kinds of coupling current, the original coupling and the coupling due to parasitic monopoles, are used to replace the sum of them.).

V. TRI-ELEMENT ANTENNA In this section, we extend the proposed technique to a trielement antenna operating at 1.9 GHz. The antenna is printed on a FR4 substrate board (100 mm 112 mm), which has a thickness of 0.8 mm and a relative

permittivity of 4.4. As shown in Fig. 15, the antenna consists of three slot elements, and each slot element is fed by a 50- microstrip line with one via-grounded end. On the bottom layer of the substrate, the ground plane (75 mm 112 mm) is printed. In

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Fig. 14. Simulated mutual couplings with different values of parameter .

Fig. 16. Simulated scattering parameters: (a) with PM; (b) without PM (“PM” means parasitic monopoles).

plane. Secondly, the freedom of designing parasitic monopoles 2 and 3 is limited since they are too close to each other. The simulated scattering parameters are plotted in Fig. 16, and as a comparison, the simulated performance without the four parasitic monopoles is also plotted in Fig. 16. Here, is almost the same as , and is almost the same as , so they are not plotted in the figure for brevity. From the figure, it is found that by adding the four parasitic monopoles the mutual and both decouplings are greatly improved, in which creases from dB to dB. Fig. 15. Geometry of the tri-element antenna with dimensions in mm (top layer in black color and bottom layer in grey color).

order to reduce mutual coupling, four parasitic monopoles are added. However, compared to the dual-slot-element antenna, there are some differences in designing the tri-element antenna. Firstly, the length of slot element 2 is different from that of elements 1 and 3 because of different locations in the ground

VI. CONCLUSION Mutual coupling is a critical problem in the design of MIMO antennas. At the base station, low mutual coupling is easy to be realized where element separations are always many wavelengths. However, for mobile terminals, acquiring low mutual coupling will be difficult owing to limited volume. Therefore, in this paper, using parasitic elements to reduce mutual coupling is

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studied. Its principle is that by a double-coupling path parasitic elements create reverse coupling to reduce mutual coupling. As an example, a dual-slot-element antenna with parasitic monopoles for mobile terminals is described. The discussion on calculated and measured channel capacity shows that the antenna can be considered as a good candidate for MIMO systems. In addition, we also extend the technique to a tri-element antenna. More importantly, by studying the current distributions, it is found that the technique is sensitive to phase relationships, which are related to relative positions between parasitic elements, and relative positions between active element and parasitic element.

where is a constant related to the time-averaged power density. It should be noted that normalization is operated in (5). Thus, we can set to unity and acquire (6). ACKNOWLEDGMENT The authors would like to thank S. Etoh, and N. Kitamoto of TOYO Corporation, Tokyo, Japan, for providing Bluetest Reverberation chamber and helping to measure channel capacity. They would also like to thank Z. Feng of Tsinghua University, Beijing, China, for suggestions and valuable discussions and the reviewers whose comments and suggestions helped to significantly improve the paper.

APPENDIX In this Appendix, we derive from (5) to (6) under the assumption of mobile wireless environment defined in [22].

(5) Because of (A1) (A2) we can get

(A3) Since the incoming wave’s orthogonal polarizations are uncorrelated, the expectation of orthogonal polarizations’ product is equal to zero and (A3) is simplified to

(A4) In addition, because the expectation is in terms of incoming wave, (A4) is derived to

(A5) In fact, and is the time-averaged power density of incoming wave’s and components, and [26]. Furthermore, XPD is defined by the incoming wave arrives in horizontal plane only and the timeaveraged power density per steradian is constant so (A5) is simplified to

(A6)

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[20] J. P. Kermoal, L. Schumacher, K. I. Pedersen, P. E. Mogensen, and F. Frederiksen, “A stochastic MIMO radio channel model with experimental validation,” IEEE J. Sel. Areas Commun., vol. 20, no. , pp. 1211–1226, Aug. 2002. [21] L. Dong, H. Choo, R. Heath, Jr., and H. Ling, “Simulation of MIMO channel capacity with antenna polarization diversity,” IEEE Trans. Wireless Commun., vol. 4, no. 4, pp. 1869–1873, Jul. 2005. [22] S. C. K. Ko and R. D. Murch, “Compact integrated diversity antenna for wireless communications,” IEEE Trans. Antennas Propag., vol. 49, no. 6, pp. 954–960, Jun. 2001. [23] M. A. Jensen and Y. Rahmat-Samii, “Performance analysis of antennas for hand-held transceivers using FDTD,” IEEE Trans. Antennas Propagat., vol. 42, no. 8, pp. 1106–1113, Aug. 1994. [24] V. Plicanic, B. K. Lau, A. Derneryd, and Z. Ying, “Actual diversity performance of a multiband diversity antenna with hand and head effects,” IEEE Trans. Antennas Propag., vol. 57, no. 5, pp. 1547–1556, May 2009. [25] P.-S. Kildal and K. Rosengren, “Correlation and capacity of MIMO systems and mutual coupling, radiation efficiency, and diversity gain of their antennas: Simulations and measurements in a reverberation chamber,” IEEE Commun. Mag., vol. 42, pp. 104–112, Dec. 2004. [26] R. G. Vaughan and J. B. Andersen, “Antenna diversity in mobile communications,” IEEE Trans. Veh. Technol., vol. 36, no. 4, pp. 149–172, Nov. 1987.

Zhengyi Li was born in Xi’an, China, in February 1982. He received the B.E. degree in information engineering from Xi’an Jiaotong University, Xi’an, China, in 2004, and the Ph.D. degree in electronic engineering from Tsinghua University, Beijing, China, in 2010. Since 2010, he has been working as Postdoctoral Researcher at Research Center for Frontier Medical Engineering, Chiba University, Chiba, Japan. His research interests include small antennas for body-centric wireless communications, MIMO antennas, and reconfigurable antennas. Dr. Li was the recipient of the 2010 Asia-Pacific Radio Science Conference (AP-RASC’10) Young Scientist Award in 2010.

Zhengwei Du was born in Sichuan Province, China, on August 21, 1971. He received the B.Sc., M.Sc., and Ph.D. degrees in engineering from the University of Electronic Science and Technology of China, Chengdu, China, in 1992, 1995, and 1998, respectively. Since 1998, he has been with Tsinghua University, Beijing, China, as a Postdoctoral Fellow (February 1998–October 1999), Research Assistant (November 1999–July 2000), Associate Professor (August 2000–December 2006), and currently, Full Professor. His main research interests include ultra wideband/short pulse electromagnetic, antenna, propagation, analysis of microwave/millimeter wave planar structures, photonic bandgap (electromagnetic bandgap) circuits, and electromagnetic compatibility/electromagnetic interference (EMC/EMI). Prof. Du is Chairman of the Microwave Integrated Circuits and Mobile Communications Professional Committee of the Microwave Society of China.

Masaharu Takahashi (M’95-SM’02) was born in Chiba, Japan, in December 1965. He received the B.E. degree in electrical engineering from Tohoku University, Miyagi, Japan, in 1989, and the M.E. and D.E. degrees in electrical engineering from the Tokyo Institute of Technology, Tokyo, Japan, in 1991 and 1994, respectively. From 1994 to 1996, he was a Research Associate, and from 1996 to 2000, an Assistant Professor with the Musashi Institute of Technology, Tokyo, Japan. From 2000 to 2004, he was an Associate Professor with the Tokyo University of Agriculture and Technology, Tokyo, Japan. He is currently an Associate Professor with the Research Center for Frontier Medical

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Engineering, Chiba University, Chiba, Japan. His main interests are electrically small antennas, planar array antennas, and EM compatibility. Dr. Takahashi is a Senior Member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan. He was the recipient of the 1994 IEEE Antennas and Propagation Society (IEEE AP-S) Tokyo Chapter Young Engineer Award.

Kazuyuki Saito (S’99-M’01) was born in Nagano, Japan, in May 1973. He received the B.E., M.E., and D.E. degrees in electronic engineering from Chiba University, Chiba, Japan, in 1996, 1998 and 2001, respectively. He is currently an Associate Professor with the Research Center for Frontier Medical Engineering, Chiba University. His main interest is in the area of medical applications of microwaves including microwave hyperthermia. Dr. Saito is a member of the Institute of Electrical, Information and Communication Engineers (IEICE), Japan, the Institute of Image Information and Television Engineers of Japan (ITE), and the Japanese Society for Thermal Medicine. He was the recipient of the IEICE Antennas and Propagation Society (AP-S) Freshman Award, the Award for Young Scientist of the URSI General Assembly, the IEEE AP-S Japan Chapter Young Engineer Award, the Young Researchers’ Award of the IEICE, and the International Symposium on Antennas and Propagation (ISAP) Paper Award in 1997, 1999, 2000, 2004, and 2005 respectively.

Koichi Ito (M’81-SM’02-F’05) received the B.S. and M.S. degrees from Chiba University, Chiba, Japan, in 1974 and 1976, respectively, and the D.E. degree from the Tokyo Institute of Technology, Tokyo, Japan, in 1985, all in electrical engineering. From 1976 to 1979, he was a Research Associate at the Tokyo Institute of Technology. From 1979 to 1989, he was a Research Associate at Chiba University. From 1989 to 1997, he was an Associate Professor at the Department of Electrical and Electronics Engineering, Chiba University, and is currently a Professor at the Department of Medical System Engineering, Chiba University. From 2005 to 2009, he was Deputy Vice-President for Research, Chiba University. From 2008 to 2009, he was Vice-Dean of the Graduate School of Engineering, Chiba University. Since April 2009, he has been appointed as Director of Research Center for Frontier Medical Engineering, Chiba University. In 1989, 1994, and 1998, he visited the University of Rennes I, France, as an Invited Professor. He has been appointed as Adjunct Professor to the University of Indonesia since 2010. His main research interests include analysis and design of printed antennas and small antennas for mobile communications, research on evaluation of the interaction between electromagnetic fields and the human body by use of numerical and experimental phantoms, microwave antennas for medical applications such as cancer treatment, and antennas for body-centric wireless communications. Dr. Ito is a Fellow of the Institute of Electronics, Information and Communication Engineers (IEICE) of Japan, a member of the American Association for the Advancement of Science, the Bioelectromagnetics Society (BEMS), the Institute of Image Information and Television Engineers of Japan (ITE) and the Japanese Society for Thermal Medicine. He served as Chair of the Technical Group on Radio and Optical Transmissions, ITE from 1997 to 2001, Chair of the Technical Committee on Human Phantoms for Electromagnetics, IEICE from 1998 to 2006, Chair of the Technical Committee on Antennas and Propagation, IEICE from 2009 to 2011, Chair of the IEEE AP-S Japan Chapter from 2001 to 2002, TPC Co-Chair of the 2006 IEEE International Workshop on Antenna Technology (iWAT2006), Vice-Chair of the 2007 International Symposium on Antennas and Propagation (ISAP2007), General Chair of iWAT2008, Co-Chair of ISAP2008, an AdCom member for the IEEE AP-S from 2007 to 2009, and an Associate Editor for the IEEE Transactions on Antennas and Propagation from 2004 to 2010. He currently serves as a Distinguished Lecturer for the IEEE AP-S, Chair of the IEEE AP-S Committee on Man and Radiation (COMAR), a member of the Board of Directors, BEMS and a Councilor to the Asian Society of Hyperthermic Oncology (ASHO). He has been appointed as General Chair of ISAP2012 to be held in Nagoya, Japan, and as a member the IEEE Life Sciences New Initiative (LSNI) Project Team.

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A Compact Wideband MIMO Antenna With Two Novel Bent Slits Jian-Feng Li, Qing-Xin Chu, Senior Member, IEEE, and Tian-Gui Huang

Abstract—A compact wideband multiple-input- multiple-output (MIMO) antenna is presented. The MIMO antenna consists of two symmetric monopoles with edge-to-edge separation of nearly at 2.5 GHz. Two novel bent slits are etched into the ground plane. At the lower frequencies, the bent slits can reduce the mutual coupling and have slight effect on the reflection coefficient. At the higher frequencies, the slits can be considered as slit antennas to widen the impedance bandwidth because the two slits are coupled fed by two 50- microstrip lines, respectively. Two triangles are cut from the ground plane. In this way, the reflection coefficient and isolation of the two slit antennas can be improved. A bandwidth of 92.7% with 10 dB and 18 dB from 2.4 to 6.55 GHz is achieved. In order to provide quantifications for the performance of the MIMO antenna in real-world usage conditions, the effects of human hand and head on the performance of the MIMO antenna are investigated. The results show that the MIMO antenna serving as a phone antenna can provide spatial and pattern diversity to combat multipath fading. Index Terms—Correlation coefficient, diversity antenna, diversity gain, multiple-input multiple-output (MIMO) antenna, phone antenna, total radiation power, wideband antenna.

I. INTRODUCTION

N

OWADAYS, there is a demand to increase the data rate of existing wireless communication systems. The application of diversity techniques, most commonly assuming two antennas in a mobile terminal, can enhance the data rate and reliability without sacrificing additional spectrum or transmitted power in rich scattering environments [1], [2]. When a multiple-input multiple-output (MIMO) antenna is applied in a multifunctional portable device, wideband and high isolation are demanded. However, the design of a compact wideband MIMO antenna with high isolation is an open issue. Various techniques have been reported to enhance isolation between the elements of a MIMO antenna. High isolation was achieved by etching slits into the ground plane [3]. Ground branches were applied in [4] to achieved low mutual coupling within a narrow frequency band. Parasitic elements were added to improve the port isolation of a MIMO antenna [5]. Since the Manuscript received April 25, 2011; revised June 23, 2011; accepted July 16, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. This work was supported by the Science Fund of China (60971052) and “the Fundamental Research Funds for the Central Universities (2009IM0167)”. The authors are with the School of Electronic and Information Engineering, South China University of Technology, Guangzhou, Guangdong 510640, China (e-mail: [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TAP.2011.2173452

implementation of additional parasitic elements occupies a significant space, this technique is not attractive for handset devices. All of the aforementioned techniques deteriorate the reflection coefficient, and therefore a wide impedance bandwidth with high isolation is difficult to obtain. A compact wideband MIMO antenna with high isolation is presented in this paper. The MIMO antenna consists of two dual-branch monopoles with edge-to-edge separation of nearly at 2.5 GHz, and the size of the monopole is 18 15 mm . Traditionally, slits were mainly used to reduce mutual coupling of element antennas, but this approach usually deteriorate the reflection coefficient. In this design, two novel bent slits are applied, which can avoid this problem. At the lower frequencies, they can reduce the mutual coupling resulted from surface currents and have slight effect on the reflection coefficient. At the higher frequencies, the two bent slits can be considered as two slit antennas because they are coupled fed by two 50microstrip lines, respectively, and they excide resonant modes at 6.3 GHz to widen the impedance bandwidth. Two triangles are cut from the ground plane to change the distribution of the ground surface currents, and therefore the reflection coefficient and isolation of the two slit antennas are improved. Moreover, a metal strip located between the two monopoles is used to decrease the mutual coupling caused by near-field. Thus, the mutual coupling between the two monopoles is further reduced. A bandwidth of 92.7% with 10 dB and 18 dB from 2.4 to 6.55 GHz is achieved, which covers 2.4/5.2/5.8-GHz WLAN, 2.5/3.5/5.5-GHz WiMAX and the lower UWB band (3.1–4.8 GHz) operation. The radiation pattern, mean effective gain (MEG), radiation efficiency, correlation coefficient and diversity gain (DG) are calculated to evaluate the diversity performance of the proposed MIMO antenna. To provide quantifications for the performance of the MIMO antenna in real-world usage conditions, the effects of human hand and head on the antenna performance including radiation efficiency, mismatch efficiency, total radiation power (TRP) and radiation pattern, are discussed. The geometry of the proposed MIMO antenna is shown in Section II. In Section III, the working mechanism of the MIMO antenna is investigated. In Section IV, the MEG, radiation efficiency, correlation coefficient and DG are calculated. The effects of human hand and head on the performance of the MIMO antenna are discussed in Section V. Finally, a conclusion is given in Section VI. II. CONFIGURATION OF THE PROPOSED MIMO ANTENNA The geometry of the proposed MIMO antenna is illustrated in Fig. 1. The MIMO antenna consists of two symmetric dual30 mm and branch 2 branch (branch 1 with length of

0018-926X/$26.00 © 2011 IEEE

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Fig. 2. Measured and simulated S-parameters of the proposed MIMO antenna.

Fig. 1. Structure of the proposed MIMO antenna.

with length of 28 mm) monopoles. The MIMO antenna is printed on the upper part of a partially grounded FR4 substrate with dimensions 78 40 1.6 mm and relative permittivity 4.4. On the back surface of the substrate, the main rectangular ground plane of 40 mm in width and 60 mm in length is printed. In order to reduce the mutual coupling caused by the surface currents and improve the impedance matching, two bent slits with a length of 22 mm (about at 6.3 GHz) are etched into the ground plane. Moreover, each slit is coupled fed by a 50 microstrip line, and consequently the slits can be considered as slit antennas. To reduce the effect of the slits on the lower part of the impedance bandwidth, the slits are bent by 90 ; to suppress the mutual coupling between the two slit antennas, they are set perpendicular to each other. Two triangles with height 3 mm and width 4 mm are cut from the ground plane to change the distribution of the ground surface currents. A metal strip of size 18 1 mm , which is placed between the two monopoles, is applied to decrease the mutual coupling caused by near-field. III. DISCUSSION OF WORKING MECHANISM The proposed MIMO antenna shown in Fig. 1 has been fabricated and tested. In Fig. 2, it can be seen that the simulated and measured results are in a good agreement. The results show a bandwidth of 92.7% with 10 dB and 18 dB from 2.4 to 6.55 GHz covering the following bands: 2.4/5.2/5.8-GHz WLAN, 2.5/3.5/5.5-GHz WiMAX and the lower UWB band (3.1–4.8 GHz) operation. A. Dual-Branch Monopole Antenna Investigation of the dual-branch monopole antenna shown in Fig. 3 can help to understand the working mechanism of the proposed MIMO antenna. The antenna presented in [6] had a similar structure (see Fig. 3), but it is not suitable for wideband application because the frequency interval between the two resonant modes is large. In Fig. 3, the length of branch 1 is 28 mm (shorter than at 2.6 GHz), the length of branch 2 is 26 mm (shorter than at 3.0 GHz), and the two

Fig. 3. Configuration of the two-branch monopole antenna.

branches can produce a resonant mode at 2.6 GHz and a resonant mode at 3.0 GHz, respectively. The inductive reactance of the dual-branch monopole antenna is compensated by the coupling capacitance introduced by the small gap between the monopole and the ground plane, and the electrical lengths of the two branches are extended. Fig. 4 shows the simulated reflection coefficients of the dualbranch monopole antenna and two cases with branch 1 only or branch 2 only. The case only with branch 1 generates a resonant mode at about 2.6 GHz, and a dual-resonance excitation at about 5.5 GHz; the case only with branch 2 generates a dual-resonance excitation at about 3.0 GHz and a resonant mode at about 5.8 GHz. When the two branches are integrated together, a wide operating band of 89% with 10 dB extending from 2.4 to 6.25 GHz is produced. The dualbranch monopole antenna with wideband and compact size is suitable to be an element of a compact wideband MIMO antenna. B. Implementation of Novel Bent Slits To analyze the working mechanism of the two novel bent slits described in Section II, two more configurations will be investigated in this section. They are: 1) MIMO monopole antenna with a conventional rectangular ground plane and 2) MIMO monopole antenna with two bent slits etched into a conventional rectangular ground plane. The S-parameters for the two configurations are given in Fig. 5. It can be observed that the reflection coefficient of the dual-branch monopole antenna (see Fig. 3) is better than that

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Fig. 6. Average current distribution of the MIMO antenna with a conventional rectangular ground plane at 4.5 GHz. Fig. 4. Simulated reflect coefficients of the two-branch monopole antenna and the two cases with branch 1 only or branch 2 only.

Fig. 5. Simulated S-parameters of MIMO antennas with different configurations of ground plane.

of the MIMO monopole antenna with a conventional rectangular ground plane. Strong near-field coupling and surface current coupling are induced when the two elements are placed closely. Fig. 6 shows the current distribution at 4.5 GHz (the central frequency of the operation bandwidth) of the MIMO monopole antenna with a conventional rectangular ground plane (monopole 1 is excited, while monopole 2 is terminated with a 50 load). There are strong coupled currents observed on the monopole 2 and the upper part of the ground plane. We can believe that the strong coupled current is one reason of the poor reflection coefficient and low isolation of the MIMO monopole antenna with a conventional rectangular ground plane. In order to improve the reflection coefficient and the isolation, two bent slits are applied as shown in Fig. 7. As can be observed in Fig. 5, the antenna with the two bent slits has better reflection coefficient and higher isolation than the MIMO antenna with a conventional ground plane. Thus, it can be concluded that the bent slits improve the reflection coefficient and also enhance the isolation effectively. In [3], slits were already used to improve isolation, although these slits had negative effect on the impedance matching, and a wide impedance bandwidth was difficult to obtain. However, the two novel bent slits applied in this paper can avoid this problem. The slits are bent forming a 90 corner, and which can help to reduce the side effect that the slits have on the current distribution at the lower part of the impedance bandwidth. Thus, a small discrepancy of the lower part of the impedance bandwidth can be seen between the two-branch monopole antenna (see Fig. 4) and the MIMO antenna with the two bent slits (see

Fig. 7. Average current distributions of the MIMO antenna with two bent slits etched into a conventional rectangular ground plane: (a) at 4.5 GHz and (b) 6.3 GHz.

Fig. 5). When comparing with Fig. 6, a large portion of the surface currents presented in Fig. 7(a) is being trapped by the bent slit located on the left-hand side of the ground plane. It demonstrates that currents flowing from left-hand side of the ground plane to right-hand side are substantially reduced. Therefore, the mutual coupling cased by the ground surface currents is reduced. Moreover, the two slits can help to widen the impedance bandwidth because they are coupled fed by the two 50- microstrip lines, respectively. Each bent slit is 22 mm in length (about at 6.3 GHz), and resonant mode at about 6.3 GHz, which does not appear in the cases without the two slits (see Figs. 4 and 5), is excided by the two bent slits. The current distribution in Fig. 7 also provides evident that the resonant mode at 6.3 GHz (see Fig. 5) is excided by the bent slits. These currents are mainly distributed along the slit located on the left-hand side of the ground plane. Moreover, the two slits are set perpendicular to each other to suppress the mutual coupling between them. C. Discussion of Metal Strip and Cutting of Triangles There is strong near-field coupling besides the ground surface currents coupling. In order to reduce the near-field coupling, the metal strip shown in Fig. 1 is used. The proposed MIMO antenna depicted in Fig. 1 provides an 8 dB improvement of isolation over the case with two bent slits etched into a conventional rectangular ground plane (see Fig. 5). The metal strip can be treated as a reflector of electromagnetic wave [7]. The reflector separates the radiation patterns of the two monopoles to decrease the unwanted mutual coupling resulted from the near-field, thus the isolation is further enhanced, especially for the frequencies near 6.3 GHz. From Figs. 2 and 5, it can also

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Fig. 9. Prototype of the proposed MIMO antenna: (a) front view and (b) back view.

Fig. 8. Effects of .

and

on the proposed MIMO antenna: (a)

and (b)

be observed that the effect of the metal strip on the frequency response of the reflection coefficient is small. The cutting of two triangles of size from the ground plane is to change the distribution of ground surface currents. The effects of and on the reflection coefficient and the mutual coupling are studied in Fig. 8(a) and (b), respectively. For the frequencies near 6.3 GHz, the reflection coefficient and the mutual coupling vary greatly with varying and . When and are chosen as 3 and 4 mm, respectively, good impedance matching and isolation for the proposed MIMO antenna can be obtained as shown in Fig. 2. IV. DIVERSITY PERFORMANCE OF THE MIMO ANTENNA The diversity performance of the proposed MIMO antenna is evaluated by the MEG, radiation efficiency, correlation coefficient, and DG. DG is defined as the improvement in signal-tonoise (SNR) ratio from the combined signal from all the antennas of the diversity system relative to the SNR from a single antenna [8]. The photos of the fabricated MIMO antenna are shown in Fig. 9. Fig. 10 displays the simulated and measured 2-D radiation patterns of the two monopoles (the tested monopole is excited, while the other one is terminated with a 50- load) at 4.5 GHz, and the gains have been normalized. The discrepancy between the measured and simulated results comes principally from our measurement setup, especially from the power loss contribution of the feeding cables of the monopoles. In small antenna measurements, it is usually difficult to efficiently choke the feeding cables to avoid currents flowing on their outer part. Moreover, these cables are very difficult to maintain perfectly

Fig. 10. Simulated and simulated radiation patterns on (a) XY-plane and (b) YZ-plane.

parallel to the length of the PCB due to the size and the proximity of the ferrite chokes. Back-radiation patterns for the two monopoles are achieved, and these special patterns can help to reduce the mutual coupling caused by near-field. Thus, the proposed MIMO monopole antenna shows good pattern diversity characteristic. To quantify the average received signal strength for each monopole, MEGs are calculated based on a series of the assumptions for mobile wireless environments defined in [4], [9]. In this paper, a cross-polarization discrimination of 0 dB, which is the average in an indoor fading environment [9], [10], is assumed. The MEGs and the ratios of to at the center frequencies of 2.4/5.2/5.8-GHz WLAN, 2.5/3.5/5.5-GHz WiMAX and the lower UWB band (3.1–4.8 GHz) are calculated [4], [11], [12]. The MEGs, ratios of to , radiation efficiencies , mismatch

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TABLE I PERFORMANCE OF THE PROTOTYPE OF THE PROPOSED MIMO ANTENNA

TABLE II SIMULATED EFFECT OF THE HAND AND HEAD ON THE PROPOSED MIMO ANTENNA

diation patterns [4], [10], [16] and are denoted as respectively:

and

,

(2) where

Fig. 11. Configuration of (a) MIMO antenna tenna hand phantom SAM head.

hand phantom, (b) MIMO an-

efficiencies and total efficiencies , which are obtained from the measured data, are listed in Table I. The maximum ratio of the to is smaller than 0.4 dB, and , and are higher than 50% and 46%, respectively. For isotropic/uniform signal propagation environments, the correlation coefficient and envelope correlation coefficient can be derived from the S-parameters [13], and they are denoted as and , respectively. Based on the conclusion in [14], and can be calculated by

(1) on . The expression contains the effect of For the Gaussian signal propagation environments: and are the and components of the probability distribution function of the incoming wave, respectively, and being Gaussian distributed, and and being uniform distributed. Thus, and can be evaluated from the ra-

(3) in which and are the and components of the complex electric field radiation pattern, respectively, and the asterisk presents the complex conjugate. Based on the measured data, for the two kinds of propagation environments are calculated and listed in Table I. It can be seen that is smaller than 0.01 for the both cases. In an ideal case (the efficiency of the two-element antenna is 100%, and the power levels of the signals received by the two antennas are the same in the diversity system), DG using a selection combiner is 10 dB, where the radio link reliability is 99% [15]. In order to achieve the diversity gain as high as the ideal case, the received signals from the two elements should exhibit poor correlation and the discrepancy of the power levels of the signals received by the two elements should be minimized [15]. A good DG can be achieved with the proposed antenna, because the signals received from the proposed MIMO antenna satisfy the criteria [4], [10], and [16] and

dB

(4)

and power unbalance of the two antenna The effects of elements on DG should be taking into account. Findings in [15], [17] show that the degradation of DG due to is given by a factor defined as (5)

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Fig. 12. Simulated (SEMCAD) 3-D radiation patterns for: (a) MIMO antenna hand phantom with monopole 1 excided and monopole 2 terminated with a standard 50- matching load; (b) MIMO antenna hand phantom with monopole 2 excided and monopole1 terminated with a standard 50- matching load; (c) MIMO antenna hand phantom SAM head with monopole 1 excided and monopole 2 terminated with a standard 50- matching load; (d) MIMO antenna hand phantom SAM head with monopole 2 excided and monopole 1 terminated with a standard 50- matching load.

The ratio of to of the antenna elements (assuming only two elements) [15] is used to illustrate the side effect of power unbalance of the signals on the DG (6) Based on the discussion above, DGs of the proposed MIMO antenna are calculated by the formula (7) where is the diversity gain of the antenna in the ideal case. The calculated DGs, which are based on the measured data, are presented in Table I. V. EFFECTS OF HAND AND HEAD With the aid of the simulation software SEMCAD-X [18], the effects of human hand and head on , TRP and

radiation pattern of the MIMO antenna are studied. The input power in this paper is normalized to 1 W or 30 dBm [19]. Fig. 11(a) shows the simulation model of the MIMO antenna hand phantom; Fig. 11(b) shows the simulation model of the MIMO antenna hand phantom SAM (specific anthropomorphic mannequin [20]) head, representing the calling mode. In Fig. 11, the MIMO antenna and the system ground plane are covered by a plastic casing with 1 mm in thickness to avoid the direct contact between the antenna and the hand/head model. From Tables I and II, it can be observed that and of the MIMO antenna hand phantom are smaller than the MIMO antenna in free space, and that is because some power is absorbed by the hand phantom. However, and of the MIMO antenna hand phantom are still larger than 27% and 70%, respectively. The SAM head also causes some power loss. Compared with the MIMO antenna hand phantom, and TRPs of the MIMO antenna hand phantom SAM head are smaller but still larger than 20% and 20 dBm, respectively. For the lower frequencies, the side effect of the hand phantom on

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the impedance matching may be compensated by those of the SAM head, Thus, of the proposed MIMO antenna hand phantom SAM head is larger as compared to the proposed MIMO antenna hand phantom. In Table II, discrepancies of and TRPs can be seen between the two monopoles, and that is because the relative positions of the hand and the head for the two monopoles are different. Fig. 12 plots the simulated 3-D radiation patterns at 2.5, 3.5, and 5.5 GHz of the MIMO antenna hand phantom and the MIMO antenna hand phantom SAM head. It can be seen that distortions of the radiation patterns owing to the presence of the hand phantom/SAM head are small, and back-radiation patterns for the two monopoles are still achieved. All the results show that the proposed antenna has good pattern diversity in real-world usage conditions.

VI. CONCLUSION A compact wideband MIMO monopole antenna has been investigated. The compact sizes of the monopole and the ground plane are 18 15 mm and 60 40 mm , respectively. A bandwidth of 92.7% with 10 dB and 18 dB from 2.4 to 6.55 GHz is achieved. Two novel bent slits have been used. At the lower frequencies, they can reduce the mutual coupling resulted from the surface current, and their effect on the reflection coefficient is slight. At the higher frequencies, the bent slits are considered as slit antennas because they are coupled fed by the two 50- microstrip lines, respectively. The resonant modes at 6.3 GHz are excided by the two slit antennas to widen the impedance bandwidth. A cutting of two triangles from the ground plane has been introduced to change the distribution of ground surface currents. In this way, the isolation of the two slit antennas is improved. A grounded metal strip located between the two monopoles has been used to decrease the mutual coupling caused by near-field, and the isolation of the proposed antenna is further enhanced. The MEG, radiation efficiency, correlation coefficient, and DG have been calculated to evaluate the diversity performance of the proposed MIMO antenna. The effects of human hand and head on the performance of the proposed MIMO antenna have been investigated by simulation software SEMCAD-X. The results show that the proposed antenna serving as a phone MIMO antenna can provide spatial and pattern diversity to combat the multipath fading in real-world usage conditions.

[4] Y. Ding, Z. W. Du, K. Gong, and Z. H. Feng, “A novel dual-band printed diversity antenna for mobile terminals,” IEEE Trans. Ant. Propag., vol. 55, no. 7, pp. 2088–2096, Jul. 2007. [5] Z. Y. Li, Z. W. Du, and K. Gong, “A dual-slot diversity antenna with isolation enhancement using parasitic elements for mobile handsets,” in Proc. Asia Pacific Microw. Conf., 2009, pp. 1821–1824. [6] J. R. Panda and R. S. Kshetrimayum, “A compact printed U-shaped dual-band monopole antenna for wireless and RFID applications,” presented at the Appl. Electromagn. Conf., Kolkata, India, 2009. [7] G. M. Chi, B. H. Li, and D. S. Qi, “Dual-band printed diversity antenna for 2.4/5.2-GHz WLAN application,” Microw. Opt. Technol. Lett., vol. 45, no. 6, pp. 561–563, Jun. 2005. [8] P. S. Kildal and K. Rosengran, “Correlation and capacity of MIMO systems and mutual coupling, radiation efficiency, and diversity gain of their aantennas: Simulations and measurements in a reverberation chamber,” IEEE Commun. Mag., vol. 42, no. 12, pp. 102–112, Dec. 2004. [9] S. C. K. Ko and R. D. Murch, “Compact integrated diversity antenna for wireless communications,” IEEE Trans. Ant. Propag., vol. 49, no. 6, pp. 954–960, Jun. 2001. [10] R. G. Vaughan and J. B. Andersen, “Antenna diversity in mobile communications,” IEEE Trans. Veh. Technol., vol. VT-36, no. 4, pp. 149–172, Nov. 1987. [11] M. Karaboikis, C. Soras, G. Tsachtsiris, and V. Makios, “Compact dual-printed inverted-F antenna diversity systems for portable wireless devices,” IEEE Trans. Ant. Propag. Lett., vol. 3, no. 1, pp. 9–14, Dec. 2004. [12] K. Rosengren and P. S. Kildal, “Radiation efficiency, correlation, diversity gain and capacity of a six-monopole antenna array for a MIMO system: Theory, simulation and measurement in reverberation chamber,” IEE Proc. Microw. Ant. Propag., vol. 152, no. 1, pp. 7–16, 2005. [13] S. Blanch, J. Romeu, and I. Corbella, “Exact representation of antenna system diversity performance from input parameter description,” IEE Electron. Lett., vol. 39, no. 9, pp. 705–707, May 1, 2003. [14] H. Paul, “The significance of radiation efficiencies when using S-parameterss to calculate the received signal correlation from two antennas,” IEEE Ant. Wirel. Propag. Lett., vol. 4, no. 1, pp. 97–99, Jun. 2005. [15] Y. Gao, X. D. Chen, and Z. N. Ying, “Design and performance investigation of a dual-element PIFA array at 2.5 GHz for MIMO terminal,” IEEE Trans. Ant. Propag., vol. 55, no. 12, pp. 3433–3441, Jun. 2007. [16] M. P. Karaboikis, V. C. Papamichael, G. F. Tsachtsiris, and V. T. Makios, “Integrating compact printed antennas onto small diversity/MIMO Terminals,” IEEE Trans. Ant. Propag., vol. 56, no. 7, pp. 2067–2078, Jul. 2008. [17] A. A. H. Azremi, J. Toivanen, and T. Laitinen, “On diversity performance of two-element coupling element based antenna structure for mobile terminal,” in Proc. Ant. Propag. Euro. Conf., 2010, pp. 1–5. [18] SPEAG SEMCAD X 13.4, Schmid and Partner Engineering AGS [Online]. Available: http://www.semcad.com [19] C. H. Li, E. Ofli, N. Chavannes, and N. Kuste, “Effects of hand phantom on mobile phone antenna performance,” IEEE Trans. Ant. Propag., vol. 57, no. 9, pp. 2763–2770, Sep. 2009. [20] IEEE Recommended Practice for Determining the Peak Spatial-Average Specific Absorption Rate (SAR) in the Human Head From Wireless Communications Devices: Measurement Techniques, IEEE Standard 1528, Dec. 2003.

REFERENCES [1] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wirel. Person. Commun., vol. 6, no. 3, pp. 311–335, 1998. [2] T. Bolin, A. Derneryd, G. Kristensson, V. Plicanic, and Z. Ying, “Twoantenna receive diversity performance in indoor environment,” IEEE Electron. Lett., vol. 41, no. 2, pp. 1205–1206, Oct. 2005. [3] F. G. Zhu, J. D. Xu, and Q. Xu, “Reduction of mutual coupling between closely-packed antenna elements using defected ground structure,” Electron. Lett. 4, vol. 45, no. 12, pp. 601–602, Jun. 2009.

Jian-Feng Li was born in Maoming, Guangdong, China. She is currently pursuing the Ph.D. degree in electronic and information engineering from South China University of Technology, Guangzhou, Guangdong, China. Her research interests include multi-band antenna and MIMO phone antenna.

LI et al.: COMPACT WIDEBAND MIMO ANTENNA WITH TWO NOVEL BENT SLITS

Qing-Xin Chu (M’99–SM’11) received the B.S., M.E., and Ph.D. degrees in electronic engineering from Xidian University, Xi’an, Shaanxi, China, in 1982, 1987, and 1994, respectively. He is currently a full Professor with the School of Electronic and Information Engineering, South China University of Technology, Guangzhou, Guangdong, China, where he is also head of Research Institute of RF and Wireless Techniques. He worked with the School of Electronic Engineering, Xidian University, from 1982 to 2003, and was the Vice-Dean and a full Professor of the school from 1997 to 2003. He undertook his research with the Department of Electronic Engineering, Chinese University of Hong Kong as a Research Associate from July 1995 to July 1997 and March to September 1998, and worked in the Department of Electronic Engineering, City University of Hong Kong as a research fellow from February to May 2001. He was Visiting Professors of the Department of Electronic Engineering, Chinese University of Hong Kong from July to October 2002, and the Department of Electronic Engineering, City University of Hong Kong from December 2002 to March 2003. He visited the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore from July to October 2004, with the Tan Chin Tuan Exchange Fellowship Award, and visited the Department of Electrical and Electronic Engineering, Okayama University, Japan from January to March 2005, with the Fellowship awarded by

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Japan Society for Promotion of Science (JSPS). His current research interests include UWB antennas and RF components, active integrated antennas, spatial power combining array, and computational electromagnetics. Prof. Chu was a recipient of the first-class Educational Award of Shaanxi Province in 2003, the top-class Science Award of Education Ministry of China and second-class Science and Technology Advance Award of Shaanxi Province in 2002, the top-class Educational Award of Shaanxi Province and the secondclass Award of Science and Technology Advance of Electronic Industry Ministry in 1995. He is a senior member of China Electronic Institute (CEI).

Tian-Gui Huang was born in Maoming, Guangdong, China, on May 5, 1986. He is currently pursuing the M.E. degree in electronic and information engineering from South China University of Technology, Guangzhou, Guangdong, China. His research interest includes UWB band-notch antenna.

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Characteristic Mode Based Tradeoff Analysis of Antenna-Chassis Interactions for Multiple Antenna Terminals Hui Li, Student Member, IEEE, Yi Tan, Buon Kiong Lau, Senior Member, IEEE, Zhinong Ying, Senior Member, IEEE, and Sailing He, Senior Member, IEEE

Abstract—The design of multiple antennas in compact mobile terminals is a significant challenge, due to both practical and fundamental design tradeoffs. In this paper, fundamental antenna design tradeoffs of multiple antenna terminals are presented in the framework of characteristic mode analysis. In particular, interactions between the antenna elements and the characteristic modes and their impact on design tradeoffs are investigated in both theory and simulations. The results reveal that the characteristic modes play an important role in determining the optimal placement of antennas for low mutual coupling. Moreover, the ability of antenna elements to localize the excitation currents on the chassis can significantly influence the final performance. To demonstrate the effectiveness of the proposed approach, a dual-band, dual-antenna terminal is designed to provide an isolation of over 10 dB for the 900 MHz band without additional matching or decoupling structures. A tradeoff analysis of bandwidth, efficiency, effective diversity gain and capacity is performed over different antenna locations. Finally, three fabricated prototypes verify the simulation results for representative cases. Index Terms—Antenna array mutual coupling, multiple-input multiple-output (MIMO) systems, mobile communication.

I. INTRODUCTION

T

HE phenomenal success of multiple-input multiple-output (MIMO) technology can be seen in its critical role of enabling high data rates in Long Term Evolution (LTE), Worldwide Interoperability for Microwave Access

Manuscript received June 01, 2010; revised February 02, 2011; accepted June 20, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. This work was supported in part by VINNOVA under Grants 200904047 and 2008-00970 and also in part by a scholarship within EU Erasmus Mundus External Cooperation Window Lot 14. H. Li, is with the Department of Electrical and Information Technology, Lund University, SE-221 00 Lund, Sweden and also with the School of Electromagnetic Engineering, Royal Institute of Technology, Sweden and the Center for Optical and Electromagnetic Research, Zhejiang University, Hangzhou, 310058, China (e-mail: [email protected]@eit.lth.se). Y. Tan and B. K. Lau are with the Department of Electrical and Information Technology, Lund University, SE-221 00 Lund, Sweden (e-mail: Yi.Tan@eit. lth.se; [email protected]). Z. Ying is with Research and Technology, Corporate Technology Office, Sony Ericsson Mobile Communications AB, SE-221 88 Lund, Sweden (e-mail: Ying. [email protected]). S. He is with the Center for Optical and Electromagnetic Research, Zhejiang University, Hangzhou, 310058, China and also with School of Electromagnetic Engineering, Royal Institute of Technology, SE-100 44 Stockholm, Sweden (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173438

(WiMAX) and IEEE802.11n. The key advantage of MIMO is its potential to linearly increase channel capacity with the number of antennas at both the transmitter and receiver, without sacrificing additional frequency spectrum and transmitted power [1]. However, implementing multiple antennas in compact terminal devices such as mobile phones is challenging, since it involves both practical and fundamental design tradeoffs [2]. Practical tradeoff considerations include the allocation of more antenna locations on the terminal and an increased likelihood of one or more antennas being detuned by the hand or head of the user. Nevertheless, most attention in the area has been on the fundamental aspect of closely spaced antennas resulting in an increase in spatial correlation and mutual coupling, which in turn degrade the performance of MIMO systems as measured by metrics such as efficiency, bandwidth, diversity gain and capacity [2]–[5]. Recent results indicate that, in a rich scattering environment, the MIMO performance of closely spaced antennas can be improved by decoupling multiple antennas, with the tradeoff being a smaller bandwidth [2], [5]. Decoupling techniques that are suitable for multiple antennas on small printed circuit boards (PCBs) are presented in [6]–[10]. Unfortunately, most of these techniques focus on the relatively high frequency bands, including the WLAN, DCS1800 and UMTS bands, and they have not been demonstrated for the mobile bands below 1 GHz, such as GSM900 and WCDMA850. To our understanding, there are several reasons for this. First, since the wavelength at 900 MHz is twice as long as that of 1800 MHz, for the same PCB, the available electrical distance between the antennas is only half of that at 1800 MHz. This complicates the isolation of the antennas. Second, some decoupling techniques, such as neutralization line [6] and quarter-wavelength slot filter [7], base their mechanisms on wavelength. If the frequency decreases, the dimensions of these decoupling structures will increase correspondingly, and they can take too much space on the PCBs. Even more importantly, the mobile chassis, which only functions as a ground plane for the antenna elements at high frequency band, becomes the main radiator at the low frequency bands [11]. Thus, different antenna elements share the same radiator, making isolation worse (e.g., the prototype in [12]). This aspect will be further explained in this paper. The above discussion reveals that the influence of the mobile chassis becomes the most critical factor for multiple antenna terminals at the low frequency bands. However, nearly all existing studies of the impact of chassis on antenna design

0018-926X/$26.00 © 2011 IEEE

LI et al.: CHARACTERISTIC MODE BASED TRADEOFF ANALYSIS OF ANTENNA-CHASSIS INTERACTIONS

focus their attention on single antenna design, e.g., [13]–[16]. In [13], a detailed study shows that self-resonant antenna elements can be replaced by smaller non-resonant antenna elements (or “coupling elements”) that utilize the chassis as the radiating structure, thereby reducing the volume of the mobile terminal antenna. Mobile chassis can also be used to enhance the bandwidth of terminal antennas [14], [15] and create multiple resonances [16]. A recent simulation study [17] concludes that the impedance, bandwidth and radiation mode of an antenna on a ground plane is often defined by the location of the antenna and its feeding point, rather than the size of the ground plane. While useful insights are provided by these studies, the results are based on the single antenna case, and hence may not be directly applicable to multiple antennas implemented on the same chassis. Some results for the multiple antenna case are presented in [18], where an oscillation of correlation coefficient is observed when two antennas with a fixed separation distance move along a large PCB with a length of . However, while the phenomenon is attributed to characteristic mode [19] (also called ‘chassis mode’ in [15], [16]), no further analysis is given. To analyze the mobile chassis, different tools can be utilized, such as resonator based equivalent circuit [20], flat dipole equivalent circuit [21] and theory of characteristic mode [22]. Among these tools, a characteristic mode based analysis is an efficient way to gain physical insight into fundamental electromagnetic properties of mobile chassis and yield valuable information on antenna design. In particular, since characteristic modes are independent of excitation, and only depend on the shape of the chassis [23], the characteristic radiation properties can be obtained from mode analysis. The purpose of this paper is to provide a framework in understanding fundamental design tradeoffs of multiple antennas on mobile chassis at low frequency bands through characteristic mode analysis and antenna simulations. The main contributions are: • Using the theory of characteristic mode and supporting simulations to give insights into the mechanisms that govern the location dependent performance of multiple antennas on a mobile chassis. • Relating the ability of a given type of antenna (i.e., monopoles and planar inverted F antennas (PIFAs)) to localize the excitation current on the chassis to the performance of multiple antennas. • Achieving good MIMO performance, including isolation, efficiency and diversity gain, by taking advantage of the characteristics of antennas on the chassis, without the need for additional matching or decoupling structures. • Providing tradeoff analyses for the performance of multiple antenna terminals with respect to the locations of the antenna elements, in terms of bandwidth, efficiency, correlation, diversity gain and capacity. It should be emphasized that even though this paper focuses on the 900 MHz band, it is only intended to highlight the practicality of our proposal for typical mobile terminals sizes. The underlying principles are based on electrical dimensions rather than absolute dimensions, and hence more general. In other words, chassis radiation of existing or future mobile devices

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with different chassis sizes is significant in other frequency bands. The paper is organized as follows: Section II briefly reviews the theory of characteristic mode and its application in providing fundamental characteristics of chassis radiation. The resonant characteristic electric fields, the eigenvectors and the modal significance (MS) [23] of a chassis are used to give helpful information on antenna design. A slot monopole on the chassis is also investigated using the characteristic mode analysis. Antenna simulations are carried out using an electromagnetic (EM) simulator in Section III. First, the properties of single monopoles and single PIFAs with different locations on the chassis are examined. The results indicate that, for a given location on the chassis, different types of antennas localize the chassis excitation currents to different extents. This insight can be used to improve the isolation between multiple antenna elements. Second, multiple antenna cases are studied to investigate the effects of chassis current localization on isolation for different antenna combinations. In Section IV, performance tradeoff analyses of different antenna locations on the mobile chassis is presented with respect to bandwidth, efficiency, correlation, effective diversity gain and capacity. Based on the analysis, three dual-antenna prototypes were fabricated, and their experimental results are presented in Section V. Finally, some conclusions are given in Section VI. II. CHARACTERISTIC MODE ANALYSIS The mode of an oscillating structure is a pattern of motion in which the entire structure oscillates sinusoidally with the same frequency. The frequencies of the modes are known as their natural frequencies or resonant frequencies. A physical object has a set of modes that depend on its structure, materials and boundary conditions. The characteristic mode analysis is a method used in electromagnetics, which gives insight into the potential resonant characteristics of a structure by finding and examining the inherent modes of the structure. The existence of the modes is independent of the excitation. However, different kinds of excitations or excitations at different locations/frequencies are expected to excite different modes, to satisfy different requirements. From this perspective, the characteristic mode analysis can provide physical insight into the fundamental electromagnetic properties of scattering objects and valuable information on antenna design. The theory of characteristic mode was first introduced by Robert Garbacz in [24] and later refined by Roger Harrington in [19] and [25]. Considering a conducting body with surface , an external electric field (or voltage) can induce a surface current on it. This surface current will further generate a scattered field . According to the boundary condition, the tangential component on the surface of the conducting body satisfies (1) Equation (1) can be rewritten with an operator (2)

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Following the approach in [19], characteristic mode is defined by the eigenvalue equation expressed as (5) In our work, this linear equation is transformed to matrix equation using the method of moments (MOM) [26]. The MOM relies on Rao-Wilton-Glisson (RWG) edge elements. The surface of the metal antenna is divided into separate triangles (see Fig. 1(d)). Each pair of triangles, having a common edge, constitutes the corresponding RWG edge element. These RWG edge elements correspond to the division of the antenna into small elementary electric dipoles. In this sense, the impedance matrix describes the interaction between different elementary dipoles. If the edge elements m and are treated as small electric dipoles, the element describes the contribution of dipole to the electric current of dipole , and vice versa. This contribution is calculated through electric field integral equation (EFIE). The size of impedance matrix is equal to the number of the edge elements. With the matrix equation, the characteristic eigenvalues , eigenvectors and characteristic electric fields of the chassis are calculated with Matlab. The chassis, with the dimensions of a typical candybar-type mobile phone (100 mm 40 mm), is modeled by a perfectly conducting board. Its eigenvalues over a frequency range from 0.5 GHz to 1.5 GHz are calculated in Matlab, and shown in Fig. 1(a). A scattered plot is employed to generate the figure and the chassis is meshed with 736 edge elements. As known from [19], the smaller the magnitude of , the more important the mode is for radiation and scattering problems, and corresponds to a resonant mode. As observed from Fig. 1(a), the lowest resonant frequency of our chassis is 1.35 GHz. The mode in our work is numbered according to the order of occurrence of its resonant frequency. The lower the resonant frequency, the smaller is the mode number. The mode number of zero (or ) denotes a non-resonant mode. To highlight the respective roles of characteristic modes and external excitation in chassis radiation, the total current on the surface of a conducting body can be expressed by the eigenvectors as (6)

Fig. 1. (a) The eigenvalues against frequency for the mobile chassis; (b) the modal significance (MS) against frequency for the mobile chassis; (c) the normalized magnitude of the total electric field of the first characteristic mode of the chassis at 1.35 GHz; (d) the normalized eigenvector of the first characteristic mode of the chassis at 1.35 GHz.

where the term can be considered as the electric field intensity on the surface due to the surface current . The operator has the dimension of impedance, and the following notations are hence introduced (3) (4)

There are two factors determining the contribution of a certain (or th) mode to the total current distribution [23], i.e., the modal-excitation coefficient (7) and the modal significance (MS) (8) Whereas accounts for the external excitation, including the influence of its position, magnitude and phase, MS represents the inherent normalized amplitude of the characteristic modes.

LI et al.: CHARACTERISTIC MODE BASED TRADEOFF ANALYSIS OF ANTENNA-CHASSIS INTERACTIONS

External excitation (e.g., port excitation) will not change the characteristic modes of the conducting body; however, its location on the structure is very important for the excitation of certain characteristic mode(s). The MS of each mode of the chassis is presented in Fig. 1(b). It can be observed that the first mode is dominant at 1.35 GHz, while the other modes only contribute slightly to the current distribution (with ). Thus, at the frequency band around 1 GHz, we focus mainly on the first mode of the chassis and its interaction with the antenna on the chassis. The characteristic total electric field of the first mode on a plane 5 mm above the chassis is evaluated at 1.35 GHz, and shown in Fig. 1(c). The field is normalized to the maximum value and presented in dB scale. The field corresponds to that of a flat half-wavelength dipole [21]. It can be observed that the electric field is stronger at the edges, especially at the corners, whereas it becomes very weak at the center of the chassis. For the single antenna case, this insight reveals that the characteristic mode can be most efficiently excited when a voltage (a port excitation) is applied at the edge or at the corner. However, if multiple antennas at the same or closely similar frequencies are integrated on the same chassis, the locations of the antennas should be carefully considered. Concerning the mutual coupling, if the antenna (e.g., a dipole) is responsive to electric field, the place where the electric field is strong is not a good location for more than one such antenna. On the other hand, if the antenna (e.g., a small loop) responds mainly to magnetic field, the place with strong magnetic field is likewise not a good location for more than one such antenna. Since most types of mobile terminal antennas base their mechanisms on electric field, we focus on electric field in this paper. The normalized eigenvector (i.e., characteristic current) of the first characteristic mode of the chassis is presented in Fig. 1(d). A sinusoidal current distribution along the length of the chassis is observed, which shows that the length of the chassis is approximately one half of a wavelength at the first resonant frequency. This current distribution is similar to that calculated in the EM simulator for an excited monopole on the chassis (see Figs. 7(a) and 8(c)). Once antennas are implemented on the chassis, the electrical length of the chassis is correspondingly increased, and its resonant frequency will be further reduced, making it closer to 900 MHz. To verify this hypothesis, the eigenvalues of the 100 mm 40 mm chassis with a planar slot monopole [27] etched in it are calculated in Matlab and shown in Fig. 2(a). The dimensions of the slot monopole are presented later in the paper (see Fig. 8(b)). The lowest resonant frequency of 1.06 GHz is observed in the figure. Moreover, when the antenna is excited with a feed, its resonant frequency can be slightly changed. Another observation from Figs. 1(a) and 2(a) is that the first resonance of the chassis, with and without the slot monopole element, is relatively wideband, which appears to substantiate the findings of [17] that the chassis size is often less important than the locations of the antenna element and its feed in determining single antenna performance. The characteristic total electric field of the first mode of the slot monopole is evaluated at 1.06 GHz and presented in Fig. 2(b). As expected, the trend of the electric field is similar to

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Fig. 2. (a) The eigenvalues against frequency for the mobile chassis with a slot monopole; (b) The normalized magnitude of the total electric field of the first characteristic mode of the slot monopole at 1.06 GHz.

that of the chassis-only case in Fig. 1(c). Due to the resonance of the slot monopole at 1.06 GHz, the positions of maximum and minimum electric fields are slightly changed. The maximum electric field occurs at the edge with the slot monopole, and the minimum value shifts slightly from the center towards the monopole side. From the perspective of isolation, the best location for another antenna should be in the region of the minimum electric field so that the characteristic mode will not be shared simultaneously by two antenna elements. This principle will be further analyzed and verified by the antenna simulations in the following section. The chassis with slot monopole is also simulated in the frequency domain solver of CST Microwave Studio, with the monopole excited by a lumped port. The total electric field is similar to the characteristic electric field in Fig. 2(b), and is thus not included here. III. ANTENNA SIMULATION In this section, according to the results of the characteristic mode analysis, the excitation ports are applied to different locations of the chassis. Full-wave antenna simulations are carried out in the frequency domain using the CST Microwave Studio software. Single monopole antenna and single PIFA cases are studied first, to identify the degree to which the radiation properties are influenced by different antenna types and locations. Our choice is based on the fact that PIFAs and low profile variants of monopole antennas are the most commonly used antenna types in today’s mobile terminals. Based on these results, multiple antenna cases are then analyzed. The size of the mobile

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Fig. 3. Geometry of quarter-wavelength top-loaded monopole and its locations mm, on the chassis in the single antenna case. The dimensions are: mm, mm. Diameter of the wire is 1 mm.

chassis is 100 mm 40 mm, which is identical to that in the previous section. The chassis consists of a 0.1 mm top copper layer and a 1.55 mm bottom FR4 layer with a permittivity of 4.7 and a loss tangent of 0.015. All antennas, except the top-loaded monopoles, are designed for dual-band (900/1900 MHz) operation. However, the focus of the study in this and the following sections are on the 900 MHz band. Note that even though the dimensions of the monopoles and PIFAs used in the paper are provided, they are specific to a given antenna location and are slightly tuned to ensure good impedance matching (i.e., reflection coefficient dB) for other locations. A. Single Antenna Cases In this sub-section, four single antenna cases are studied: quarter-wavelength top-loaded monopole at the center (MC) or edge (ME) of the chassis, and PIFA at the center (PC) or edge (PE) of the chassis. The geometry of the monopole and its location on the mobile chassis are shown in Fig. 3. Perfect electric conductor (PEC) is assumed as the antenna material. The top load (i.e., a circular plate with thickness of 0.1 mm) is used to help match the monopole and slightly reduce its height, without changing the radiation characteristics. The monopole is first put at the edge of the chassis, and then moved to the center with its dimension unchanged. The same monopole antenna on an infinite ground plane (MIG) is also presented for comparison. All the antennas are well matched at 0.92 GHz. Real and imaginary parts of the simulated input impedance and the magnitude of the reflection coefficients are shown in Fig. 4(a) and (b), respectively. As can be seen in Fig. 4(a), the input impedances of MC and MIG share a similar trend, whereas that of ME is quite different. As explained in the previous section, the characteristic mode for the eigenvalue is easily excited when the antenna is located at the edge of the chassis [13], since the resonance of chassis is close to 0.92 GHz. The high radiation resistance in the ME case is mainly due to the excitation of the characteristic mode, which increases the bandwidth dramatically (see Fig. 4(b)). The PIFA cases are studied in a similar way. The geometry and different locations of the single PIFA are shown in Fig. 5. The PIFA is integrated onto a hollow carrier (i.e., the shaded regions), which is commonly used in mobile phones. The simulated carrier has a thickness of 1 mm, a permittivity of 2.7 and a loss tangent of 0.007. To further separate the effect of the edge

Fig. 4. (a) Input impedances and (b) reflection coefficients of the simulated top-loaded monopole at different locations with finite/infinite ground plane.

Fig. 5. Geometries of the PIFA and its locations on the chassis in the single mm, mm, antenna case. The dimensions are: mm, mm, mm, mm, mm, mm, mm, mm.

from that of the characteristic mode, one more case is included, i.e., the PIFA in the center rotated by 90 and moved to the longer edge of the chassis (RPC), as illustrated in Fig. 5(b). A PIFA on an infinite ground plane (PIG) is used for comparison. From Fig. 6(a), it can be observed that the input impedance of

LI et al.: CHARACTERISTIC MODE BASED TRADEOFF ANALYSIS OF ANTENNA-CHASSIS INTERACTIONS

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Fig. 7. Normalized magnitude of current distributions for: (a) monopole at the edge, (b) monopole at the center, (c) PIFA at the edge, (d) PIFA at the center.

Fig. 6. (a) Input impedances and (b) reflection coefficients of the simulated PIFA at different locations with finite/infinite ground plane.

PC in Fig. 6(b), the characteristic mode excitation is observed to offer significantly larger bandwidths for the ME and PE cases than for the MC and PC cases, respectively. Second, the current of PIFA is more localized than that of monopole at either the center or the short edge. In other words, its radiation depends less on the chassis than that of the monopole. Therefore, in addition to the concept of characteristic mode, localization of chassis current is also important in determining the isolation between antenna elements: The more localized the induced current on the chassis, the less is the current that couples from one antenna port into other antenna port(s). Nonetheless, it should be noted that an antenna with more localized current is an indication of a smaller effective radiator, which inevitably leads to a reduction of bandwidth. This aspect can be seen in the narrower bandwidths of the PC and PE cases, relative to the MC and ME cases, respectively. Further analysis of the localized current phenomenon is provided in Section IV. B. Dual-Antenna Cases

PE is notably different from all other cases. With the help of the chassis, both the input resistance and reactance become larger in amplitude and flatter over frequency. As a result, the bandwidth is significantly improved (see Fig. 6(b)). To confirm that the larger bandwidth of PE is primarily the result of characteristic mode excitation, rather than due to the PIFA being at the chassis edge, the effect of the edge can be examined by comparing the bandwidths of RPC and PC. Since the difference in bandwidth between the two cases is negligible, it can be concluded that the edge effect is unlikely to have contributed to the wideband behavior in the PE case. In order to gain further insights into the influence of chassis on the characteristics of monopole and PIFA at different locations, normalized current distributions are given for four distinct cases in Fig. 7. The normalization is performed against the peak current in each case. Two conclusions can be drawn from the current distributions. First, when the antenna is at the short edge, regardless of its type, the characteristic mode of the chassis is excited (see Fig. 7(a) and (c)), and the current is distributed over the whole chassis. This current distribution is similar as the eigenvector of the first characteristic mode (see Fig. 1(d)), especially for the ME case. This further verifies the strong excitation of the first characteristic mode. When the antenna is at the center, the current is more confined to the immediate vicinity of the antenna. By comparing ME and MC in Fig. 4(b) and PE and

In this subsection, different combinations of antenna types, including monopole-monopole (MM), PIFA-PIFA (PP) and monopole-PIFA (MP), and antenna locations (at the edge(s) and at the center) are studied to shed light on the effect of characteristic mode and current localization on the isolation level between two antenna elements on the chassis. In all the simulations, two antennas (of monopole(s) and/or PIFA(s)) are integrated onto the same chassis of dimensions 100 mm 40 mm. One antenna is fixed at one short edge, and the other antenna is placed either at the opposite short edge or at the center. A planar slot monopole [27] rather than the top-loaded monopole is used as the fixed monopole at the edge, considering antenna dimensions and matching problem. The schematic drawing of the antenna setup and the geometry of the slot monopole are shown in Fig. 8. The slot monopole is etched into the ground plane on a substrate of FR4. It is fed by a microstrip line (i.e., the dashed line in Fig. 8(b)) on the other side of the substrate. The width of both of the slots is mm. Good antenna matching is achieved by optimizing the value of . The radiation pattern and polarization of the slot monopole are only slightly different from those of the top-loaded monopole when they are implemented on the mobile chassis, since they both strongly excite the chassis, which acts as a radiator. The normalized current distribution when the slot monopole is excited is shown in Fig. 8(c). It is observed

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Fig. 8. (a) The schematic drawing of the locations of antennas in the dual-antenna case. (b) The geometry of the slot monopole. The dimensions are: mm, mm, mm, mm, mm, mm, mm, mm, mm. (c) The normalized current distribution of the slot monopole on the chassis.

that the degree of chassis excitation is similar as that when the top-loaded monopole is used (Fig. 7(a)). The simulation results are shown in Fig. 9. It is interesting to note that, in all dual-antenna cases, the isolation improves when one antenna is moved to the center (i.e., the two antennas become closer). This phenomenon contradicts with intuition and the common knowledge on the relationship between antenna separation distance and port isolation. However, this situation can be explained by the characteristic mode analysis in Section II and the single antenna simulations above. When the antenna elements are at the two edges, they excite the chassis simultaneously. Since the chassis not only functions as a ground plane, but also as the main radiator for both antenna elements, the port isolation must be low. The mutual coupling, in this case, not only comes from the field in free space and the conventional ground plane current, but also from the radiation of the shared chassis. Thus, it is difficult to achieve angle and polarization diversities for the antenna elements in this setup.

Fig. 9. The simulated scattering parameters of dual-antenna terminals with different locations and combinations of antenna elements: (a) M-M combination, (b) M-P combination, with PIFA at the edge or the center of the ground plane, and (c) P-P combination.

When one antenna is moved to the center, the chassis is not efficiently excited, and hence the current is more localized. The chassis is only utilized as the main radiator by the antenna (either the monopole or the PIFA) at the chassis edge. Consequently, angle and polarization diversities can be more easily achieved for the edge-and-center placement, which enhances the isolation.

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Fig. 10. Normalized magnitude of current distributions for the M-P case: (a) PIFA at the edge, monopole excited, (b) PIFA at the edge, PIFA excited, (c) PIFA at the center, monopole excited, (d) PIFA at the center, PIFA excited.

It is also observed that different dual-antenna combinations offer different degrees of improvement in isolation, when considering different placement options of a given combination. The most dramatic improvement is achieved in the M-P combination, in which the monopole is the fixed antenna and the PIFA is either at the edge or the center of the ground plane. This improvement is mainly due to the localized current achieved by the PIFA when it is at the center. Another reason is that employing antennas of different types can reduce mutual coupling to some extent by taking advantage of angle diversity in their radiation patterns. The improvement in the isolation of the P-P combination is better than that of the M-M combination, and this is attributed to the localized current behavior of the PIFAs, as shown in Fig. 7(c) and (d) for the single antenna cases. By taking into consideration both characteristic mode and current localization, isolation of over 10 dB is achieved in the M-P combination, which can be considered low enough for terminal applications involving frequencies lower than 1 GHz. In addition, the antennas are easy to design and tune, since no additional matching or decoupling structures are needed. From the perspective of bandwidth, the monopole antenna performs well, whereas the bandwidth of the PIFA is narrow, especially when it is placed at the center of the chassis. Thus, the P-P combination is impractical, even though the isolation is improved for the center-and-edge placement, in comparison to the edge-and-edge placement. The M-M combination is likewise impractical, due to the difficulties in implementing a low profile monopole at the center: Its dimensions tend to be large and it is difficult to achieve good matching. In addition, the isolation between the monopoles is only 7 dB at the center frequency. Consequently, the M-P combination is more attractive for mobile terminal applications. As has been suggested in [12], the monopole can be used as the main antenna to cover both downlink and uplink frequencies, whereas the narrowband PIFA can be used as a diversity antenna for only the downlink frequencies. C. Discussions For the M-P combination, normalized current distributions are shown in Fig. 10. In Fig. 10(a) and (b), when the two antennas are at the edges, the characteristic mode is easily excited, resulting in strong electric fields at the two edges. Therefore, if

Fig. 11. Performance tradeoffs of the dual-antenna terminal with respect to the PIFA location in terms of the (a) relative bandwidth, (b) average efficiency, (c) magnitude of complex correlation coefficient and average EDG, and (d) average channel capacity.

one antenna is excited, the other antenna is also strongly excited, which leads to poor isolation. In Fig. 10(c), the PIFA is

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Fig. 12. Prototypes with the slot antenna at one edge and (a) the PIFA at the opposite edge, (b) the PIFA at the center, (c) the rotated PIFA at the center.

influenced to some extent, since the characteristic mode is efficiently excited by the monopole; whereas in Fig. 10(d), when the PIFA is excited, due to its localized current, the chassis acts primarily as a common ground rather than a radiator. Thus, good isolation is achieved. Rather than only the slot monopole, different monopole types, including the most frequently used folded monopole (such as the monopole in [12]), have also been simulated. The trend of isolation enhancement is the same when the PIFA moves away from the edge to the center location. The slot monopole is used in our work due to the convenience of fabrication and matching. Concerning the bandwidth of PIFA, we note that the PIFA can be made tunable to cover different bands according to different requirements. IV. TRADEOFF ANALYSIS OF DUAL-ANTENNA TERMINALS In this section, the performance tradeoffs of dual-antenna terminals are investigated with respect to different locations of the PIFA on the chassis for the M-P combination in Section III.B. The different PIFA locations are meant to induce different levels of characteristic mode excitation. The PIFA is moved gradually from the edge to the center, in steps of 5 mm. is the distance between the PIFA location and the edge (see Fig. 8(a)). When the PIFA is at the edge, mm. The relative bandwidth of the two antennas is shown in Fig. 11(a). Here, the relative bandwidth is defined as the ratio of the 6 dB impedance bandwidth to the center frequency. It is obvious that the bandwidth of the monopole is much wider than that of the PIFA, and it is almost constant regardless of the PIFA’s location. That is one reason that the monopole is used as the main radiator in the M-P combination. The relative bandwidth of the PIFA falls quickly when it is moved away from the edge, since the chassis no longer contributes significantly to the PIFA’s radiation. Indeed, it is observed that the bandwidth this almost unchanged when the PIFA is moved around the center location. The efficiencies of both antennas, including the radiation efficiency at the center frequency and the average total efficiency over a given bandwidth, are presented in Fig. 11(b). Overall, the efficiencies of both antennas increase when the PIFA is moved from the edge to the center. The radiation efficiency is ana-

Fig. 13. Measured scattering parameters for the slot antenna at one edge and (a) the PIFA at the opposite edge (b) the PIFA at the center and (c) the rotated PIFA at the center.

lyzed first. The highest radiation efficiency of the PIFA appears at the edge and decreases by 15% when it is moved to the center. This is because the chassis excitation helps to increase the radiation resistance of the PIFA at the edge (see Fig. 6(a)). According to expression (9) is the radiation resistance and represents the where conduction-dielectric losses (which is almost constant over

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Fig. 14. Simulated and measured antenna patterns for the antenna system in measured , ( ) simulated Fig. 12(a): (—) simulated , ( ) measured . (a) Monopole, , (b) Monopole, , (c) Monopole, , (d) PIFA, , (e) PIFA, , (f) PIFA, .

the given range of frequency), efficiency can be high if the radiation resistance is large. For the monopole, the radiation efficiency does not change appreciably, since it always takes advantage of the chassis to radiate efficiently. The total efficiency is given by (10) When the PIFA is at the edge, the total efficiencies are relatively low for both antennas, due to strong mutual coupling (i.e., large ). As the PIFA moves away from the edge, the total efficiency of the monopole increases greatly, regardless of the bandwidth within which it is calculated. The total efficiency of the PIFA increases as it is moved towards the center of the chassis, if it is only measured at the center frequency. However, the trend changes when it is measured within a 30 MHz bandwidth, because of its narrowing impedance bandwidth with (see Fig. 11(a)). Therefore, the optimal position of the PIFA can be different, depending on the efficiency bandwidth requirement.

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Fig. 15. Simulated and measured antenna patterns for the antenna system in measured , ( ) simulated Fig. 12(b): (—) simulated , ( ) measured . (a) Monopole, , (b) Monopole, , (c) Monopole, , (d) PIFA, , (e) PIFA, , (f) PIFA, .

Correlation coefficient and diversity gain are important metrics for evaluating the performance of multiple antenna systems. Fig. 11(c) presents the magnitude of complex correlation coefficients at the center frequency, together with the average effective diversity gain (EDG) over the given bandwidths. EDG [12] is defined by (11) where is the total efficiency of the antenna with the highest efficiency and DG is the (apparent) diversity gain. In this paper, DG is calculated with the maximum ratio combining (MRC) method and taken at 1% probability. All the EDGs (over different bandwidths) improve as the PIFA is moved towards the center. Though the improvement becomes less obvious when calculated over a larger bandwidth, a minimum enhancement of 2.3 dB can be observed within a bandwidth of 30 MHz. The smallest correlation coefficient of 0.11 is achieved when mm, which corresponds to the PIFA structure at nearly the center location of the chassis. The average channel capacity calculated under the equal power (EP) and water-filling (WF) conditions for

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dB is presented in Fig. 11(d). The WF procedure is performed over the antenna elements. The Kronecker model and uniform 3D angular power spectrum (APS) is assumed. There is no correlation between the (base station) transmit antennas, whereas the (mobile terminal) receive antennas are correlated according to their radiation patterns and the 3D APS. The capacity is averaged over 10 000 i.i.d. Rayleigh realizations at each frequency. The channels are normalized with respect to the i.i.d. Rayleigh case, which means that the correlation, total efficiency and power imbalance (efficiency imbalance) are taken into account in the capacity evaluation. As reference cases, the average capacities for the 2 2 i.i.d. Rayleigh channel with the EP and WF schemes are 11.29 bits/s/Hz and 11.32 bits/s/Hz, respectively. Similar to the figure of EDG, the largest capacity is achieved when mm, due to the low correlation and high efficiency of the monopole when the PIFA is at the center. Because of the PIFA’s narrow bandwidth, the power imbalance becomes serious at frequencies away from the center frequency. This means that one antenna (or spatial channel) is not efficiently used, and thus the average channel capacity decreases. In general, the average capacity increases when the PIFA is moved to the center, and the improvement is less obvious with an increase in bandwidth. For the WF case, the power imbalance is accounted for in the transmit power allocation, so the channel is more efficiently used than in the EP case. Thus, the capacity improvement of WF over EP increases with power imbalance, which increases with bandwidth. V. EXPERIMENTS AND DISCUSSIONS The PIFAs and monopoles used by the dual-antenna prototypes in Section IV are dual-band antennas and they cover both 880 MHz–960 MHz and 1880 MHz–1990 MHz frequency bands. Three prototypes are fabricated for the slot monopole at one edge and (i) the PIFA at the opposite edge, (ii) the PIFA at the center, and (iii) the rotated PIFA at the center (see Fig. 12). The scattering (or S) parameters are measured with a vector network analyzer and shown in Fig. 13. The isolation is improved from 5 dB to 13 dB when the PIFA is moved to the center. As a tradeoff, the bandwidth of the PIFA is reduced from 30 MHz to 12 MHz. In practice, PIFA can be made tunable to cover different bands according to the given requirement. The scattering parameters are almost unchanged when the PIFA is rotated by 90 degrees. The far field electric field patterns are measured in a Satimo Stargate-64 antenna measurement facility. For cases (i) and (ii), the patterns at the center frequency of the low band are shown in Figs. 14 and 15, respectively. The patterns of the case (iii) (as illustrated in Fig. 12(c)) are not included here, because the pattern of the monopole is similar to that of the monopole in Fig. 12(b), and the pattern of PIFA is similar to that of the PIFA in Fig. 12(b) after a 90 rotation. The measured patterns agree well with the simulated ones. The slight differences are caused by influences of the feeding cables. The correlations calculated from the measured patterns are 0.5, 0.18, and 0.19, respectively, for the three prototypes in Fig. 12. Due to some cable influence [12] and practical difficulties in measuring antennas with very high correlation, the measured correlation for the case with the

Fig. 16. Measured efficiencies (a) low frequency band (b) high frequency band for the slot monopole at one edge (ME) and (i) the PIFA at the opposite edge (PE) (ii) the PIFA at the center (PC) and (iii) the rotated PIFA at the center (RPC).

antennas at the edges (i.e., Fig. 12(a)) is slightly lower than the simulated one. The measured efficiencies over two operating bands are shown in Fig. 16. In general, the measured efficiencies are slightly lower than the simulated ones due to fabrication and experimental tolerances. At the low frequency band, when the PIFA is at the edge, the efficiencies of the monopole are relatively low around the center frequency due to high mutual coupling. When the PIFA is at the center, the efficiencies of monopole approach that of a single monopole on mobile chassis, whereas the PIFA efficiency becomes more narrowband. At the high frequency band, the efficiencies of the monopole are around 70% (-1.5 dB), since the coupling is not significant. The highest efficiency of the PIFA is 75% (-1.2 dB), and good efficiency is kept in downlink band. All these results agree well with simulations. VI. CONCLUSION In this work, fundamental design tradeoffs of multiple antennas on a mobile chassis are studied in the context of characteristic mode excitation and the ability of antennas to localize chassis currents. The goal is to provide useful information and a

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design framework for optimal implementations of multiple antennas on a mobile chassis according to different requirements. The results for the 900 MHz band show that whereas the PIFA has more localized currents than the monopole, especially when it is at the center of the chassis, it is the monopole-PIFA combination that achieves the best isolation of over 10 dB (13 dB for the measured case). Utilizing characteristic mode and chassis current localization in the design of multiple antennas has the advantage of not requiring any additional matching or decoupling structures. Three prototypes are fabricated and measured to test three selected cases, and the results are found to be in good agreement with those from simulations. Since a mobile terminal user can significantly influence the results obtained in this study, the effects of user on antennachassis interaction is an interesting topic for future work. ACKNOWLEDGMENT The authors are thankful to Prof. J. B. Andersen of Aalborg University and Prof. A. Karlsson of Lund University for helpful discussions. REFERENCES [1] M. A. Jensen and J. W. Wallace, “A review of antennas and propagation for MIMO wireless communications,” IEEE Trans. Antennas Propag., vol. 52, no. 11, pp. 2810–2824, Nov. 2004. [2] B. K. Lau, , C. Oestges, A. Sibille, and A. Zanella, Eds., “Multiple antenna terminals,” in MIMO: From Theory to Implementation. San Diego, CA: Academic Press, 2011, pp. 267–298. [3] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Personal Commun., vol. 6, pp. 311–335, Mar. 1998. [4] Z. Ying and D. Zhang, “Study of the mutual coupling, correlations and efficiency of two PIFA antennas on a small ground plane,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., Washington, DC, July 2005, pp. 305–308. [5] B. K. Lau, J. B. Andersen, G. Kristensson, and A. F. Molisch, “Impact of matching network on bandwidth of compact antenna arrays,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3225–3238, Nov. 2006. [6] A. Diallo, C. Luxey, P. L. Thuc, R. Staraj, and G. Kossiavas, “Enhanced two-antenna structures for universal mobile telecommunications system diversity terminals,” IET Microw. Antennas Propag., vol. 2, no. 1, pp. 93–101, 2008. [7] H. Li, J. Xiong, and S. He, “A compact planar MIMO antenna system of four elements with similar radiation characteristics and isolation structure,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 1107–1110, 2009. [8] Y. Gao, X. Chen, Z. Ying, and C. Parini, “Design and performance investigation of a dual-element PIFA array at 2.5 GHz for MIMO terminal,” IEEE Trans. Antennas Propag., vol. 55, no. 12, pp. 3433–3441, Dec. 2007. [9] B. K. Lau and J. B. Andersen, “Simple and efficient decoupling of compact arrays with parasitic scatterers,” IEEE Trans. Antennas Propag., submitted for publication. [10] S. Dossche, S. Blanch, and J. Romeu, “Optimum antenna matching to minimize signal correlation on a two-port antenna diversity system,” Elect. Lett., vol. 40, no. 19, pp. 1164–1165, Sep. 2004. [11] K. Solbach and C. T. Famdie, “Mutual coupling and chassis-mode coupling small phases array on a small ground plane,” presented at the Eur. Conf. Antennas Propag. (EuCAP), Edinburgh, U.K., Nov. 11–16, 2007. [12] V. Plicanic, B. K. Lau, A. Derneryd, and Z. Ying, “Actual diversity performance of a multiband diversity antenna with hand and head effects,” IEEE Trans. Antennas Propag., vol. 57, no. 5, pp. 1547–1556, May 2009. [13] J. Villanen, J. Ollikainen, O. Kivekas, and P. Vainikainen, “Coupling element based mobile terminal antenna structure,” IEEE Trans. Antennas Propag., vol. 54, no. 7, pp. 2142–2153, July 2006.

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[14] T. Taga and K. Tsunekawa, “Performance analysis of a built-in planar inverted-F antenna for 800 MHz band portable radio units,” IEEE J. Select. Areas Commun., vol. ACE-5, no. 5, pp. 921–929, 1987. [15] W. L. Schroeder, A. A. Vila, and C. Thome, “Extremely small wideband mobile phone antenna by inductive chassis mode coupling,” in Proc. 36th Eur. Microw. Conf., Manchester, U.K., Sep. 10–15, 2006, pp. 1702–1705. [16] W. L. Schroeder and C. T. Famdie, “Utilisation and tuning of the chassis modes of a handheld terminal for the design of multiband radiation characteristics,” in Proc. IEE Wideband Multiband Antennas and Arrays, Sep. 7, 2005, pp. 117–122. [17] S. R. Best, “The significance of ground-plane size and antenna location in establishing the performance of ground-plane-dependent antennas,” IEEE Antennas Propag. Mag., vol. 51, no. 6, pp. 29–42, Dec. 2009. [18] C. Luxey and D. Manteuffel, “Highly-efficient multiple antenna -system for small MIMO devices,” presented at the Int. Workshop Antenna Technol. (IWAT), Lisbon, Portugal, Mar. 1–3, 2010. [19] R. F. Harrington and J. R. Mautz, “Theory of characteristic modes for conducting bodies,” IEEE Trans. Antennas Propag., vol. AP-19, no. 5, pp. 622–628, Sep. 1971. [20] P. Vainikainen, J. Ollikainen, O. Kivekas, and I. Kelander, “Resonator-based analysis of the combination of mobile handset antenna and chassis,” IEEE Trans. Antennas Propag., vol. 50, no. 10, pp. 1433–1444, Oct. 2002. [21] U. Bulus, C. T. Famdie, and K. Solbach, “Equivalent circuit modeling of chassis radiator,” presented at the German Microw. Conf. (GeMIC2009), Munich, Germany, Mar. 16–18, 2009. [22] C. T. Famie, W. L. Schroeder, and K. Solbach, “Numerical analysis characteristic modes on the chassis of mobile phones,” presented at the Eur. Conf. Antennas Propag. (EuCAP), , France, Nov. 6–10, 2006. [23] M. C. Fabres, E. A. Daviu, A. V. Nogueiram, and M. F. Bataller, “The theory of characteristic modes revisited: A contribution to the design of antennas for modern applications,” IEEE Trans. Antennas Propag. Mag., vol. 49, no. 5, pp. 52–68, Oct. 2007. [24] R. J. Garbacz, “A generalized expansion for radiated and scattered field,” IEEE Trans. Antennas Propag., vol. AP-19, pp. 662–668, May 1971. [25] R. F. Harrington and J. R. Mautz, “Computation of characteristic modes for conducting bodies,” IEEE Trans. Antennas Propag., vol. AP-19, no. 5, pp. 629–639, Sep. 1971. [26] S. N. Makarov, Antenna and EM Modeling With MATLAB. New York: Wiley-interscience, 2002. [27] C. I. Lin and K. L. Wong, “Printed monopole slot antenna for internal multiband mobile phone antenna,” IEEE Trans. Antennas Propag., vol. 55, no. 12, pp. 3690–3697, Dec. 2007. Hui Li (S’08) received the Bachelor’s degree in optical engineering from Tianjin University (TJU), China, in 2007. She is currently working towards the Ph.D. degree at the Royal Institute of Technology (KTH), Sweden. From 2007 to 2009, she pursued a Ph.D. degree at the Joint Center (with KTH) for Optical and Electromagnetic Research, Zhejiang University (ZJU), China. In 2010, she was awarded the EMECW (Erasmus Mundus External Cooperation Window) scholarship and visited the Department of Electrical and Information Technology at Lund University for 13 months. In 2011, she received the CSC (Chinese Scholarship Council) scholarship, and continued her Ph.D. study in KTH. Her current research interests include compact antennas in MIMO systems, antenna-user interactions, reconfigurable antennas, and RFID antennas in wireless communications.

Yi Tan received the Bachelor’s degree in China, in 2003. He is currently working towards the Master’s degree at Lund University, Sweden. During 2004–2007, he was an RF Engineer in Laird Technologies, Beijing, where he worked on mobile antenna design and production. In 2008, he started working towards a Master degree in Lund University. In 2010, he took a year off from his Master study to work as a Project Assistant at the Department of Electrical and Information Technology, Lund University.

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Buon Kiong Lau (S’00–M’03–SM’07) received the B.E. degree (with honors) from the University of Western Australia, Perth, Australia and the Ph.D. degree from Curtin University of Technology, Perth, in 1998 and 2003, respectively, both in electrical engineering. During 2000 to 2001, he worked as a Research Engineer with Ericsson Research, Kista, Sweden. From 2003 to 2004, he was a Guest Research Fellow at the Department of Signal Processing, Blekinge Institute of Technology, Sweden. Since 2004, he has been at the Department of Electrical and Information Technology, Lund University, where he is now an Associate Professor. He has been a Visiting Researcher at the Department of Applied Mathematics, Hong Kong Polytechnic University, China, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, and Takada Laboratory, Tokyo Institute of Technology, Japan. His primary research interests are in various aspects of multiple antenna systems, particularly the interplay between antennas, propagation channels and signal processing Dr. Lau is an Associate Editor for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION and a Guest Editor of the 2012 Special Issue on MIMO Technology for the same journal. From 2007 to 2010, he was a Co-Chair of Subworking Group 2.2 on “Compact Antenna Systems for Terminals” (CAST) within EU COST Action 2100. Since 2011, he is a Swedish national delegate and the Chair of Subworking Group 1.1 on “Antenna System Aspects” within COST IC1004.

Zhinong Ying (SM’05) is an expert of antenna technology in the Network Research Lab., Technology office, Sony Ericsson Mobile Communication AB, Lund, Sweden. He joined Ericsson AB in 1995. He became Senior Specialist in 1997 and Expert in 2003 in his engineer career at Ericsson. His main research interests are small antennas, broad and multi-band antenna, multi-channel antenna (MIMO) system, near-field and human body effects and measurement techniques. He has been Guest Professor at Zhejiang University, China since 2002. He has authored and

coauthored over 80 papers in various of journal, conference and industry publications. He holds more than 70 patents and pending in the antenna and mobile terminal areas. He contributed a book chapter to the well known Mobile Antenna Handbook 3rd edition. He invented and designed various types of multi-band antennas and compact MIMO antennas for the mobile industry. One of his contributions in the 1990s is the development of non-uniform helical antenna. The innovative designs are widely used in mobile terminal industry. His patented designs have reached a commercial penetration of more than several hundreds million products in worldwide. Mr. Ying received the Best Invention Award at Ericsson Mobile in 1996 and Key Performer Award at Sony Ericsson in 2002. He was nominated for President Award at Sony Ericsson in 2004 for his innovative contributions. He served as TPC Co-Chairmen in International Symposium on Antenna Technology (iWAT), 2007, and served as session organizer of several international conferences including IEEE APS, and a reviewer for several academic journals. He was a member of scientific board of ACE program (Antenna Centre of Excellent in the European 6th Framework Programme) from 2004 to 2007.

Sailing He (M’92–SM’98) received the Licentiate of Technology and the Ph.D. degree in electromagnetic theory from the Royal Institute of Technology (KTH), Stockholm, Sweden, in 1991 and 1992, respectively. Since then he has worked at KTH, Stockholm, Sweden, as an Assistant Professor, an Associate Professor, and a Full Professor. He is also with Zhejiang University (ZJU, China) as a Distinguished Professor of a special program organized by the central government of China, as well as a joint research center between KTH and ZJU. His current research interests include electromagnetic metamaterials, optoelectronics, microwave photonics and biomedical applications. He has first-authored one monograph (Oxford University Press) and authored/coauthored about 400 papers in refereed international journals. He has given many invited/plenary talks in international conferences, and has served in the leadership for many international conferences. Prof. He is a Fellow of OSA (Optical Society of America) and SPIE (The International Society for Optical Engineering).

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Multiple Antenna Systems With Inherently Decoupled Radiators Mauro Pelosi, Mikael Bergholz Knudsen, Member, IEEE, and Gert Frølund Pedersen

Abstract—In multiple antenna systems mutual coupling needs to be minimized. We propose an alternative novel decoupling technique, investigating several multiple antenna configurations for small handsets through measurements and numerical simulations. The influence of different novel designs on performance metrics such as total loss, antenna isolation and envelope correlation coefficient are investigated. By varying antenna impedance bandwidth and antenna location with respect to the handset, both planar inverted F antenna (PIFA) and inverted F antennas (IFA) were investigated in different UMTS frequency bands in proximity with the user’s body. Results show that antennas may experience very different losses and envelope correlation coefficients depending on their relative position with respect to the handset, as the influence of the user’s hand is not symmetrical in most cases. Narrow-band antennas are inherently decoupled when integrated on the same handset, while also other parameters such as frequency duplex distance and interaction with the user’s body influence the mutual coupling. Index Terms—Hand phantom, isolation, multiple input multiple output (MIMO) systems, small antennas.

of the other radiator instead [1]. Moreover, antennas exhibiting high mutual coupling are also expected to be highly correlated, resulting in poor MIMO performance [2]. When antennas insist on the same ground-plane structure they utilize it to enhance their radiation [3]. However, the effects resulting from the combination of the chassis and the antennas are very complicated, and sometimes counterintuitive phenomena are observed. In fact reducing the distance between antennas may have the unexpected effect of lowering the mutual coupling, as the contribution of finite-sized ground-planes needs to be taken into account [4]. Despite several techniques have already been proposed in literature in order to mitigate the effect of the mutual coupling in small handsets, their practical implementation in a commercial product is not mature yet. In fact the non-idealities and the additional complexities in the proposed solutions often do not pay off enough to justify their integration. A. Decoupling Methods Review

I. INTRODUCTION

M

OBILE terminals’ market is facing a growing demand for a panoply of new services, as multiple communication standards need to be supported. Small terminal antennas cannot be designed as single-port components anymore, as they have to coexist and interact with multiple radiators collocated on the same printed circuit board (PCB). Having a good isolation and a low envelope correlation coefficient is fundamental to achieve good overall performance in multiple antenna systems for diversity and MIMO purposes. However, improving isolation is one of the most challenging tasks, as when conventional multiple antennas share the same ground-plane at low frequencies, the PCB acts as the main radiator; it is therefore difficult to achieve satisfactory antenna isolation because of the high coupling. The mutual coupling compromises the efficiency of a multiple antenna system, as a certain fraction of the available power delivered to one antenna is not radiated but dissipated in the load Manuscript received June 01, 2010; revised May 28, 2011; accepted July 25, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. This work was supported by the Smart Antenna Front End (SAFE) Project within the Danish National Advanced Technology Foundation framework. M. Pelosi and G. F. Pedersen are with the Section of Antennas, Propagation and Radio Networking (APNet), Department of Electronic Systems, Faculty of Engineering and Science, Aalborg University, DK-9220 Aalborg, Denmark (e-mail: [email protected]; [email protected]). M. B. Knudsen is with the Intel Mobile Communications Denmark Aps, DK-9220 Aalborg Øst, Denmark (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173437

Existing decoupling methods can be broadly grouped into five categories: 1) Antenna Spacing and Angular Orientation Variation: The earlier intuitive attempts to lower the mutual coupling between antenna arrays have always been to keep a reasonable distance between the radiating elements [1]. However a miniaturization of the array size has become an indispensable feature in small handsets, not allowing anymore a sufficient spacing between array elements [5]. It has already been shown that mutual coupling mainly depends on the distance between the open-ended sides of PIFA antennas [6]. However, as the mutual coupling also depends on the surface-current distribution on the PCB [7], a larger spacing does not automatically results in better isolation level [4]. As the relative angular orientation of the PIFAs is also playing a role in the mutual coupling mechanism [6], it is clear that a proper design process needs to include a methodical investigation of the possible solutions, keeping always in mind that sometimes the best design option in Free Space (FS) is not the most appropriate when the effect of the human user is properly taken into account [8]. 2) Decoupling Networks: The use of decoupling networks for closely spaced antennas is proposed in several works [10]–[14], and intends to introduce an additional impedance matching network. Despite the proposed solutions provide satisfactory results, often they fail to be to be feasible in practical mobile devices [14]. In fact a decoupling network exhibits ohmic losses due to the non-idealities in the components [10] and can drastically reduce the usable space on the handset. Moreover it seems that the provided decoupling is

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very narrow-band in nature [11], following a trend similar to Fano’s law for impedance matching [15], [16]. 3) Parasitic and Coupling Elements: Another possibility that has been well-studied is the use of distributed parasitic elements in between the radiators that serve the same purpose of a decoupling network realized with lumped components [17]–[19]. By field cancellation, the element is able to artificially add a coupling path between the radiators [17]. Despite this solution has the advantage of suffering less from ohmic losses, its practical implementation is conditioned and limited to particular configurations, as the decoupling can be very sensitive to small changes in the close by environment of the antennas [17]. The design procedure of these parasitic elements differs from the analytical formulation of the aforementioned decoupling networks. In fact the final structure is often a sub-optimal result of an optimization process that tries to minimize the footprint of the parasitic element and maximize both decoupling bandwidth and isolation level. This approach may lead to reduced physical insight, as the underlying coupling mechanisms are often too complicated to be properly investigated analytically. 4) Defected Ground-Plane Structures: The possibility of using defected ground-plane structures has been explored in several works [20]–[24]. This solution intends to embed filtering capabilities in the PCB by modifying the ground-plane structure itself. Despite the reached isolation levels might seem very appealing, often the modifications in the ground-plane structure are so severe and unrealistic [20] that no practical handset would be able to bear it. In fact the industrial design of mobile phones poses strict limitations on the allowed modifications, imposing to the antenna designer several “forbidden areas” that cannot be violated. Having slits in the middle of a typical bar-type mobile phone with antennas at the top and bottom of the PCB is thereby not feasible, while for clamshell models the slits might be put in the hinge area with less problems. 5) Neutralization Lines: More recently the use of neutralization lines between different antennas has been very popular in literature [4], [25]–[28], providing many interesting designs. The neutralization line proposes to create an additional coupling path opposite to the original one [4]. This is achieved by changing the shape, width and orientation of the neutralization line with respect to the antennas, as again no general rule exists due to the complicated coupling interaction of the ground-plane with the antennas. This method can be identified as a generalization of the parasitic element decoupling technique, with the possibility of positioning neutralization lines either between the radiators [4] or between the ground-plane and the individual radiators [27]. The solution offers a high degree of flexibility, allowing also dual-band operation [28]. However, it is still unclear the real performance of this technique when the influence of the user’s hand is properly taken into account [8], as the corresponding detuning might result in spoiling the very sensitive decoupling mechanism. Moreover, at very low frequencies the footprint would be too large [29]. B. Proposed Decoupling Method More and more antennas have to be integrated in a limited volume. The concurrent trend towards size reduction is counter-

acted by fundamental limitations for small antennas operating in a given volume, so that a tradeoff between bandwidth, efficiency and physical size has always to be established [30]. Consequently, a small antenna size and high antenna efficiency can coexist only sacrificing the impedance bandwidth. A bandwidth reduction has always been seen as a drawback in conventional antenna design, as this leads to the impossibility of covering all the frequency range required by a given communication standard. However, if proper countermeasures are taken, this impairment could become a benefit. In fact if the antennas are narrow-band, their isolation is expected to be inherently better, as they are electrically smaller. In full-duplex radio communication systems the radio transmitter is active at the same time as the radio receiver, using only one radiator for both receiving and transmitting frequency bands. If we imagine switching to a novel paradigm where we separate receiving and transmitting antennas by using two individual radiators exhibiting a higher isolation, the requirements on the duplex filters could be potentially lowered. This approach is called hereinafter transceiver separation mode (TSM). In this paper we will study the influence of the impedance bandwidth on different performance metrics such as total efficiency, antenna isolation and envelope correlation coefficient through finite-difference time-domain (FDTD) simulations and measurements. Numerical simulations offer the advantage of performing huge parametric investigations, which are very important in the preliminary design stage, as they avoid the measurement biases and uncertainties [31]. By using two antenna types, the PIFA and the IFA radiating in different frequency bands, two distinct operating modes will be investigated: the MIMO mode (MM) and the transceiver separation mode respectively. In MIMO mode two antennas resonating at the same frequency for a given UMTS band are present at the same time on the handset. In transceiver separation mode individual antennas only cover half of the duplex for each corresponding UMTS band, the transmitting (TX) or receiving (RX) half respectively. Recent studies have shown that the antenna total efficiency strongly depends on the way the mobile device is held by the human hand while the user’s head has a minor impact [31], [32]. As handset antennas radiate more and more in close proximity with the human body, its influence cannot be neglected anymore. Moreover, there is a lack of knowledge concerning the impact of the user’s body on antenna isolation and envelope correlation coefficient, as hand phantoms representative of average use have to be used. For this purpose the influence of several hand phantoms will be studied, taking also into account the user’s head. The paper is organized as follows: Section I motivates the proposed investigation providing also a review of existing decoupling methods and proposing a novel paradigm. Section II describes the used antenna performance metrics while Section III explains the parametric simulations setup. Section IV shows some preliminary investigations which compares simulated and measured handsets. Section V describes the parametric simulations results, Section VI proposes design guidelines and Section VII provides concluding remarks.

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II. DESCRIPTION OF THE ANTENNA PERFORMANCE METRICS In our investigation the total efficiencies of the antennas have been calculated in the following way:

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is parallel and it uses the supercomputer facilities at Aalborg University (Fyrkat) [36], allowing demanding simulations to be run in a limited time. B. Handset Characteristics

(1) (2) , and , are the radiation and where total efficiencies of the first and second antenna respectively, while and are the total losses expressed in dB (3) (4) The envelope correlation coefficient can be calculated in a straightforward manner using solely the scattering parameters according to the following equation [33]: (5) However this first solution is not reliable if the antenna system exhibit losses [34], so that we adopted a more precise formulation that computes the envelope correlation coefficient through the complex radiation patterns. Under the assumption of antennas operating in a uniform multi-path environment, we can express the envelope correlation coefficient as [35] (see (6) at the bottom of the page) where

The handset ground-plane has been modeled as a Perfect Electric Conductor (PEC) plate representing the typical dimensions of a bar-type mobile phone (40 mm 100 mm). When IFA antennas were used, the ground-plane size was reduced in order to embed them in the same structure. Though we know that the ground-plane contribution is significant especially at low frequencies, this choice was made to keep the same overall size of the handsets for all designs. C. Antenna Pair Operating Mode In our investigations each antenna pair on the handset was used in two different operating modes: 1) MIMO Mode: In this case each radiator was resonating at the same frequency for a given UMTS band. 2) Transceiver Separation Mode: In this case each individual antenna only covered half of the duplex for the corresponding UMTS band, the transmitting (TX) or receiving (RX) one respectively. D. Antenna Types The PIFAs consisted of a main planar element parallel to the ground-plane. In order to achieve a quarter-wavelength characteristic, the planar element was connected to the ground-plane by a shorting wire. The IFAs consisted of several metallic strips coplanar to the ground-plane.

(7)

E. Antenna Impedance Bandwidth

(8)

1) Normal-band (NOB); 2) Medium-band (MEB); 3) Narrow-band (NAB). We defined the antenna impedance bandwidth as the range of frequencies having a reflection coefficient lower than , satisfying a criterion usually considered acceptable in most handheld devices. Concerning the MIMO mode case, antennas covering the full duplex in a given UMTS band were named “normal-band.” If the antennas only covered half of the frequency duplex they were named “medium-band,” while “narrow-band” antennas represented the case in which only slightly more than one UMTS channel was covered (8 MHz). In the transceiver separation case, normal-band antennas covered only the TX or RX half duplex, while narrow-band ones slightly more than one UMTS channel as in the aforementioned MIMO mode case. Despite the previous definitions do not reflect consolidated design approaches, they are needed to

, and , are the vertical and horizontal polarized complex radiation patterns of antennas 1 and 2 respectively, while is the solid angle for a spherical coordinate system. XPR stands for cross-polar discrimination and in our case are equal to 1 because of the multi-path environment hypothesis. III. PARAMETRIC SIMULATIONS SETUP The following paragraphs describe in detail the parametric numerical investigations that were performed in this study. A. FDTD Simulation Code The numerical simulations were conducted using our in-house FDTD code, choosing a space step size of 1 mm and an energy based termination criterion. The FDTD code

(6)

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TABLE I FREQUENCY RANGE AND RESONANCE FREQUENCY FOR DIFFERENT UMTS FREQUENCY BANDS

AND

FOR

TABLE II DIFFERENT UMTS FREQUENCY BANDS AND IMPEDANCE BANDWIDTHS

TABLE III DESCRIPTION OF ALL ANTENNA PAIRS; ANTENNA PAIRS 1–39 ARE USED IN MIMO MODE, WHILE 40–65 ONES IN TRANSCEIVER SEPARATION MODE Fig. 1. Antenna pair configurations.

better comprehend the influence of the antenna impedance bandwidth. It is then understood that antennas not covering the full range of frequencies will need a frequency tuning stage in a later practical implementation. F. UMTS Frequency Band In order to investigate the effect of different frequencies and duplex distances, several UMTS bands were investigated: 1) Band I (BI); 2) Band II (BII); 3) Band V (BV). The corresponding frequency ranges and resonance frequencies can be found in Table I. G. Antenna Location The location of the antenna with respect to the handset is a very important feature, as it influences many different performance metrics. In our study four different locations were chosen: Top Left (TL), Top Right (TR), Bottom Left (BL), and Bottom Right (BR). H. Antenna Pair Configurations Each antenna pair configuration consists of a combination of the antenna type and the location with respect to the handset (Fig. 1). All antenna pairs are described in Table III. I. Geometrical Features of Antennas The geometry of the antennas was simple and without the use of matching circuits. The impedance bandwidth of the PIFA antennas was mainly determined by the height of the main plate with respect to the ground-plane , while for the IFA antennas by the distance between the top IFA strip and the ground-plane . Table II shows the aforementioned features for different UMTS bands and impedance bandwidths. Fig. 2 shows the geometrical features of both PIFA and IFA antennas for different UMTS frequency bands and impedance bandwidths in MIMO mode. For brevity reasons only configurations 3 and 5 are shown, while as in MIMO mode both antennas are identical, only the antennas at the top of the handset

are displayed. The geometrical features of the other configurations (C1, C2, C4) are very similar to the aforementioned antennas, as only minor adjustments were needed to retune them at the correct resonance frequency. Concerning the transceiver separation mode, the geometry of the antennas was slightly adjusted to tune them at the corresponding TX or RX resonance frequency, so that their layout is not shown. The shorting wire for PIFA antennas was always positioned at the right top edge of the main plate for bands I, II, while in band V it was located at its top left edge; the feeding was very close to the shorting wire in all cases (Fig. 2). In the IFA antenna case the distance between the shorting and feeding strip was slightly modified in different configurations to achieve a better impedance matching. In order to resonate at band V PIFA antennas had a dielectric substrate of , while IFA antennas a 1 mm thick relative permittivity dielectric superstrate of . J. Antenna Pair Proximity With Phantoms The antenna pair on the handset was studied in FS and while in proximity with the user’s hand. The influence of the user’s head was investigated by using the Specific Anthropomorphic Mannequin (SAM) phantom according to the standard right cheek position [37]. Thanks to a recent grip study [32], it was possible to generate detailed Computer Aided Design (CAD)

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Fig. 3. Hand phantoms (H1-H6).

TABLE IV DESCRIPTION OF THE HAND PHANTOMS

Fig. 2. Antenna layout for several configurations; the ground-plane is shown in grey, and only its top part is displayed. The layout is shown in scale; the small grey round markers represent the feeding point, while the white ones represent the shorting point.

models of hand phantoms consistent with the average use. The dimensions of the hand phantoms were adjusted according to a hand anthropometric study [38], while their dielectric properties were chosen to comply with the homogeneous material representing an average of different tissues [39]. Six different grips were investigated (H1-H6), consisting of different palm-handset gaps (firm/soft grip styles) and index finger locations as described in Fig. 3 and Table IV. As the position of the index finger is one of the main factors in determining the interaction of the antenna with the human hand [8], different configurations were studied. As in the handset different heights were used for the PIFA antennas, the gap between the hand phantoms and the PIFA main element was not constant. The reason for this choice was to investigate the potential of a buffer air superstrate as in [40], which showed beneficial effects in terms of total efficiency and proximity effects robustness. This means that there was always a 10 mm gap between the ground-plane and the tip of the index finger. IV. PRELIMINARY INVESTIGATIONS A. Simulation and Measurement Setup The purpose of this section is to validate the concept of narrow-band antenna decoupling by comparing a significant set of configurations in TSM mode, simulating, manufacturing and measuring four handsets in FS. Both high (Band I) and low (Band V) UMTS frequency bands are studied, comparing normal-band and narrow-band antennas. The four handsets consisted of a pair of PIFA antennas on a ground-plane of size

Fig. 4. Simulated and manufactured handsets 1–4. Handset 1 had a white Sty. rofoam brick only used as support

40 mm 100 mm. The geometrical properties of the handsets are illustrated in Fig. 4 and summarized in Table V that also shows results. B. Simulation and Measurement Results The following Figs. 5, 6 show a comparison between the simulated and measured scattering parameters , , and for all 4 handsets. A fair agreement is observed despite a frequency shift is observed due to imperfections in the manufacturing and the cable influence in the low band. Fig. 5 refers to the comparison between handsets 1 and 2 in the high band (BI), showing that when narrow-band antennas are used it is possible to have a isolation. Fig. 6 compares handsets 3 and 4 in the low band (BV), showing that of isolation are still possible despite the high original coupling of normal-band

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Fig. 5. Comparison of the simulated and measured scattering parameters for handsets 1, 2 (band I).

Fig. 6. Comparison of the simulated and measured scattering parameters for handsets 3, 4 (band V).

TABLE V DESCRIPTION OF THE MANUFACTURED AND SIMULATED HANDSETS 1–4 WITH TOTAL EFFICIENCY. THE TOTAL EFFICIENCY IS SIMULATED IN FDTD AND MEASURED IN ANECHOIC CHAMBER IN CORRESPONDENCE OF THE BEST IMPEDANCE MATCH OF EACH RECEIVING ANTENNA (RX)

Concerning band I, the total efficiencies are very good in both normal-band and narrow-band cases. The high loss in the measured narrow-band antenna in band V can be explained by the fact that ohmic losses tend naturally to increase as the bandwidth shrinks, while other effects such as imperfect soldering, contact losses and non-ideal dielectric substrate concur in lowering the total efficiency. This happens while keeping the mutual coupling very low, which is instead the dominant loss factor in the normal-band antennas. V. PARAMETRIC SIMULATIONS RESULTS A. MIMO Mode

antennas. Table V shows the simulated and measured total efficiencies for handsets 1–4.

1) Total Loss: In this paragraph the results concerning the total loss are presented, combining in a single figure of merit absorption, coupling, and mismatch loss according to (3). Fig. 7 shows the total loss in free space for different configurations and

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Fig. 7. Total loss in free space for MIMO mode; A1 and A2 refer to antenna 1 and 2 respectively, as shown in Fig. 1.

Fig. 8. Total loss in presence of hand phantom 1 for MIMO mode; A1 and A2 refer to antenna 1 and 2 respectively, as shown in Fig. 1.

UMTS bands, therefore only coupling and mismatch losses are accounted for. Total loss is generally low in bands I, II, while in band V it is higher due to the stronger coupling at lower frequencies. As the impedance bandwidth of the antennas shrinks, a reduction in the total loss is observed, as the coupling is lower when antennas get narrow-band. Fig. 8 shows the total loss when the handset is held by the human hand. The hand phantom is H1, representing a typical firm grip style with the position of the index finger in the proximity of the top-right handset region. UMTS bands I, II exhibit comparable loss as they are closer in frequency, while the loss for band V is higher. In configuration 1 the top-left antenna is less affected by the proximity of the hand, as the index finger is not close. When both antennas are at the bottom (C2), they suffer a similar loss because of the effect of the palm. Similar consideration can be done for C3, C4, and C5, where the antennas are more or

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Fig. 9. Total loss in presence of phantom 1 for MIMO mode; A1 and A2 refer to antenna 1 and 2 respectively, as shown in Fig. 1.

less affected depending on their relative position with respect to the hand. By comparing bottom antennas in configurations C4 and C5, it can be observed that IFA antennas experience the lowest loss, as they exhibit a larger gap with respect to the palm. Narrow-band antennas generally exhibit the lowest loss in bands I, II, while the situation is different in band V. In fact the antennas closer to the palm suffer also a larger frequency detuning, which in the narrow-band case translates to a higher mismatch loss. Despite narrow-band antennas exhibit the lowest coupling loss, if they are strongly detuned their total loss may increase. By comparing the total loss for both antennas (A1-A2), it can be seen how the influence of the hand may significantly affect the antennas in different ways. Similar tendencies were found for the other hand phantoms’ configurations, where soft grip hands experienced the smallest losses. In Fig. 9 the SAM phantom is added to H1, showing a trend similar to Fig. 8. The presence of the SAM does not further degrade the antenna performance, showing a modest increase in the total loss confirming that the influence of the hand is more important than the head’s one. 2) Worst Case Isolation: We define the worst case isolation as the maximum value of in dB over the frequency range corresponding to a particular bandwidth (Fig. 10). This peak value in MIMO mode is typically located in correspondence of the antenna resonance frequency in free space, while it can be shifted if the antennas are detuned because of the interaction with the human body. In Fig. 11 we compare the worst case isolation for different normal-band antenna configurations. The presence of the hand generally improves the isolation when compared to the free space case. Soft grip hands have better isolation than firm grip ones. This may be explained by the fact that soft grip hands influence the detuning of the antennas in asymmetric ways, thus leading to an increase in isolation. When moving from band I to band II and V, the isolation gets worse; this is due to the higher coupling at lower frequencies. Similar conclusion can be derived for the medium-band case. Concerning band V in Fig. 12 it is important to remark that the high isolation is mainly determined by the detuning of the antennas.

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Fig. 10. Example of worst-case isolation.

Fig. 12. Worst-case isolation in free space and in presence of hand phantoms 1–6 with narrow-band antennas in MIMO mode.

Fig. 11. Worst-case isolation in free space and in presence of hand phantoms 1–6 with normal-band antennas in MIMO mode.

Fig. 13. Worst-case isolation for different configurations in MIMO mode.

In configurations 4 and 5 soft grip hands have worse isolation than firm grip ones. This may be explained by noting that soft grip hands exhibit a larger gap between the antennas and the palm of the hand, leading therefore to less detuning and worse isolation. In Fig. 13 it can be seen how narrow-band antennas generally lead to a better isolation. There is little difference between the case with only hand and hand with SAM, as most of interaction is driven by the hand alone. 3) Envelope Correlation Coefficient: In Fig. 14 it can be seen the envelope correlation coefficient in free space for different configurations depending on the impedance bandwidth of the antennas. is typically lower in bands I, II, and when narrow-band antennas are used. In band V the envelope correlation coefficient is higher, as in this frequency range the coupling is stronger. When narrow-band antennas are used they exhibit higher than their normal-band counterparts. This may be due to the fact that besides mutual coupling, also the level of mismatch influences the envelope correlation coefficient, so that a bad mismatch may further correlate the antennas.

In Fig. 15 it is shown the influence of the hand phantom 1 on the envelope correlation coefficient. A higher is generally observed, especially in the configurations with larger total loss. In configuration 2 narrow-band antennas exhibit a smaller loss, so that the envelope correlation coefficient gets smaller. In Fig. 16 normal-band antennas are compared, studying the influence of both hand and SAM phantoms. Concerning bands I, II, there is small difference in the envelope correlation coefficient between different phantoms’ configurations, while in band V the SAM has a larger impact. Similar considerations can be done for Fig. 17, where the envelope correlation coefficient is still low for bands I, II but higher for band V. B. Transceiver Separation Mode 1) Total Loss: In Fig. 18 the total loss is displayed in the free space case for different configurations. The total loss is always lower for narrow-band antennas, as they exhibit better isolation and therefore less coupling loss. The benefit of narrow-band antennas is more evident at lower frequencies, where the coupling loss is higher. In Fig. 19 the in-

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Fig. 14. Envelope correlation coefficient in free space in MIMO mode.

Fig. 15. Envelope correlation coefficient in presence of hand phantom 1 in MIMO mode.

fluence of the user’s hand is shown using hand phantom 1 (H1). It can be seen that narrow-band antennas have always a total loss lower than their normal-band counterparts. This beneficial effect is more evident in band V, as both coupling and absorption loss are smaller because of a reduced interaction with the hand phantom. There is a similar trend for the remaining hand phantoms, with firm grip styles (H1-H3) having larger total losses than soft grip ones (H4-H6). Depending on the position of the index finger and the proximity of the palm of the hand the different configurations are diversely affected. 2) Worst Case Isolation: Fig. 20 displays the worst-case isolation for normal-band antennas for different configurations. Considerations similar to the MIMO mode can be made; the coupling increases from band I to band V, as we are moving towards lower frequencies. The presence of the user’s hand is generally beneficial to the isolation, while depending on the grip style the coupling may change. Comparing Figs. 17 and 18 we

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Fig. 16. Envelope correlation coefficient with normal-band antennas in MIMO mode.

Fig. 17. Envelope correlation coefficient with narrow-band antennas in MIMO mode.

can see how narrow-band antennas always have the best isolation when compared to normal-band ones. VI. FURTHER DESIGN INSIGHTS Optimizing an antenna design to meet today’s requirements is becoming more and more challenging. Beside single antenna specifications such as total radiated power (TRP) or total isotropic sensitivity (TIS), no concise figure of merit (FOM) exists so far to assess the performance of multiple antenna systems [41]. The standardization efforts of the just concluded COST Action 2100 have suggested throughput as one of the FOMs to focus on [42]. However, considering a given rich scattering environment a high throughput may either depend on smart signal processing or on a well designed antenna system. Despite the need of cross-layer optimization, it is still important to properly understand which parameters influence MIMO performance. A good performance for a MIMO array requires that all the antennas should exhibit both similar and high

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Fig. 18. Total loss in free space in transceiver separation mode; TX and RX represent the transmitting and receiving antennas respectively, and their location with respect to the handset is described in Table III.

Fig. 19. Total loss in presence of hand phantom 1 in transceiver separation mode; TX and RX represent the transmitting and receiving antennas respectively, and their location with respect to the handset is described in Table III.

mean effective gain (MEG). Furthermore the cross correlation between the array branches should be low. If the MEGs are either low and dissimilar, the cross correlation plays a minor role as even being low would not help in recovering the MIMO performance because of the fact that the other performance metrics are already compromised. On the other hand, if both branches exhibit good and similar MEGs, the cross-correlation role is more determinant. However correlation is very seldom an issue in small handsets, as the presence of the human user always has decorrelating effects [43]. As cellular systems are inherently interference limited [44], the antenna array can still provide some benefits by offering beamforming and interference cancellation capabilities in case the two branches do not have similar MEGs. All the aforementioned considerations imply that the most important things in a MIMO array for small handsets is the MIMO-favorable channel, the received

Fig. 20. Worst-case isolation in free space and in presence of hand phantoms 1–6 with normal-band antennas in transceiver separation mode.

Fig. 21. Worst-case isolation in free space and in presence of hand phantoms 1–6 with narrow-band antennas in transceiver separation mode.

signal level and the similarities of the total efficiencies in both branches. If for example one antenna suffers severely from absorption loss because of the influence of the hand while the other one is less affected, this might result in very poor MIMO performance independently of correlation level [45], reducing MIMO to a bare antenna selection scheme. Having a good signal level requires to have high total antenna efficiencies, meaning that various parameters such as mismatch, coupling and absorption loss need to be jointly minimized. Mismatch loss depends on the antenna impedance being different from the characteristic reference impedance, and typically a well-designed antenna does not need additional matching networks. In literature we find several examples of adaptive impedance matching techniques that claim to provide significant benefits [46]–[48], but often they focus on worst case scenarios that have a low probability to happen in realistic mobile phone usage. As mismatch loss is most of times in the order of 0.5–1.5 dB for typical configurations including the influence

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of the user’s body [8], an additional device to tune back the impedance match perfectly to 50 would not be justified because of the additional complexities and losses. As shown in several contributions absorption loss is more significant than mismatch loss [8], [32], however little work has been done so far in order to mitigate this problem. In fact absorption loss is often seen as inevitable and common to any mobile device, while the recent events of the iPhone 4 “antenna-gate” have made aware even the general public of the fact that any antenna design must be done considering the effect of the human user and especially the hand’s influence. A good antenna design results in an improved link budget that has positive effects on both battery duration and network operators. Unfortunately there is no general rule in designing an antenna system for a small handset, as this is often a strict tradeoff between the conflicting expectations of antenna engineers and industrial designers. It is then very important to conduct proper usability studies before fixing the location of the antennas, as particular “death-grips” may result in a complete spoiling of the antenna performance. It has already been shown that keeping the fingers or the palm of the hand as far as possible from the antenna region is always beneficial [8], but often is very hard to optimize for talk and data modes at the same time. It is good practice to embed a certain degree of robustness in the antenna radiation mechanism [48], so that the disturbance caused by the close by environment can be minimized. This is achievable by confining the near fields of the antennas, by choosing a proper location and finally by respecting small clearance areas around the antenna structure [40]. It is also important to minimize coupling loss as much as possible as its contribution to the total efficiency is significant especially at the lower frequencies. However the choice of any decoupling technique needs to be considered carefully, as the additional complexities might results in a poor net benefit. VII. CONCLUSION In this paper we investigated through measurements and FDTD simulations two different cases, the MIMO mode and the transceiver separation mode. By using different antenna types for UMTS bands I, II, and V, it was possible to study the influence of the impedance bandwidth on several performance metrics such as total loss, isolation and envelope correlation coefficient in MIMO mode. The influence of the user’s body has been investigated using different hand grips and the SAM phantom. By changing the location of the antennas with respect to the handset several configurations have been investigated. Concerning the transceiver separation mode, a novel paradigm has been introduced, using individual antennas to cover the transmitting and receiving bands of the corresponding frequency duplex with the aim of lowering the requirements of the duplex filters by providing a better isolation. Results confirm that absorption loss is the most relevant factor in determining the total loss. The user’s hand is the main responsible for absorption loss, while the head does not contribute significantly. Firm grip hand phantoms have higher losses than soft grip ones, as the most important features are the position of the index finger and the palm-handset gap; a buffer air superstrate is confirmed to be always beneficial in reducing the interaction of the antennas with the user’s hand. While mismatch loss

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is not an issue in bands I, II, it is more important in band V when narrow-band antennas are detuned. The location of the antennas on the handset is very important. In fact depending on the location with respect to the handset each antenna may experience significantly different loss because of the proximity of the human hand. In fact the gap between the radiating element and the palm or the index finger can drastically change the total loss of the antennas. The envelope correlation coefficient has been derived using the far field pattern approach for different configurations, showing in free space low values for bands I, II and higher values at lower frequencies where the coupling was stronger. The gets generally smaller when the impedance bandwidth shrinks, but if a high level of mismatch is present the envelope correlation coefficient may rise. When the total loss increases because of the user’s body interaction an increase in the is observed, especially in bands I, II. In band V the situation is different, as the smaller coupling is beneficial to the envelope correlation coefficient. Concerning the isolation, many different factors were found to concur in the isolation potential of one antenna pair. The coupling is stronger at lower frequencies as the ground-plane becomes the main radiator, while a smaller frequency duplex distance correspond to a lower isolation. When the antenna impedance bandwidth shrinks, the isolation tends to improve, and this effect is more evident in the transceiver separation mode. If the antennas exhibit a bad impedance matching at a given frequency, they will have a better isolation. The location and orientation of the antennas concur in determining the antenna isolation; however because of the radiation on a finite size ground-plane a smaller antenna spacing does not always translate in a smaller mutual coupling. Using two different antenna types may help in getting a better isolation, while the close proximity of the human hand with the antennas has generally a beneficial effect, as a better isolation can be achieved. However this improvement has to be traded-off with other negative phenomena such as frequency detuning and absorption loss increase. In brief narrow-band antennas exhibit attractive features that may lead to novel design paradigms that may lower the requirements of the duplex filters. Though high losses have been observed in the manufactured and measured handsets in the low band, more research is needed to understand the loss mechanism, especially when narrow-band antennas are used, as the high current flow may increase the ohmic losses. The combination of MIMO mode with the transceiver separation mode is currently under investigation. As a general conclusion it is important to remark that the antenna design cannot ignore the influence of the human body, as the success of multiple antenna systems strongly depend on having high efficiency, small coupling and low envelope correlation coefficient. ACKNOWLEDGMENT The authors wish to express their gratitude to the Danish Center for Scientific Computing (DCSC). REFERENCES [1] R. G. Vaughan and J. B. Andersen, “Antenna diversity in mobile communications,” IEEE Trans. Veh. Technol., vol. 36, no. 4, pp. 149–172, Nov. 1987.

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[2] A. Derneryd and G. Kristensson, “Signal correlation including antenna coupling,” Electron. Lett., vol. 40, no. 3, pp. 157–159, Feb. 2004. [3] O. Kivekäs, J. Ollikainen, T. Lehtiniemi, and P. Vainikainen, “Effect of the chassis length on the bandwidth, SAR, and efficiency of internal mobile phone antennas,” Microw. Opt. Technol. Lett., vol. 36, pp. 457–462, Mar. 2003. [4] A. Diallo, C. Luxey, P. L. Thuc, R. Staraj, and G. Kossiavas, “Enhanced two-antenna structures for universal mobile telecommunications system diversity terminals,” IET Microw. Antennas Propag., vol. 2, pp. 93–93, 2008. [5] P. Vainikainen, J. Holopainen, C. Icheln, O. Kivekäs, M. Kyrö, M. Mustonen, S. Ranvier, R. Valkonen, and J. Villanen, “More than 20 antenna elements in future mobile phones, threat or opportunity,” in Proc. 3rd Eur. Conf. on Antennas Propag. (EuCAP’2009), Mar. 23–27, 2009, pp. 2940–2943. [6] H. Carrasco, H. D. Hristov, R. Feick, and D. Cofré, “Mutual coupling between planar inverted-F antennas,” Microw. Opt. Technol. Lett., vol. 42, no. 3, pp. 224–227, Aug. 2004. [7] K.-L. Wong, J.-H. Chou, S.-W. Su, and C.-M. Su, “Isolation between GSM/DCS and WLAN antennas in a PDA phone,” Microw. Opt. Technol. Lett., vol. 45, pp. 347–347, 2005. [8] M. Pelosi, O. Franek, M. B. Knudsen, G. F. Pedersen, and J. B. Andersen, “Antenna proximity effects for talk and data modes in mobile phones,” IEEE Antennas Propag. Mag., vol. 52, no. 3, pp. 15–27, Jun. 2010. [9] B. K. Lau, J. B. Andersen, G. Kristensson, and A. F. Molisch, “Impact of matching network on bandwidth of compact antenna arrays,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3225–3238, Nov. 2006. [10] C. Volmer, J. Weber, R. Stephan, K. Blau, and M. A. Hein, “An eigenanalysis of compact antenna arrays and its application to port decoupling,” IEEE Trans. Antennas Propag., vol. 56, no. 2, pp. 360–370, Feb. 2008. [11] B. K. Lau, J. B. Andersen, G. Kristensson, and A. F. Molisch, “Impact of matching network on bandwidth of compact antenna arrays,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3225–3238, Nov. 2006. [12] J. B. Andersen and H. Rasmussen, “Decoupling and descattering networks for antennas,” IEEE Trans. Antennas Propag., vol. 24, no. 6, pp. 841–846, Nov. 1976. [13] S.-C. Chen, Y.-S. Wang, and S.-J. Chung, “A decoupling technique for increasing the port isolation between two strongly coupled antennas,” IEEE Trans. Antennas Propag., vol. 56, no. 12, pp. 3650–3658, Dec. 2008. [14] R. A. Bhatti, S. Yi, and S. Park, “Compact antenna array with port decoupling for LTE-standardized mobile phones,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 1430–1433, 2009. [15] R. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances,” J. Franklin Inst., vol. 249, no. 1, 2, pp. 57–3, 1950. [16] G. Shaker, S. Safavi-Naeini, and N. Sangary, “Q-Bandwidth relations for the design of coupled multi-element antennas,” in Proc. IEEE Antennas Propag. Society Int. Symp. (APSURSI’2009), Jun. 1–5, 2009, pp. 1–4. [17] A. C. K. Mak, C. R. Rowell, and R. D. Murch, “Isolation enhancement between two closely packed antennas,” IEEE Trans. Antennas Propag., vol. 56, no. 11, pp. 3411–3419, Nov. 2008. [18] P. Ferrer, J. Arbesu, and J. Romeu, “Decorrelation of two closely spaced antennas with a metamaterial AMC surface,” Microw. Opt. Technol. Lett., vol. 50, no. 5, May 2008. [19] A. Abe, N. Michishita, Y. Yamada, J. Muramatsu, T. Watanabe, and K. Sato, “Mutual coupling reduction between two dipole antennas with parasitic elements composed of composite right-/left-handed transmission lines,” in Proc. IEEE Int. Workshop on Antenna Technol. (iWAT’2009), Mar. 2–4, 2009, pp. 1–4. [20] C. Chi-Yuk, C. Chi-Ho, R. D. Murch, and C. R. Rowell, “Reduction of mutual coupling between closely-packed antenna elements,” IEEE Trans. Antennas Propag., vol. 55, no. 6, pp. 1732–1738, Jun. 2007. [21] G. Yue, C. Xiaodong, Y. Zhinong, and C. Parini, “Design and performance investigation of a dual-element PIFA array at 2.5 GHz for MIMO terminal,” IEEE Trans. Antennas Propag., vol. 55, no. 12, pp. 3433–3441, Dec. 2007. [22] C. Younkyu, J. Seong-Sik, D. Ahn, C. Jae-Ick, and T. Itoh, “High isolation dual-polarized patch antenna using integrated defected ground structure,” IEEE Microw. Wireless Compon. Lett., vol. 14, no. 1, pp. 4–6, Jan. 2004. [23] H. Li, J. Xiong, and S. He, “A compact planar MIMO antenna system of four elements with similar radiation characteristics and isolation structure,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 1107–1110, 2009.

[24] F.-G. Zhu, J.-D. Xu, and Q. Xu, “Reduction of mutual coupling between closely-packed antenna elements using defected ground structure,” Electron. Lett., vol. 45, no. 12, pp. 601–602, Jun. 2009. [25] A. Diallo, C. Luxey, P. Le Thuc, R. Staraj, and G. Kossiavas, “Enhanced two-antenna structures for universal mobile telecommunications system diversity terminals,” IET Microw. Antennas Propag., vol. 2, no. 1, pp. 93–101, Feb. 2008. [26] A. Chebihi, C. Luxey, A. Diallo, P. Le Thuc, and R. Staraj, “A novel isolation technique for closely spaced PIFAs for UMTS mobile phones,” IEEE Antennas Wireless Propag. Lett., vol. 7, pp. 665–668, 2008. [27] H. Minseok and C. Jaehoon, “Small-size printed strip MIMO antenna for next generation mobile handset application,” Microw. Opt. Technol. Lett., vol. 53, no. 2, pp. 48–352, 2011. [28] I. Dioum, A. Diallo, C. Luxey, and S. M. Farsi, “Compact dual-band monopole antenna for LTE mobile phones,” in Proc. Loughborough Antennas Propag. Conf. (LAPC), Nov. 8–9, 2010, pp. 593–596. [29] J. Holopainen, O. Kivekäs, C. Icheln, and P. Vainikainen, “Internal broadband antennas for digital television receiver in mobile terminals,” IEEE Trans. Antennas Propag., vol. 58, no. 10, pp. 3363–3374, Oct. 2010. [30] D. M. Pozar, “New results for minimum Q, maximum gain, and polarization properties of electrically small arbitrary antennas,” in Proc. 3rd Eur. Conf. on Antennas Propag. (EuCAP 2009), Mar. 23–27, 2009, pp. 1993–1996. [31] L. Chung-Huan, E. Ofli, N. Chavannes, and N. Kuster, “Effects of hand phantom on mobile phone antenna performance,” IEEE Trans. Antennas Propag., vol. 57, no. 9, pp. 2763–2770, Sep. 2009. [32] M. Pelosi, O. Franek, M. B. Knudsen, M. Christensen, and G. F. Pedersen, “A grip study for talk and data modes in mobile phones,” IEEE Trans. Antennas Propag., vol. 57, no. 4, pp. 856–865, Apr. 2009. [33] S. Blanch, J. Romeu, and I. Corbella, “Exact representation of antenna system diversity performance from input parameter description,” Electron. Lett., vol. 39, no. 9, pp. 705–707, May 2003. [34] P. Hallbjorner, “The significance of radiation efficiencies when using S-parameters to calculate the received signal correlation from two antennas,” IEEE Antennas Wireless Propag. Lett., vol. 4, pp. 97–99, 2005. [35] R. G. Vaughan and J. B. Andersen, “Antenna diversity in mobile communications,” IEEE Trans. Veh. Technol., vol. 36, no. 4, pp. 149–172, Nov. 1987. [36] [Online]. Available: http://www.dcsc.aau.dk/index.php?id=26 [37] Recommended practice for determining the peak spatial-average specific absorption rate (SAR) in the human body due to wireless communications devices: experimental techniques, IEEE Standard 1528, 2003. [38] T. M. Greiner, “Hand anthropometry of US army personnel,” Natick/TR-92/011, 1991. [39] C. Gabriel, “Tissue equivalent material for hand phantoms,” Phys. Med. Biol. PMB-52, pp. 4205–4210, 2007. [40] M. Pelosi, O. Franek, M. B. Knudsen, and G. F. Pedersen, “Influence of dielectric loading on PIFA antennas in close proximity to user’s body,” Electron. Lett., vol. 45, no. 5, pp. 246–247, Feb. 2009. [41] P. Kyosti, J.-P. Nuutinen, and T. Jamsa, “MIMO OTA test concept with experimental and simulated verification,” in Proc. 4th Eur. Conf. on Antennas Propag. (EuCAP’2010), Apr. 12–16, 2010, pp. 1–5. [42] R. Verdone, “Pervasive Mobile & Ambient Wireless Communications,” in COST 2100 Final Report. Berlin: Springer, 2011. [43] B. Yanakiev, J. Ø. Nielsen, M. Christensen, and G. F. Pedersen, “Antennas in real environments,” in Proc. 5th Eur. Conf. on Antennas Propag. (EuCAP’2011), Apr. 11–15, 2011, pp. 1–5. [44] J. G. Andrews, C. Wan, and R. W. Heath, “Overcoming interference in spatial multiplexing MIMO cellular networks,” IEEE Wireless Commun., vol. 14, no. 6, pp. 95–104, Dec. 2007. [45] A. A. H. Azremi, J. Ilvonen, R. Valkonen, J. Holopainen, O. Kivekas, C. Icheln, and P. Vainikainen, “Performance analysis of broadband coupling-Element-Based multiantenna structure for mobile terminal with hand effects,” in Proc. IEEE 21st Int. Symp. on Personal Indoor and Mobile Radio Communications (PIMRC’2010), Sep. 26–30, 2010, pp. 1111–1116. [46] P. Ramachandran, Z. D. Milosavljevic, and C. Beckman, “Adaptive matching circuitry for compensation of finger effect on handset antennas,” in Proc. 3rd Eur. Conf. on Antennas Propag. (EuCAP’2009), Mar. 23–27, 2009, pp. 801–804. [47] E. L. Firrao, A.-J. Annema, and B. Nauta, “An automatic antenna tuning system using only RF signal amplitudes,” IEEE Trans. Circuits Syst. II: Expr. Briefs, vol. 55, no. 9, pp. 833–837, Sep. 2008.

PELOSI et al.: MULTIPLE ANTENNA SYSTEMS WITH INHERENTLY DECOUPLED RADIATORS

[48] J. Anguera, A. Andujar, A. Camps, C. Puente, and C. Picher, “Mitigation of the finger loading effect in handset antennas,” in Proc. 3th Eur. Conf. on Antennas Propag. (EuCAP’2010), Apr. 12–16, 2010, pp. 1–4. Mauro Pelosi was born in 1982 and is from Picinisco, Italy. He received the B.Sc. and M.Sc. degrees (summa cum laude) in telecommunications engineering from University of Cassino, Cassino, Italy, in 2004 and 2007, respectively, and the M.Sc. degree in electrical engineering and the Ph.D. degree in wireless communications from Aalborg University, Aalborg, Denmark, in 2006 and 2009, respectively. Currently, he is a Postdoctoral Fellow at the Department of Electronic Systems, Aalborg University. He is also Deputy Project Manager for the Smart Antenna Front End (SAFE) Project sponsored by the Danish National Advanced Technology Foundation. His research interests include computational electromagnetics, innovative multiple antenna systems and antenna proximity effects with focus on the influence of the user’s body. He is also involved in the COST Action 2100 on “Pervasive Mobile & Ambient Wireless Communications” and the ICT COST Action IC1004 on “Cooperative Radio Communications for Green Smart Environments.”

Mikael Bergholz Knudsen (S’99–M’01) was born in 1964. He received the B.S. degree in electrical engineering from Aarhus Teknikum, Denmark, in 1989, and the M.S. and Ph.D. degrees from Aalborg University, Denmark, in 1992 and 2001, respectively. In 1993, he joined Maxon Telecom A/S, Aalborg, Denmark, where he designed RF circuitry for both analog and digital mobile phones. From 1998 to 2001, he worked as an industrial Ph.D. student for Siemens Mobile Phones A/S, Denmark, while he at the same time studied at Aalborg University, CPK.

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He is now with Intel Mobile Communications Denmark, where he is engaged in the system design and development of RF transceiver chips for mobile phones. His areas of interest include RF system design and handset antenna performance including more than one antenna.

Gert Frølund Pedersen received the B.Sc. E.E. degree (with honors) in electrical engineering from College of Technology, Dublin, Ireland, in 1991, and the M.Sc. E.E. and Ph.D. degrees from Aalborg University, Aalborg, Denmark, in 1993 and 2003, respectively. At present, he is a Full Professor heading the Antennas, Propagation and Radio Networking (APNet) Group at Aalborg University. His research has focused on radio communication for mobile terminals including small antennas, antenna-systems, propagation and biological effects and has more than 100 publications including more than 15 patents. He has also worked as consultant within small antennas and developed more than 50 dedicated designs for small mobile terminals starting with the first internal antenna for mobile phones in 1993 with very low SAR, First internal triple-band antenna in 1998 with low SAR and high efficiency and various antenna diversity systems rated as the most efficient on the market. Recently he has been involved in establishing the method to measure over the air (OTA) communication performance for mobile terminals adopted by 3 GPP for measurements also including the antenna. Further he is involved in small terminals for 4G including several antennas (MIMO systems) and ultrawideband antennas to enhance the data communication. Prof. Pedersen is the Chairman of COST 2100 SWG 2.2 which is working on the coming OTA Standard for multi-antenna terminal testing for 3 GPP and CTIA. He is also the Project Manager for the Smart Antenna Front End (SAFE) Project sponsored by the Danish National Advanced Technology Foundation.

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A Pattern Reconfigurable U-Slot Antenna and Its Applications in MIMO Systems Pei-Yuan Qin, Y. Jay Guo, Senior Member, IEEE, Andrew R. Weily, Member, IEEE, and Chang-Hong Liang, Senior Member, IEEE

Abstract—A new compact pattern reconfigurable U-slot antenna is presented. The antenna consists of a U-slot patch and eight shorting posts. Each edge of the square patch is connected to two shorting posts via PIN diodes. By switching between the different states of the PIN diodes, the proposed antenna can operate in either monopolar patch or normal patch mode in similar frequency ranges. Therefore, its radiation pattern can be switched between conical and boresight patterns electrically. In addition, the plane with the maximum power level of the conical pattern can be changed between two orthogonal planes. Owing to a novel design of the switch geometry, the antenna does not need dc bias lines. The measured overlapping impedance bandwidth of the two modes is 6.6% with a center frequency of 5.32 GHz. The measured radiation patterns agree well with simulated results. The antennas are incorporated in a 2 2 multiple-input-multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system to demonstrate the improvement in system capacity. In the real-time MIMO-OFDM channel measurement, it is shown that compared to omnidirectional antennas, the pattern reconfigurable antennas can enhance the system capacity, with 17% improvement in a line-of-sight (LOS) scenario and 12% in a non-LOS (NLOS) scenario at a signal-to-noise ratio (SNR) of 10 dB. Index Terms—Microstrip antennas, multiple-input-multipleoutput (MIMO), reconfigurable antennas, slot antennas.

I. INTRODUCTION

I

N the past few years, reconfigurable antennas have received significant attention due to their ability to improve the performance of wireless communication systems [1]–[10]. Typical parameters of an antenna that can be reconfigured are frequency, radiation pattern, polarization or combinations of the above. Pattern reconfigurable antennas have the potential to

Manuscript received June 10, 2010; revised May 10, 2011; accepted June 06, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. This work was supported by the DIISR Australia-China special fund CH080270. P.-Y. Qin is with the Science and Technology on Antenna and Microwave Laboratory, Xidian University, Xi’an, Shaanxi 710071, China and also with the Department of Electronic Engineering, Macquarie University, North Ryde, NSW 2109, Australia and CSIRO ICT Centre, Epping, NSW 1710, Australia (e-mail: [email protected]). Y. J. Guo and A. R. Weily are with the CSIRO ICT Centre, Epping, NSW 1710, Australia. C.-H. Liang is with the Science and Technology on Antenna and Microwave Laboratory, Xidian University, Xi’an, Shaanxi, 710071, China. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173439

avoid noise sources by changing the null position, to save energy by better directing the signal toward intended users and to provide larger coverage by redirecting the main beam [7]–[10]. Among the reported pattern reconfigurable antenna designs, several [8]–[10] feature the capability to switch between boresight and conical patterns. A conical radiation pattern is generally one for which the maximum directivity is off boresight (where boresight corresponds to the direction normal to the plane containing the antenna) and the pattern shape resembles a cone. In [8], a wide-band L-probe circular patch antenna with dual feeds was presented. Unfortunately, an integrated matching network consisting of switches needs to be designed in order to reconfigure the radiation pattern electrically. In [9] and [10], single feed pattern reconfigurable square-ring patch antennas were designed with air gaps to increase the impedance bandwidth, and dc bias networks were used to drive the PIN diodes. In most conventional reconfigurable antenna structures, dc bias lines are required to control the switching elements, which can make the whole antenna structure more complicated or even degrade the antenna performance. This hinders the wide applications of reconfigurable antennas. Therefore, a reconfigurable antenna structure without bias lines is desired. Very recently, reconfigurable antennas have found new applications in adaptive multiple-input-multiple-output (MIMO) systems [11]–[20], enabling the dynamic change of radiating characteristics of each antenna element according to the usually fast changing channel conditions. Generally, there are two methods to increase the MIMO system capacity by employing reconfigurable antennas. The first is to reduce the correlation of sub-channels by using polarization or pattern reconfigurable antennas. Specifically, this is implemented by switching between different configurations of reconfigurable antenna arrays according to the varying channel conditions. The polarization or pattern diversity in some of the configurations can be used to realize low correlation of the sub-channels. The second is to increase the signal power received by switching the antenna radiation patterns according to the channel information. In [12]–[15], the capacity of a MIMO system was improved by using polarization reconfigurable antennas to reduce the sub-channel correlation. In [16]–[20], pattern reconfigurable antennas were incorporated in MIMO systems to enhance the system capacity. In [16], a MIMO system with pattern reconfigurable antennas was tested in an anechoic chamber with artificial objects acting as the scatterers that made up a multipath environment. The system capacity increase was mostly attributed to the increase of average receiver signal-to-noise ratio (SNR) by changing the main beam direction. In [17]–[20],

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QIN et al.: A PATTERN RECONFIGURABLE U-SLOT ANTENNA AND ITS APPLICATIONS IN MIMO SYSTEMS

the capacity of a MIMO system was increased by exploiting antenna pattern diversity to introduce sub-channel decorrelation to the MIMO system. For the experiments in [17], the reference antenna was set to be one configuration of the reconfigurable antenna. It is known that an omnidirectional antenna can receive rich multipath, which can lead to low sub-channel correlation [20]. Therefore, a capacity comparison between systems with reconfigurable and omnidirectional antennas is necessary for highlighting the effect of pattern diversity on the sub-channel correlation. In this paper, a new pattern reconfigurable microstrip U-slot patch antenna using eight PIN diodes is proposed. Eight shorting posts are implemented around the patch to change the operating mode of the antenna from monopolar patch mode to normal patch mode. In addition, the two modes are designed to resonate in similar frequency ranges. Therefore, the proposed antenna can electrically reconfigure the radiation pattern between conical and boresight patterns with an overlapping impedance bandwidth. Furthermore, the plane with the maximum power level of the conical pattern can be varied between two orthogonal planes when the antenna operates in the monopolar patch mode. To demonstrate the benefit of using the proposed reconfigurable antennas to increase the system capacity, four antennas have been employed in a 2 2 MIMO-OFDM demonstrator. Omnidirectional antennas are used as a reference for capacity comparison. Channel measurements conducted in both line-ofsight (LOS) and non-LOS (NLOS) indoor environments show significant capacity enhancement. Part of this work has been described in [21]. The present paper extends the work in [21] significantly by providing the antenna design principles and showing the equivalent circuits of the antenna with PIN diodes. We also present a parametric study on the antenna resonant frequency and describe the measured reflection coefficient, radiation pattern, gain and efficiency of the antenna. In addition, a discussion on the measured realized gain of the antenna is given. Furthermore, the pattern reconfigurable antenna is applied to a MIMO- orthogonal frequency division multiplexing (OFDM) system and the capacity comparison between systems with pattern reconfigurable antennas and omnidirectional antennas is shown. Compared with antennas in [8]–[10], the proposed antenna has three main advantages. Firstly, only a single bias-tee, which superimposes the bias voltage on the RF signal, is needed to control the PIN diodes in the proposed antenna. Consequently, the complex bias network for PIN diodes or the matching network for dual feeds is not required as part of the printed antenna structure, which greatly simplifies the device. Secondly, the proposed antenna is compact and of low profile since it is designed on a single layer microwave substrate. Thirdly, compared to antennas in [8]–[10] which can switch between two radiation patterns, the proposed antenna has three different patterns in a similar frequency band. The larger number of patterns gives the proposed antenna more flexibility to improve the system capacity of a wireless link. However, a disadvantage of the proposed antenna is the use of eight PIN diodes, the loss of which will reduce the antenna realized gain.

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Fig. 1. Configurations of the patch antenna with PIN diodes (a) antenna in Ref. [23] with two shorting posts; (b) antenna with four shorting posts; (c) antenna with eight shorting posts.

The effect of the loss of PIN diodes on the antenna gain is discussed at the end of Section IV. This paper is organized as follows. In Section II, the operating principle and structure of the proposed antenna are described. Section III presents parametric studies of the antenna. Simulated and measured performances of the antenna are provided in Section IV. In Section V, the effects of the pattern reconfigurable antenna on the capacity of a 2 2 MIMO-OFDM system in indoor environments are analyzed. The paper concludes in Section VI with a summary and suggestions for further work. II. ANTENNA DESIGN A. Design Guidelines Microstrip patch antennas excited in the normal patch mode for boresight radiation and monopolar mode for conical radiation have been reported in [22] and [23], respectively. In [23], the monopolar mode is excited by two shorting posts located to the left and right of the feeding point, which is shown in Fig. 1(a). If PIN diodes are used to connect the shorting posts

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Fig. 3. Schematics of the pattern reconfigurable U-slot antenna.

Fig. 2. Simulated normalized radiation pattern (a) antenna in Ref. [23]; (b) antenna in Fig. 1(b).

and the microstrip patch, it is possible for this single antenna to operate in monopolar patch mode or normal patch mode by switching between the different states of the PIN diodes. However, according to [23], the resonant frequency of the monopolar mode is roughly a factor of 2.5 below the fundamental normal patch mode. In order to design an antenna with two modes resonating at similar frequency ranges and having a reasonably wide frequency bandwidth, we have taken three measures in the design process. Firstly, compared with the antenna in [23], we use two shorting posts at either side of the feed point. In order to simplify the bias network, the shorting posts are implemented around the edge of the patch and connected to the patch via PIN diodes, which is shown in Fig. 1(b). It is well known that the resonant frequency of a patch antenna loaded with reactive components can be varied depending on the type of reactance used [24], [25]. When the shorting posts are connected to the microstrip patch, the antenna operates in the monopolar patch mode. In this case, the increase in the number of shorting posts will increase the resonant frequency. On the other hand, when all the shorting posts are disconnected from the patch, the antenna operates in the normal patch mode. In this case, the increase in the number of shorting posts will reduce the resonant frequency. Therefore, the frequency difference between the two modes becomes smaller as the number of the shorting posts increases. The effect of the number of shorting posts on the antenna resonant frequency will be detailed in Section III.

Secondly, we examine the normalized far-field radiation patterns for the antennas operating in monopolar patch mode in Fig. 1(a) and (b), which is given in Fig. 2(a) and (b), respectively. The antennas are analyzed using the time domain solver of CST Microwave Studio [26]. For the antenna in Fig. 1(a), as is described in [23], two identical conical patterns are located in two orthogonal planes . For the antenna in Fig. 1(b), the maximum power level of the conical pattern in the plane are 6 dB greater than that in the plane . The qualitative explanation of this behavior is that the two shorting posts connected to each edge of the patch can be treated as a shorting wall that suppresses the E-field at the centre of that edge. Therefore, the maximum power level in the plane is lower than that in the plane . In order to have another similar conical pattern with the maximum power level located at the plane for the antenna in Fig. 1(b), four shorting posts are inserted into the substrate around the other two edges of the microstrip patch, which can be seen in Fig. 1(c). Finally, as the probe-fed microstrip patch antenna has a narrow impedance bandwidth that precludes its use in typical communication systems, a U-slot is etched on the patch to increase its impedance bandwidth [27]. B. Antenna Structure The layout of the proposed pattern reconfigurable U-slot antenna is shown in Fig. 3. A U-slot is inserted into a square patch of dimensions . Each side of the patch is connected with two shorting posts via PIN diodes. The radius of the shorting posts is 0.7 mm. The feeding probe connected to the U-slot patch through the ground plane and substrate is offset from the top edge of the patch by . Since the length of the PIN diode is less than the width of the gap , conducting ring pads are placed around the shorting posts to enable attachment of the PIN

QIN et al.: A PATTERN RECONFIGURABLE U-SLOT ANTENNA AND ITS APPLICATIONS IN MIMO SYSTEMS

TABLE I DIMENSIONS OF THE PATTERN RECONFIGURABLE U-SLOT ANTENNA

Fig. 4. Equivalent circuit for PIN diode (a) forward bias (b) reverse bias.

diodes. The parameters and dimensions of the antenna are given in Table I. Beam lead PIN diodes (MA4AGBLP912) are used as the switching elements. The equivalent circuit used in the simulation software is presented in Fig. 4. According to the PIN diode datasheet [28], the resistor is 4 in the forward bias state and the capacitor in the parallel circuit is 0.025 pF in the reverse bias state. The resistor is 10 representing the net dissipative resistance of the diode in the reverse bias state. For the zero bias state, the value of is almost infinity which is equal to an open circuit and the loss caused by the resistor is negligible. The orientation of the diodes is also shown in Fig. 3. As all PIN diodes are mounted across the ground and the center patch, only a bias tee attached to the SMA connector is needed to control the PIN diodes. When the bias voltage is supplied from the coaxial probe, opposite bias conditions are applied to diodes in group A and B due to their reversed orientation. When the dc voltage is zero, all diodes are turned off. In this case, the antenna operates in the normal patch mode and radiates a boresight pattern (State I). When the dc voltage is negative, diodes in group B are on, and the other diodes are off. In this case, the antenna has four shorting posts connected and can be regarded as a monopolar patch antenna, which radiates a conical pattern with the maximum power level in the z-y plane (State II). Changing the polarity of the dc voltage from negative to positive, diodes in group A are on, and all the other diodes are off. In this case, a similar conical pattern can be observed with the maximum power level in the z-x plane (State III). The possible radiation patterns of the reconfigurable U-slot antenna and the corresponding diode states are summarized in Table II. III. PARAMETRIC STUDY Three important parameters which affect the input reflection coefficients of the two modes of the proposed reconfigurable antenna are the radius of the shorting posts, the distance between

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TABLE II THREE STATES OF THE PATTERN RECONFIGURABLE U-SLOT ANTENNA

shorting posts and the patch , and the number of the shorting posts. Also it is well known that the U-slot plays an important role on the performance of the patch antenna. Since a parametric study of the U-slot has already been reported [29], we only examine the effects of the former three parameters in this paper. The other parameters remain constant and their values are given in Table I. As the shorting posts have the same effect on the reflection coefficients of States II and III for the monopolar patch mode, only the results for State II are presented for the parametric analysis. In order to better analyze the effect of the parameters, the equivalent circuits of the antenna with PIN diodes for States I and II are given in Fig. 5(a) and (b), respectively. In the equivalent circuits, a parallel resonant circuit is used to model the patch antenna with a U-slot. The purpose of the electrical models in Fig. 5 is to give a physical insight into the behavior of the antenna for the parametric analysis, but not to exactly predict the antenna input impedance. A similar method has been used in [30] for the parametric analysis of a microstrip patch antenna. Fig. 5(a) shows the equivalent circuit of the antenna operating in the normal patch mode. The microstrip patch with a U-slot is represented by a circuit . For the normal patch mode, only the PIN diodes and the shorting posts that are attached to the radiating edges are considered in the equivalent circuit, and the effects of the two PIN diodes and shorting posts at each edge are combined together to simplify the equivalent circuit. As the PIN diodes are all zero bias, according to the PIN diode datasheet, is almost infinity. Therefore, the equivalent circuit of the PIN diode in this state is an inductor in series with a capacitor . The parasitic capacitance between the shorting posts and the patch is modeled by a capacitor . The shorting post is represented by a shunt inductor . The imaginary part of the input admittance from the reference plane on the right hand side of Fig. 5(a) is investigated by using CST Microwave Studio. Simulation results show that it is capacitive with a capacitance within the antenna operating frequency range. Fig. 5(b) shows the equivalent circuit of the antenna operating in the monopolar patch mode. As with the circuit of the normal patch mode, the microstrip patch with a U-slot is also represented by a circuit . In the monopolar patch mode (State II), four PIN diodes (diodes A) are reverse bias. According to the analysis in the last paragraph, the total effect

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Fig. 5. The equivalent circuits of the proposed antenna for (a) State I (normal patch mode) and (b) State II (monopolar patch mode).

of the shorting posts with PIN diodes in zero bias state is capacitive. The only difference between the zero and reverse bias states is the value of the net dissipative resistor of the PIN diodes. Therefore, a capacitor is used to model the total capacitive effect of the shorting posts connected with diodes A. A resistor is used to represent the losses in the four PIN diodes. On the other hand, four shorting posts are connected to the patch by PIN diodes B that are in the forward bias state. Those PIN diodes are modeled by an inductor in series with a resistor . In addition, the effects of the shorting posts and the parasitic capacitance between the patch and the shorting posts are represented by an inductor and a capacitor , respectively. The imaginary part of the input admittance from the reference plane on the right hand side of Fig. 5(b) is investigated. Simulation results show that it is inductive with an inductance within the antenna operating frequency range.

A. The Radius of Shorting Posts Fig. 6(a) and (b) show the effects of the radius of shorting posts on the resonant frequencies of the monopolar patch and normal patch modes, respectively. It is observed that the resonant frequency of the monopolar patch mode increases with the radius of the shorting posts. This is due to the fact that when the radius increases the inductance from the shorting posts reduces, which makes decrease; hence, the resonant frequency of the parallel circuit in Fig. 5(b) increases. For the normal patch mode, the resonant frequency remains almost unaffected by the radius change of shorting posts. This is because that in Fig. 5(a) is almost stable within the changing range of the shorting post radius, which is evidenced by the simulation results. Therefore, the radius of the shorting posts can change the resonant frequency of the monopolar patch mode but has little effect on that of the normal patch mode.

Fig. 6. Simulated performance of the proposed antenna as a function of (a) input reflection coefficient of monopolar patch mode; (b) input reflection coefficient of normal patch mode.

B. The Distance Between Shorting Posts and the Patch Fig. 7(a) and (b) show the effects of on the resonant frequencies of the monopolar patch and normal patch modes, respectively. As seen from Fig. 7, the resonant frequency of the monopolar patch mode increases when is reduced. However,

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Fig. 8. Photograph of the pattern reconfigurable U-slot antenna.

Fig. 7. Simulated performance of the proposed antenna as a function of (a) input reflection coefficient of monopolar patch mode; (b) input reflection coefficient of normal patch mode.

the resonant frequency of the normal patch mode decreases with . This can be attributed to the fact that when decreases, the parasitic capacitance between the shorting posts and the patch increases. The increased capacitance reduces the inductive effect from the reference plane in Fig. 5(b), but increases the capacitive effect from the reference plane in Fig. 5(a) and the in Fig. 5(b). The decreased and the increased have reverse effects on the resonant frequency of the monopolar patch mode (the resonant frequency of a parallel circuit). However, the simulation results show that the effect of outweighs that of , which leads to an increase of the resonant frequency of the monopolar patch mode. On the other hand, the larger capacitance will decrease the resonant frequency of the parallel circuit in Fig. 5(a), which will shift the resonant frequency of the antenna in normal patch mode to a lower value. C. The Number of the Shorting Posts In the design guidelines (Part A of Section II), it is stated that an increase in the number of shorting posts will increase the resonant frequency of the monopolar patch mode, but reduce that of the normal patch mode. The reason is as follows. For the monopolar patch mode, the increased number of shorting posts means that for the diodes in forward bias state, more inductors

are paralleled, which makes the effective inductance decrease. And for the diodes in reverse bias state, more capacitors are paralleled, which makes the effective capacitance increase. Simulation results show that the decrease of the total inductance outweighs the increase of the total capacitance on the resonant frequency of the circuit in Fig. 5(b). Therefore, the resonant frequency of the monopolar patch mode is increased when the number of the shorting posts increases. On the other hand, for the normal patch mode, since the PIN diodes connected to the radiating edges are all zero bias, the increased number of shorting posts means more capacitors are paralleled, which makes increase; hence, the resonant frequency of the normal patch mode (the resonant frequency of a parallel circuit in Fig. 5(a)) will be decreased. IV. SIMULATED AND MEASURED RESULTS OF THE ANTENNA Based on the above analysis, a pattern reconfigurable U-slot antenna was designed and fabricated. The proposed antenna was etched on a 3.175-mm-thick RT/Duroid 5880 substrate (dielectric constant , ). A photograph of the fabricated prototype is shown in Fig. 8. Figs. 9 and 10 show the simulated and measured reflection coefficients versus frequency for three different states of the antenna, respectively. Compared with the simulated results the measured resonant frequencies for State II and III are slightly higher. This discrepancy can be mostly attributed to the inaccuracies in the fabrication of the shorting posts. As is shown in Section III, the resonant frequency of the monopolar mode is quite sensitive to the radius and position of the shorting posts. However, the simulated overlapping impedance bandwidth of the three states is 6.5% with a center frequency of 5.24 GHz. The corresponding measured bandwidth is 6.6% centered at 5.32 GHz, which agrees reasonably well with the simulated results. Radiation patterns were measured for the three states of the proposed antenna using a spherical near-field (SNF) antenna measurement system. Simulated and measured normalized

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Fig. 9. Simulated input reflection coefficient for the proposed antenna.

Fig. 10. Measured input reflection coefficient for the proposed antenna.

radiation patterns are compared for both co-polarization and cross-polarization. Figs. 11 and 12 display the z-x and z-y plane radiation patterns for the three states of the antenna at 5.3 GHz, respectively. For State I, boresight radiation patterns with a maximum cross-polarization level of 20 dB are shown in Figs. 11(a) and 12(a). For State II, a symmetrical conical pattern with the maximum power level in the z-y plane directed at (elevation angle) 44 is plotted in Figs. 11(b) and 12(b). For State III, an asymmetrical conical pattern with the maximum power level in the z-x plane directed at (elevation angle) 45 is drawn in Figs. 11(c) and 12(c). It can be seen from Fig. 11(c) that the pattern is asymmetrical and there is 1 dB difference between the left and right maximum power level of the conical pattern. This is due to the position of the probe feed. Simulation results show that if we put the probe feed at the center of the patch, the difference between the left and right maximum power level in Fig. 11(c) will become smaller. However, in that case the overlapping impedance bandwidth of the two modes will be reduced. This can be viewed as a compromise for the antenna to provide good overlapping impedance bandwidth and radiation patterns. In Fig. 11, the simulated cross-polarization patterns for the three states are not given since they are very small compared to the measured ones. Additionally, the realized gain was measured using the gain comparison technique [31]. The losses of the cable and bias tee have been calibrated out of the gain measurement. The measured gains for the three states are plotted in Fig. 13. The mea-

sured efficiencies of State I, State II and State III at 5.3 GHz are 86.6%, 45.1% and 45.4%, respectively, where the measured efficiency is obtained from the difference between the measured gain and directivity. From Fig. 13, it can be seen that the measured gain of State III is 0.5 dB greater than that of State II, which can be mostly attributed to the asymmetry of the conical pattern of State III and slight variations in the resistance of individual diodes. Furthermore, at 5.3 GHz the gain of State I is approximately 3 dB greater than those of State II and III, which is mainly due to the loss of the PIN diodes. On the one hand, for State II and III, four PIN diodes, each acting as a 4 resistor , are attached to the antenna, but for State I all PIN diodes are turned off. To examine the effect of , we have simulated several different values of at 5.3 GHz. Simulation results show that when decreases to zero the realized gain increases by 2 dB and 1.75 dB for State II and III, respectively. On the other hand, for State II and III, diodes with finite value also have more losses than the diodes in zero bias state which is approximately lossless. Simulation results show that at 5.3 GHz when changes from 10 to infinity the realized gain increases by 0.32 dB and 0.27 dB for State II and III, respectively. Therefore, the loss of State II and III is much greater than that of State I and the corresponding gain is much lower. In order to increase the gains of State II and III, low loss elements such as radio frequency microelectromechanical system (RF MEMS) switches could be used. However, the disadvantages of using currently available RF MEMS are the higher cost and lower reliability than PIN diodes. V. APPLICATION TO MIMO-OFDM SYSTEMS Since the proposed pattern reconfigurable antenna is compact and can vary its radiation pattern without dc bias network, it can be easily applied to a MIMO system. The performance of a MIMO system is affected by the spatial correlation which is a function of the channel characteristics and the antenna array properties. Therefore, the antenna elements can be treated as additional parameters of the MIMO system. In this section, a typical example for the application of pattern reconfigurable antennas in a MIMO-OFDM system is described. A. Antenna Array in MIMO-OFDM System In previous sections, the design of a single pattern reconfigurable antenna is presented. In this sub-section, we incorporate the pattern reconfigurable antennas into a 2 2 MIMO-OFDM system. At each end of the MIMO-OFDM system, there are two reconfigurable antennas working as a two-element array. However, this does not imply that the array operates as a traditional beamforming array. Rather, each antenna has its own radiation characteristics. As each reconfigurable antenna has three states, there are nine configurations of the antennas at each end. For each measurement, the configuration of the receive antennas is the same as the transmit antennas. Table III gives nine configurations of the reconfigurable antennas. When two antennas are located close to each other, the mutual coupling can produce pattern distortion and should be eliminated. Therefore, the spacing of the two antennas at both ends is set to be one wavelength in order to keep the mutual coupling

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Fig. 11. Measured and simulated z-x plane normalized radiation patterns of the proposed antenna at 5.3 GHz (a) State I, (b) State II, (c) State III.

Fig. 12. Measured and simulated z-y plane normalized radiation patterns of the proposed antenna at 5.3 GHz (a) State I, (b) State II, (c) State III.

TABLE III NINE CONFIGURATIONS OF THE RECONFIGURABLE ANTENNAS AT TRANSMIT END

Fig. 13. Measured gain of the proposed antenna.

to an acceptable level. The measured results in Fig. 14 show that the mutual coupling is lower than 20 dB for all configurations at this spacing. The mutual coupling results for configurations 4, 7 and 8 are not shown since they have the same results as the configurations 2, 3 and 6, respectively. For the reference antenna, in our study, commercially available omnidirectional antennas (Sky-Cross SMA-5250-UA) are used that have omnidirectional patterns with peak gain at 2.2 dBi. The spacing of the two antennas is also set to be one wavelength to keep the mutual coupling below 20 dB. When evaluating the MIMO antenna array performance, the envelope correlation coefficient is another critical parameter as

it provides a measure of antenna diversity performance. The antenna diversity will be better if the correlation coefficient is lower. The envelope correlation coefficient can be calculated using the farfield radiation patterns of the antennas [32]

(1)

where is a complex vector indicating the electric field radiated from the element. The envelop correlation coeffi-

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Fig. 14. Measured mutual coupling coefficient for different antenna configurations.

TABLE IV ENVELOPE CORRELATION COEFFICIENT OF NINE CONFIGURATIONS OF THE ARRAY

Fig. 15. (a) Layout of the indoor MIMO-OFDM testing environments; (b) orientation of the reconfigurable antennas.

B. MIMO-OFDM Demonstrator

TABLE V ENVELOPE CORRELATION COEFFICIENT OF THREE STATES OF THE ANTENNA

Actual MIMO-OFDM channel coefficients were measured by the MIMO-OFDM hardware demonstrator developed by CSIRO ICT Centre (Sydney, Australia) [34]. It operates at 5.25 GHz and supports an operational bandwidth of 40 MHz. The receive antennas are connected to an antenna array positioner controlled by a computer. The channel training sequence is designed to estimate the frequency response over 117 OFDM subcarriers in a 40 MHz bandwidth with a subcarrier spacing of 312.5 kHz. C. Measurement Location and Process

cient between the patterns generated at the two ports of the antenna array for different configurations (Table III), as well as between the patterns excited by a single antenna for different states (Table II), is estimated by using (1) according to the simulated radiation patterns. Table IV gives the envelope correlation coefficient for different antenna configurations at 5.25 GHz. It is evident that the envelope correlation coefficients of the configurations (2, 3, 4, 6, 7, 8) having pattern diversity are lower than those (1, 5, 9) with the same antenna patterns, and they are comparable to the results of the antennas in [33] that employ both the pattern and polarization diversity. Table V shows the envelope correlation coefficient for different antenna states at 5.25 GHz. It is observed that all the coefficients between different antenna states are below 0.5, which satisfy the criterion for enabling the antenna to provide a good level of diversity [32].

The 2 2 MIMO-OFDM channel measurement was conducted in the CSIRO ICT Centre indoor environment, which consists of both concrete and gypsum-board walls, glass windows and wooden doors. The channel was measured in LOS over a 5 m distance and NLOS over an 8 m distance. The layout of the LOS and NLOS testing scenarios is shown in Fig. 15(a). For the LOS scenario, both the transmitter and receiver are located in the same laboratory (Lab 1) equipped with some metal bookshelves and cabinets. For the NLOS scenario, the transmitter and receiver are placed in two adjacent laboratories (Lab 1 & 2). Each reconfigurable antenna is placed vertically as shown in Fig. 15(b). In the LOS scenario, the reconfigurable antennas at transmit (Tx1) and receive ends are configured to face each other. In the NLOS scenario, the reconfigurable antennas at transmit (Tx2) and receive ends are configured to face the negative and negative directions, respectively. The reference

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receive antenna location samples and MIMO sub-channels. The normalization is performed as follows:

(3)

Fig. 16. MIMO-OFDM demonstrator with reconfigurable antennas.

antennas are located with the omnidirectional pattern aligning with the horizontal plane (x-y plane). For each measurement, the antenna positioner moves the receive antenna array to 10 location samples with 0.05 wavelength increments. The position of the transmit antennas is fixed. In each scenario only the antenna configuration is changed. Any other factors that can possibly vary the channel characteristics, such as the number of the scatterers and their positions, remain the same. The measurement is performed in the night to avoid the human activities, so the testing environment is entirely static. A photograph of the MIMO-OFDM demonstrator with reconfigurable antennas at the receive end and the dc power supply is shown in Fig. 16. D. Channel Measurement and Capacity Estimation The MIMO-OFDM channel is characterized by its coefficient matrix , the element of which is the complex ratio of the signal output from the th receive antenna over the signal input to the th transmit antenna at the th OFDM subcarrier and the th location sample. The Shannon capacity of a MIMOOFDM channel is given by [34]

(2) is the system capacity in bits/second/Hz, is the where number of sub-carriers, n is the number of location samples, is the number of receive antennas, is the number of transmit antennas, is the identity matrix, is the normalized channel matrix, the superscript denotes the conjugate transpose, and SNR is the average signal-to-noise-ratio over all receive array elements. The capacity of a wideband channel is the average value of the capacities over all subcarriers of the MIMO-OFDM system and the 10 location samples. It is convenient to use the normalized channel matrix so that the capacity of the channel can be derived as a function of the average SNR per receive antenna over all OFDM subcarriers,

where denotes the Frobenius norm of the channel matrix. In the MIMO-OFDM channel measurement, the peak gain of the omnidirectional antenna is 2.2 dBi. But the gain of different states of the reconfigurable antennas varies from 2.8–6.4 dBi at 5.25 GHz. The antenna gain of each configuration is preserved in . The lower gain of the omnidirectional antenna can lead to a lower value of . Therefore, compared to the proposed antenna, if all channel matrices are normalized to a common factor, the reference antenna will suffer a capacity loss due to the smaller . In this section, we aim to show that the proposed antenna has the ability to improve the system capacity by using pattern diversity to reduce the sub-channel correlation. If the gain of the antenna is taken into account, the extent of the enhancement of the system capacity derived only from the pattern diversity will not be explicitly shown. Therefore, the gain effect on the capacity should be eliminated in order to realize a fair comparison. In order to separate the effect of pattern diversity on the system capacity from the effect of antenna gain, two different channel matrix normalization methods are employed. The first is that the channel matrix of each antenna configuration is normalized independently (Method I). In this case, the antenna gain is not included in the capacity calculation. Therefore, only the effect of the sub-channel correlation is kept in the capacity evaluation [35]. The second is that the channel matrix of each antenna configuration is normalized with respect to that of the reference antenna (Method II). In this way, not only the sub-channel correlation but also the relative received power difference, is preserved in the capacity calculation. Figs. 17 and 18 show the system capacity percentage improvement for different antenna configurations based on channel normalization Method I and Method II, respectively. For each scenario, the capacity improvement is the difference in capacity between the system with one configuration of reconfigurable antennas which gives the largest capacity and the system with reference antennas. Then the improvement is normalized with respect to the capacity of reference antennas. For channel matrix normalization Method I, it can be observed from Fig. 17(a) that compared with omnidirectional antennas, the proposed pattern reconfigurable antennas improve the system capacity by 17% and 12% for the LOS and NLOS cases, respectively, at an SNR of 10 dB. This is because that with antenna pattern diversity the correlation of sub-channels is reduced. Therefore, the system capacity is improved, especially for the environments with insufficient scatterers. In our experiments the best configurations, which lead to the largest system capacity improvement, are the configuration six and eight for the LOS and NLOS scenarios, respectively. An explanation of this is as follows. Although the antennas with omnidirectional patterns in the horizontal plane are considered to be a good solution for MIMO systems as they can receive rich multipath in that

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Fig. 17. Percentage improvement of the reconfigurable antenna MIMO system capacity versus SNR for Method I. The benchmark is (a) omnidirectional antenna and (b) antenna configuration 1.

Fig. 18. Percentage improvement of the reconfigurable antenna MIMO system capacity versus SNR for Method II. The corresponding omnidirectional antenna MIMO system capacity is used as the benchmark.

plane, it turns out that there are still many multipath components outside the azimuth plane which can be received by other states of the reconfigurable antennas. Therefore, system capacity improvement is possible by using pattern reconfigurable antennas. In addition, since antenna configuration 1 (Table III) acts as a two-element rectangular patch antenna array with boresight radiation of each element, a comparison of the capacity of the system with configuration 1 and the best configurations is conducted, which is given in Fig. 17(b). It can be seen that at an

SNR of 10 dB, the system capacity is improved by 18% and 13% for the LOS and NLOS scenarios, respectively. Furthermore, as is seen from Fig. 17, the percentage improvement of the system capacity for the LOS scenario is greater than that for the NLOS scenario. This is due to the fact that generally the sub-channel correlation in an indoor LOS environment is larger than that in an NLOS environment. Therefore the extent of improvement of the system capacity by reducing the correlation of MIMO sub-channels is larger for the LOS scenario. For channel matrix normalization Method II, the best configuration is antenna configuration one (Table III) in terms of the system capacity for both scenarios. It can be seen from Fig. 18 that at an SNR of 10 dB, the peak improvement is 285% and 264% for the LOS and NLOS scenarios, respectively, which are much higher than those in Fig. 17. The reason that antenna configuration one outperforms other configurations as well as omnidirectional antennas to such a great extent lies in the higher gain of the antennas in configuration one. Specifically, the of the system with configuration one is much greater than that with other configurations. By Method II, this effect is taken into account because the channel matrix of each antenna configuration is normalized to a common value. In this way, the normalized channel matrix of the antenna configuration one is scaled up by a large factor due to the normalization; hence, the improvement of the capacity is significantly larger. From channel matrix normalization Method I, it is known that the pattern diversity of the proposed antenna can be exploited to improve the system capacity by reducing the sub-channel correlation, which is evidenced by the fact that antenna configurations six and eight outperform the other configurations and the omnidirectional one in the LOS and NLOS scenarios, respectively. When the gain of different configurations is considered, however, it is found that the effect of antenna gain outweighs the effect of the channel decorrelation on the system capacity. Therefore, the antenna configuration one which has the largest antenna gain becomes the best in both scenarios. In this situation, the pattern diversity loses its effect on system capacity due to the large gain difference of different antenna states. In order to employ the pattern diversity of the proposed antenna in a practical way that the gain difference is included in the capacity calculation, we need to improve the realized gain of antenna States II and III. As discussed at the end of the Section IV, compared to State I, the lower gain of State II and III is mostly attributed to the losses of PIN diodes. Therefore, low loss switches, such as RF MEMS, should be used to make the gains of States II and III close to that of State I. An updated antenna prototype with RF MEMS could be designed and adopted in our future work. Reference [17] also demonstrates the capability of a pattern reconfigurable antenna to improve the MIMO system capacity. Compared to [17], our work has three main differences. First, the mechanism of the pattern reconfigurability of the antenna in [17] uses mutual coupling of two closely spaced antennas. The pattern diversity will be reduced if the antenna separation is increased. Therefore, the spatial diversity, which is another effective scheme [36] to improve the system capacity, can not be efficiently employed together with the pattern diversity in a MIMO system. However, as the way to reconfigure the pattern of our

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antenna is changing the antenna operating modes, there is no space limitation on our antenna. Second, in our experiments, at an SNR of 10 dB, the capacity percentage improvement is 17% and 12% for the LOS and NLOS scenarios, respectively. These results are larger compared to the average 10% improvement reported in [17]. Admittedly, since the capacity measurement is heavily dependent on the testing environment, the improvement could be significantly different for other test scenarios. Third, as has already been mentioned in the introduction, the reference antenna in [17] is chose to be one configuration of the antenna. While in our work, omnidirectional antennas are used for reference. Since omnidirectional antennas can receive rich multipath in the horizontal plane, this comparison can highlight the effect of pattern diversity on MIMO system capacity. VI. CONCLUSION A new design of a pattern reconfigurable patch antenna is presented. Shorting posts around the patch are used to change the antenna operating modes. The antenna can switch between three different radiation patterns by employing PIN diodes. It is compact but can realize an overlapping frequency bandwidth of 6.6% with a center frequency of 5.32 GHz for the three states by etching a U-slot into the patch. Compared to most conventional pattern reconfigurable antennas, the proposed antenna does not need additional dc bias lines to control the PIN diodes, which greatly simplifies the antenna structure. Due to the simple structure and pattern reconfigurability, the antenna has the ability to improve the performance of a wireless communication system considerably. To demonstrate the antenna’s capability of increasing the system capacity, four antennas are applied to a 2 2 MIMO-OFDM system and the indoor channel measurement is conducted. Capacities of the system with pattern reconfigurable antennas and reference omnidirectional antennas are compared based on two channel matrix normalization methods. The comparison indicates that, for normalization Method I, the system capacity is improved by 17% and 12% for the LOS and NLOS scenarios, respectively, at an SNR of 10 dB by using the pattern reconfigurable antennas. When the gain effect is considered, the configuration with the greatest antenna gain produces the largest system capacity. Therefore, in order to use the pattern diversity to enhance the system capacity effectively in a practical way, the gain of antenna States II and III needs to be improved to approach that of State I. Future research includes integrating RF MEMS switches with the proposed antenna to increase the gain of antenna States II and III. Furthermore, work will focus on designing combined pattern and polarization reconfigurable antennas to achieve higher system capacity improvement. ACKNOWLEDGMENT The authors would like to thank M. Shen for assisting with the attachment of PIN diodes and Dr. H. Suzuki, Dr. Z. Chen and Dr. W. Ni for the discussion on the subject of MIMO communication. In addition, we appreciate the constructive comments from the anonymous reviewers.

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[24] P. Bhartia and I. J. Bahl, “Frequency agile microstrip antennas,” Microw. J., pp. 67–70, Oct. 1982. [25] D. L. Sengupta, “Resonant frequency of a tunable rectangular patch antenna,” Electron. Lett., vol. 20, no. 15, pp. 614–615, Jul. 1984. [26] CST Studio SuiteTM 2009 Computer Simulation Technology, Germany. [27] T. Huynh and K. F. Lee, “Single-layer single-patch wideband microstrip antenna,” Electron. Lett., vol. 31, no. 16, pp. 1310–1312, Aug. 1995. [28] M/A-COM Data Sheet for MA4AGBLP912 Beam Lead PIN Diode. [29] S. Weigand, G. H. Huff, K. H. Pan, and J. T. Bernhard, “Analysis and design of broadband single-layer rectangular U-slot microstrip patch antennas,” IEEE Trans. Antennas Propag., vol. 51, no. 3, pp. 457–468, Mar. 2003. [30] J. Anguera, E. Martinez, C. Puente, C. Borja, and J. Soler, “Broadband dual-frequency microstrip patch antenna with modified Sierpinski fractal geometry,” IEEE Trans. Antennas Propag., vol. 52, no. 1, pp. 66–72, Jan. 2004. [31] C. A. Balanis, Antenna Theory: Analysis and Design, 3rd ed. New York: Wiley, 2005. [32] R. Vaughan and J. Andersen, “Antenna diversity in Mobile Communications,” IEEE Trans. Veh. Technol., vol. VT-36, no. 4, pp. 149–172, Nov. 1987. [33] Z. N. Chen and T. S. P. See, “Diversity and its applications in ultrawideband antennas,” presented at the IEEE Int. Workshop on Antenna Tech., Santa Monica, CA, Mar. 2009. [34] H. Suzuki, T. V. Tran, and I. B. Collings, “Characteristics of MIMOOFDM Channels in indoor environments,” J. Wireless Commun. Netw., vol. 2007, no. 19728, Jan. 2007. [35] M. A. Jensen and J. W. Wallace, “A review of antennas and propagation for MIMO wireless communications,” IEEE Trans. Antennas Propag., vol. 52, no. 11, pp. 2810–2824, Nov. 2004. [36] C. B. Dietrich, Jr., K. Dietze, J. R. Nealy, and W. L. Stutzman, “Spatial, polarization, and pattern diversity for wireless handheld terminals,” IEEE Trans. Antennas Propag., vol. 49, no. 9, pp. 1271–1281, Sep. 2001. Pei-Yuan Qin was born in Liaoning, China, in 1983. He received the Bachelor of Engineering degree in electronic engineering from Xidian University, Xi’an, China, in 2006. He is currently a joint Ph.D. student of Xidian University, China and Macquarie University, Australia. From 2008 to 2010, he was a Ph.D. student visitor to the CSIRO ICT Centre, Australia funded by the China Scholarship Council (CSC). His research interests are in the areas of reconfigurable antennas and filters, reconfigurable reflectarrays, and MIMO communications.

Y. Jay Guo (SM’96) received the Bachelor Degree and Master Degree from Xidian University, Xi’an, China, in 1982 and 1984, respectively, and the Ph.D. degree from Xian Jiaotong University, China, in 1987. He was awarded an honorary Ph.D. degree in 1997 by the University of Bradford, U.K., for his world leading research in Fresnel antennas. Currently, he is the Research Director of Advanced Broadband Networks and Services Theme, CSIRO ICT Centre, Australia, and the Director of the Australia China Research Centre for Wireless Communications. From August 2005 to January 2010, he served as the Research Director

of the Wireless Technologies Laboratory, CSIRO ICT Centre. Prior to joining CSIRO, he held various senior positions in a number of international companies including Fujitsu, Siemens and NEC, managing the development of advanced technologies for the third generation (3G) mobile communications systems. He is an Adjunct Professor at Macquarie University, Australia, and a Guest Professor at the Chinese Academy of Science (CAS) and Shanghai Jiaotong University. He has published three technical books Fresnel Zone Antennas, Advances in Mobile Radio Access Networks, and Ground-Based Wireless Positioning, 59 journal papers and over 80 refereed international conference papers. He holds 18 patents in wireless technologies. Dr. Guo is a Fellow of IET. He was the recipient of the Australian Engineering Excellence Award and the CSIRO Chairman’s Medal. He has served on the organizing and technical committees of numerous national and international conferences. He was Chair of the Technical Program Committee (TPC) of 2010 IEEE Wireless Communications and Networking Conference (WCNC) and 2007 IEEE International Symposium on Communications and Information Technologies (ISCIT), and is the TPC Chair of IEEE ISCIT2012. He has been the Executive Chair of Australia China ICT Summit since 2009. He was a Guest Editor of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, Special Issue on Antennas and Propagation Aspects of 60–90 GHz Wireless Communications. Currently, he is serving as a Senior Guest Editor for the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, Special Issue on Challenges and Dynamics for Unmanned Autonomous Vehicles.

Andrew R. Weily (S’96–M’01) received the B.E. degree in electrical engineering from the University of New South Wales, Australia, in 1995 and the Ph.D. degree in electrical engineering from the University of Technology Sydney (UTS), Australia, in 2001. From 2000 to 2001, he was a Research Assistant at UTS. He was a Macquarie University Research Fellow then an ARC Linkage Postdoctoral Research Fellow from 2001 to 2006 with the Department of Electronics, Macquarie University, Sydney, NSW, Australia. In October 2006, he joined the Wireless Technology Laboratory at CSIRO ICT Centre, Sydney. His research interests are in the areas of reconfigurable antennas, EBG antennas and waveguide components, leaky wave antennas, frequency selective surfaces, dielectric resonator filters, and numerical methods in electromagnetics.

Chang-Hong Liang (M’80–SM’83) was born in Shanghai, China, in December 1943. He graduated from Xidian University (Formerly Northwest Telecommunications Institute), Xi’an, China, in 1965 and continued his graduate studies until 1967. From 1980 to 1982, he worked at Syracuse University, New York, as a Visiting Scholar. Since 1986, he has been a Professor and Ph.D. student advisor in the School of Electronic Engineering, Xidian University. He has published numerous papers and five books. He has wide research interests, which include computational microwave and computational electromagnetics, microwave network theory, microwave measurement method and data processing, lossy variational electromagnetics, electromagnetic inverse scattering, and electromagnetic compatibility. Prof. Liang is a fellow of Chinese Institute of Electronics (CIE) and a Director of the Academic Committee of National Key Lab of Antenna and Microwave Technology. He has received the titles of “National Distinguished Contribution” and “National Excellent Teacher.” He is the Editor-in-Chief of the Journal of Xidian University.

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Multiple Element Antenna Efficiency and its Impact on Diversity and Capacity Jane X. Yun, Student Member, IEEE, and Rodney G. Vaughan, Fellow, IEEE

Abstract—A desirable characteristic of a multiple element antenna (MEA) is to be compact, but a smaller size tends to lead to higher ohmic and mutual coupling losses. A metric for the efficiency of the MEA would help clarify the tradeoffs between compactness and performance. In a MIMO/diversity antenna, the total efficiency seen at each port directly affects the signal-to-noise ratio (SNR) in the diversity branch. The SNR after diversity combining governs the performance of the diversity antenna system. In this paper, MEA efficiencies is therefore discussed and formulated in the context of mutual coupling and diversity combining. The impact of MEA efficiency on the diversity gain and the information theoretical capacity is also formulated and demonstrated using measurements of example MEAs. With these formulations, an equivalent number of idealized (lossless, uncorrelated, uncoupled, equal power) branches can be found for an MEA, and this defines the diversity order and the capacity order of the MEA. With this metric, the performance of different MEAs can be compared. Index Terms—Antenna correlation, capacity, diversity gain, MEA total efficiency, multiple element antenna (MEA), mutual coupling.

I. INTRODUCTION

E

FFICIENCIES of single element antennas are well understood and defined in IEEE Standards [1], [2]. But for an MEA used for MIMO communications, definitions of efficiencies are not yet clarified. Since power is transferred between elements by mutual coupling, the antenna efficiencies of MEA elements are not only decided by the element loss, but also by the mutual coupling and the diversity combining method which includes the terminations. A formulation of the MEA efficiency needs to include these effects, and it should apply to both the transmit case and the receive case. The efficiency of each element directly impacts the MEA transmitting and receiving capability. In an MIMO system, the signal-to-noise ratio (SNR) of a receive branch is proportional to the efficiency of the element. The combination of the branch SNRs governs the antenna diversity gain and its capacity performance. How the MEA efficiency impacts the MEA performance in a Rayleigh fading scenario is discussed in [3], but an important part of the MEA efficiency for compact designs,—mutual Manuscript received June 24, 2010; revised January 26, 2011; accepted September 23, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. The authors are with the School of Engineering Science, Simon Fraser University, Burnaby, BC V5A 1S6, Canada (e-mail: xyun@sfudotca; rvaughan@sfudotca). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173444

coupling loss,—is omitted in order to study the impact of efficiency caused by the element ohmic loss and impedance mismatch loss only. Also, averaged efficiency (cf.[3]) or the highest efficiency among all the elements (cf.[4]) is used, instead of considering the impact of each element when the total efficiency of each element is different. Often, MIMO antennas must be mounted on complex platforms. The available space can be critical and the designer may be forced to use different types of elements. In fact, different types of elements are often deployed in order to reduce correlation and mutual coupling. Different element types normally have different radiation efficiencies. In some compact implementations, this difference can be up to about 6 dB. This paper develops efficiency formulas for MEAs. The formulation reveals the duality of the embedded element trans-mit efficiency and the embedded element receive efficiency. The multiple conditions on the circuit model impedances can be identified in order to make these efficiencies the same. Also, we use the terms total transmit/receive efficiency of the embedded element for the total efficiency of the embedded element. The loss due to mutual coupling, which can be a dominant part of the antenna loss, changes with the type of diversity combining and the terminations of the elements. Therefore, the formulation of the efficiencies considers the embedded element losses with different diversity schemes. The analysis of the losses is demonstrated with measurements of an example MEA. An MEA total efficiency, in the form of a matrix containing the total efficiency of each embedded element, accounts for the impact of individual element efficiencies on the diversity gain and capacity. By comparing these performance metrics before and after the MEA total efficiency is included, the impact of antenna efficiency is separated from the impact of antenna correlation. The formulation is not limited to Rayleigh channels but Rayleigh channels are used in the examples. The rest of paper is laid out as follows. Section II develops the efficiency formulas for an MEA. Section III takes this efficiency and incorporates it into the MEA diversity gain, and Section IV does the same for the information theoretical capacity. Section V concludes the paper. II. EMBEDDED ELEMENT EFFICIENCIES OF MEA For single element antennas, the radiation efficiency is expressed in terms of the transmit case. It is well established and featured in Standards [1], [2]. From a simplified circuit model, the radiation efficiency is normally written as , where is the radiation is the ohmic resistance of the antenna. To resistance and include the impedance mismatch, the antenna total efficiency where can be expressed in the form

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Fig. 1. Transmission line circuit model of the th embedded element of an -element MEA, when the th element is transmitting and the other elements , and the other are present and terminated. The transmit source resistance is . elements are loaded with their transmitting source resistances, denoted (a) is the th transmitting element and (b) is one of the other terminated elements (taking the th element as an example here). For simultaneous combining, there similar circuits to (b). is the power accepted by the network are to the right of the dashed line, from the th transmitting element. The source reactance and the antenna self reactance are assumed to be tuned out for simplicity.

and is the reflection coefficient at the antenna port. However, for MEAs, efficiencies are impacted by mutual coupling, the diversity combining, and the terminations of the elements. Mutual coupling causes power transfer from one element to other elements. This transferred power is then dissipated in different ways: in the terminating resistances; as ohmic losses in the elements and the transmission lines; and as radiation from the elements. In practice, there are also ohmic loss and radiation from the MEA support structure, and this is part of the “embedded element”. In a simplified circuit model these powers can be included into the element’s radiation and ohmic losses, respectively. In terms of the termination of the elements, diversity schemes can be categorized as simultaneous (including Optimal Combining (OC), Maximum Ratio Combining (MRC), Equal Gain Combining (EGC), and Selection Combining (SC)) and nonsimultaneous combining (Switch Combining (SwC)), as discussed in Appendix A. The MEA efficiency is formulated based on the analysis of the losses for both combining schemes in the transmit and receive cases, respectively. The analysis of the losses is confirmed with the measurement of an example of a transmitting MEA. A. Transmitting MEAs Fig. 1 gives the transmission line circuit model of the th embedded element of an -element MEA, when only the th element is transmit excited and all the other elements are present, not transmit excited, and terminated with their transmit source resistances. The dashed line represents the transmit port of the th embedded element. To the left hand side of the dashed line is the th transmit source, and the right hand side is the embedded element, which includes the th transmitting element in Fig. 1(a) and the other elements terminated and excited by mutual coupling. One of these terminated elements is depicted in Fig. 1(b). The reactance of the power source and the antenna self reactance are, in principle, able to be tuned out, so reactances are not included for brevity, although their inclusion is straightforward.

In Fig. 1(a), the th element is excited with the transmit source , which is the only external power source of the th em, and the bedded MEA element. The source resistance is resistance representing the ohmic loss of the transmission line . The raconnecting the power source to the th element is , is associated with the radiation of the diation resistance, th element in the presence of other elements. is the associated ohmic loss of this element. The current causes power loss in the other elements if there is non-zero mutual coupling. The total power lost from the th element to all the other elements through mutual coupling is represented via the sum of in the circuit model in the voltage sources Fig. 1(a). In Fig. 1(b), each of the non-transmit-excited elements is excited by mutual coupling. Taking the th element as an example, the total mutual coupling excitation on this element is . Some of the power transferred by mutual , and the coupling is then radiated by this element via and (the transmit rest dissipates as ohmic loss in . source resistance of the th element) and It is emphasized that the currents and in Fig. 1 are the currents caused by the transmit excitation of the th element only. For simultaneous combining, all the elements are excited by their own transmitters, so there are circuits similar to that in Fig. 1 for the MEA, and the total current in each element is the sum of these circuit currents, by superposition. For non-simultaneous combining, the unselected elements are open cir, from the circuit model viewcuited, i.e., point. In a physical situation with real-world devices this may not mean a zero current, but the circuit model still includes any mutual coupling. This is because the selected element is treated as embedded, so that any mutual coupling with the unselected elements is included through the embedded element resistances and . 1) For Simultaneous Combining (All Elements Connected to Fixed Transmit Loads): For the th embedded element, although only the th element is transmit excited, the radiation is not only from this element but also from the other elements through mutual coupling. for siThe th embedded element transmit efficiency multaneous combining is the ratio of the total power radiated from all the elements (this is denoted below as ) to the power accepted by the network (to the right of the dashed line in Fig. 1) from the transmit source (to the left of the dashed . So the embedded element transmit effiline), denoted ciency of the th element is written as

(1) where

(2)

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and is the total power radiated by all the elements from the excitation of the th element; is the ohmic loss in all the elements; is the loss in all the loads of the non-transmit-excited elements. is the ohmic loss in all the transmission lines of the non-transmit-excited elements. When the situation reduces to a single element, the above transmit efficiency is the same as the classical single antenna . radiation efficiency The total transmit efficiency of the embedded element at the th transmit port includes the matching efficiency at the transmit , as well as its embedded transmit efficiency, as port, (3) where (4) and is the reflection coefficient at the port of the th element. 2) For Non-Simultaneous Combining With all Unselected Elements Open Circuited: In this case, the currents of the unselected elements in the circuit model are zero, so the radiated power and losses induced on these elements are zero. The th embedded element transmit efficiency is then in the same form as the classical single antenna radiation efficiency:

Fig. 2. Transmission line circuit model of th embedded element of the -element MEA, when the th element is receiving and the other elements are present and terminated. (a) is one of the terminated elements (taking the th element as similar circuits an example here). For simultaneous combining, there are is the power absorbed by the as (a). (b) is the th receiving element. network (to the left of the dashed line) from the receiving port (the dashed line).

1) For Simultaneous Combining (All Elements Connected to Fixed Receiving Loads): The th embedded element receive efis defined here as the ratio of the power delivficiency ered to the loads of all the elements (the wanted power) to the absorbed power of the MEA owing to the reception of the th element, as

(5) where

(7) where

(6)

B. Receiving MEAs In Fig. 2, the dashed line represents the receive port of the th embedded element. The left hand side of the dashed line is the th receiving embedded element, including the receiving similar element and the other elements. Again, there are circuits to Fig. 2(a) for the non-receiving elements, but only the th element is shown here. To the right hand side of the dashed line in Fig. 2(b), the , provides the received power on the voltage source, receive port, and it is the only external source for this emis the power absorbed bedded element circuit model. (discussed in [5] and [6]) by the th embedded element (to the left of the dashed line). The absorbed power includes the power dissipated in all the receiving loads (which is considered as the wanted power); the power dissipated as the ohmic losses of all the elements and transmission lines (which is “wasted” power); and the power radiated by all the non-receiving elements (which is excited by mutual coupling and considered as “wasted” power). If there is an impedance mismatch at the receive port (the dashed line in Fig. 2), some of the received power is reflected in a transmission line style, back to the th antenna element, where and dissipated . it is re-radiated by

(8) and is the absorbed power at the embedded element; is the radiated power from all the nonand receiving elements and is the ohmic loss on these elements, both excited by mutual coupling. As indicated is in Fig. 2(b), The reflected power the total received power minus the absorbed power , so . It changes the total receive efficiency it is not part of of the embedded element. The total receive efficiency of the embedded element at the th , analogously to (3) and (4), is receive port (9) where, as above (10) For a single element receive antenna, (7) reduces to . This receive efficiency is not the same

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as the radiation efficiency. In fact it is not an antenna parameter, because in the receive case the metric is to measure how much power is delivered to the load (which is not part of the antenna) rather than to radiation. However, (7) and (8) are simand , and ilar to (1) and (2), except that and , are interchanged respectively. The efficiency for the receive case and the transmit case, although having a different physical basis, can be related in the sense of dual equations. The receive and transmit efficiencies are often assumed to be the same in MIMO communications system studies, but for this assumption, specific conditions are required related to the impedance matching, as follows. Consider an MEA which is impedance matched across the dashed line in Figs. 1 and 2 for both the transmit and receive case, so for all , and (2) and (8) are equivalent. It follows in (1) equals to in (7) only when that and the same combining detail is deployed. Under the above conditions, an embedded element receive efficiency can be found from the embedded element transmit efficiency, for the same MEA with the same combining detail. 2) For Non-Simultaneous Combining With all Unselected Elements Open Circuited: Similar to the non-simultaneous transmit case, since the unselected elements are open circuited, the power lost on these elements is zero in the circuit model. The embedded element receive efficiency is, therefore, in the same form as that for a single element antenna: (11) where (12) and measure how much In the above formulas, wanted power is radiated/received per unit accepted/absorbed power by the embedded element. On the other hand, these also indicate how much power is wasted through mutual coupling in the forms of ohmic loss and re-radiation. It is difficult to physand (although they could be simuically measure lated) with their definitions in (1), (2) and (7), (8). Instead, with (3), (4), (9) and (10), they can be found from the embedded element total efficiency and matching efficiency, both of which can be measured. In Section III, an example MEA is measured to demonstrate this process. The results demonstrate the impact of the diversity scheme on the power radiated and lost in the embedded elements. C. Demonstration of MEA Efficiencies With an Example MEA Fig. 3(a) is a 12-element hollow slot cube MEA [7] without the feed lines, and Fig. 3(b) demonstrates the schematic coaxial feed for the 10th element. The MEA is measured for simultaneous combining (one port is excited and the remaining ports are terminated with 50 ) and non-simultaneous combining (one port is excited and the rest are open circuited). The reflection coefficient of each port is measured with a multiport Network Analyzer for convenience (Agilent E5071B and E5091A [8]) from (4) and these results are given in [7]. The derived

Fig. 3. (a) Photo and (b) schematic of the hollow cube MEA example.

Fig. 4. (a) Matching efficiency, total efficiency and (b) transmit efficiency of each embedded element in the slot cube MEA example for simultaneous (simu) and non-simultaneous (non-simu) diversity schemes.

is given in Fig. 4(a). The total efficiency of each embedded element is measured with a 5 meter spherical near field chamber (SG64 [9]) and the results are included in Fig. 4(a). The defrom (3) for each diversity scheme are compared in rived Fig. 4(b). In Fig. 4, for simultaneous combining, each embedded eleis ment of the MEA has wideband match to 50 [7], so close to unity. The mutual coupling between any two elements is low but not negligible (transmission coefficients are mostly lower than , as given in [7], and the reflection coefficients and losses are low). With a large number of the , the total power lost from the excited MEA elements element to the loads of the non-excited elements (by mutual coupling) is significant. Therefore, as can be seen from (1) and (2), is low, which causes a low . This the resulting of each port in is demonstrated with the measured Fig. 4(a). For non-simultaneous combining, the non-excited elements are open circuited, so, based on (5) and (6), there is no power lost to the loads of these elements through mutual coupling (in the is much higher, as shown in Fig. 4(b). circuit model), and is thereby mainly decided by . In this particular example, is lower than in the simultaneous combining case, owing to a worse impedance match that the embedded element has for the non-simultaneous combining case. and result in a high The measured which confirms the low mutual coupling loss suggested in (5) and (6).

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D. MEA Total Efficiency Matrix As noted above, the total efficiency for each embedded element can be different. A diagonal matrix is used to include all the total efficiencies of embedded element of an MEA, viz.,

.. .

.. .

.. .

.. .

effective branches, and this is not necessarily the same as the number of elements in the MEA. For the example of Rayleigh channels, the probability density function of the SNR of the MRC signal from the equivalent diversity branches can be expressed as [14]

(13)

and this is here referred to as the MEA total efficiency. In this section, the MEA efficiencies were formulated and applied to the analysis of how the radiated power, received power and losses are impacted by mismatch, mutual coupling, diversity combining, and the associated terminations of the MEA. In Section III, the impact of the MEA total efficiency on the diversity and capacity performances is presented. The receive efficiency, as presented above, is difficult to measure. It is often assumed, as below, that the MEA receive efficiency is the same as its transmit efficiency for simplicity, although they are different quantities. III. IMPACT OF MEA TOTAL EFFICIENCY ON DIVERSITY GAIN The diversity performance of an MEA is measured by its , which has several definitions as diversity gain [10], introduced in Appendix B. In this Section, a signal processing approach [10]–[12] is used to calculate the diversity gain for different combining methods. For a lossless MEA with Maximum Ratio Combining (MRC), the calculation is summarized in [10]–[12] as follows. First, the correlation coefficient matrix of the MEA, , is estimated. The correlation is elaborated in Appendix C. The estimate can be from: time series analysis of physical measurements; embedded element patterns and a modeled propagation channel; or, in certain conditions, from network impedances or S-parameters [13]. The modeled channel includes probability density functions for the polarized incoming wave angular spectra. Then can be orthogonalized using singular value decomposition (SVD), here interpreted as returning the non-zero singular values, denoted (14) column of the non-zero singular values, . so is an Since the antenna correlation coefficients are essentially unaffected by the antenna losses (see Appendix C), the singular values do not contain any information regarding the loss. Therefore, the singular values, which correspond to the mean SNRs of the signals that would be received by the equivalent lossless, is the number of non-zero uncorrelated antenna branches.

.. .

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(15) is the number of poles in the Laplace space, and the where residues are

(16) and is the order of the pole, meaning that there are uncorre. The CDF is lated branches with the same mean SNR, (17) and this simplifies when the orders of all the poles are ones, as

(18) A. Formulation of the Impact of on the Diversity Gain The approach of (14)–(17) includes the impact of the antenna correlation coefficient, but it corresponds to a lossless MEA with MRC. When the antenna is lossy, this approach needs to be modified. Taking receive diversity as an example, loss in the embedded MEA elements reduces the receive SNR of each recan be ceive branch. The impact of this reduced SNR on included by scaling the correlation coefficients with the receive total efficiency, see (19) shown at the bottom of the page, and now (20)

.. .

.. .

.. .

(19)

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Fig. 5. (a) Computed and (b) measured ([3]@ 2008 IEEE) CDF vs. SNR of a 2-element orthogonal half wavelength lossy dipole MEA with Selection Combining.

Equation (19) defines a scaled correlation coefficient matrix, , (in either the transmit or receive mode) which is weighted by the positive square root of of the MEA represents from both sides. It is important to note that the reduced SNR on each receive branch, rather than a reduced is no longer correlation. Note also that the diagonal of unity because of the scaling. Likewise, the scaled singular value , contains the impact of the embedded column matrix, element total efficiencies on the equivalent lossless and uncorrelated branches of the MEA. With (20), (15), (16), and (17), the CDF of the MRC combined SNR with the impact of MEA total efficiency can be found. Other combination techniques can follow the same method, should this be required. For example, the CDF of Selection Combining (SC) in a Rayleigh environment is (21)

B.

Reduction of a Dipole MEA With SC

To demonstrate and verify the above formulas including the , the CDF of an MEA with impact of MEA efficiency on SC, was computed with (19)–(21), and compared with a published measurement result in [3]. The MEA comprised two orthogonal half wavelength lossy dipoles. The total efficiencies of the embedded elements are 0.51 and 0.59 [3], respectively. The elements are assumed uncorrelated, as suggested in [3], so the correlation coefficient matrix is a 2 2 identity matrix. In Fig. 5(a) the solid curves are the SC CDFs of idealized MEAs (uncorrelated and lossless) having 1 to 2 antenna

branches from the left to the right. The dashed curve is the computed SC CDF of the 2-element orthogonal half wavelength lossy dipole MEA, which agrees very well with the measured result in Fig. 5(b) from [3]. The possible sources of the difference are the measurement uncertainties of the efficiency and the finite correlation of an implemented antenna. of Element-Symmetric and -Asymmetric MEA There is a special class of MEA structures which are symmetric in the sense that each element sees an identical structure of elements around it. The analysis of these structures becomes simplified because if all the terminating impedances are the same, then under the same conditions, all the elements will see the same impedance on transmit, and will invoke the same total radiation and losses, and the same efficiencies. So an averaged (across the branches) efficiency can be used, and and can be simplified as

C.

(22) Conversely, for a general MEA, there is asymmetry in the sense that the elements will have different losses and efficiencies. It is of interest to compare the difference in diversity performance of the element-asymmetric MEA, with the behavior of the element-symmetric one. Fig. 6 gives the computed SC CDF curves of three element-symmetric MEAs in Fig. 6(a) and the curves of the same MEAs but with asymmetric element efficiencies in Fig. 6(b). Each MEA comprises three uncorrelated half wavelength

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Fig. 6. Selection combining CDFs of (a) uncorrelated, symmetric (b) uncorrelated, asymmetric (c) correlated, symmetric and (d) correlated, asymmetric 3-element half wavelength dipole MEAs.

dipole elements with the element efficiencies given in the figures. To verify the impact of correlation on element-asymmetric MEAs, the CDFs of correlated MEAs are also computed in Fig. 6(c) and (d). Fig. 6 gives the computed SC CDF curves of three element-symmetric MEAs in Fig. 6(a) and the curves of the same MEAs but with asymmetric element efficiencies in Fig. 6(b). Each MEA comprises three uncorrelated half wavelength dipole elements with the element efficiencies given in the figures. To verify the impact of correlation on element-asymmetric MEAs, the CDFs of correlated MEAs are also computed and presented in Fig. 6(c) and (d). In Fig. 6(a), with the decrease of the element efficiency, the CDF curve translates to the left of the figure towards the lower decreases. The spacing between any two SNR direction, so adjacent dashed curves is 1 dB, which corresponds to the difference of the element efficiencies. The computed CDF curve for agrees well with the MEA with element efficiency of the published measured result of the same MEA in [3], and the agreement helps to verify the formulation from measurements. In Fig. 6(b), the averaged (in decibel) efficiency of each , , and , respectively, asymmetric MEA is and equals to the element efficiency of the symmetric MEAs in Fig. 6(a). It is obvious that the CDF curves of the corresponding symmetric and asymmetric MEAs are the same. This observation in turn indicates that it is reasonable to use averaged [3]

(rather than the highest [4]) element efficiency for the MEA in a simple way. Fig. 6(c) and (d) are for the same symmetric and same asymmetric MEAs as in Fig. 6(a) and (b), respectively, but the elements are correlated. A correlation coefficient matrix is used as an example. The computed results show that, although the correlation changes the slope of the CDF curves, the spacing between the adjacent curves is again 1 dB, and the averaged (in decibel) efficiency can still be used to find the asymmetric MEA diversity performance in a simple way. The last observation suggests that the requirement of having uncorrelated elements for using (dB-)averaged element efficiency in [3] does not seem to be necessary. D. Diversity Gain Reduction of a Slot Cube MEA Due to the Impact of the MEA Total Efficiency The above discussions of the impact of MEA efficiency on the diversity performance are based on idealized dipole models, although some results are verified with published measurement. Here, the MRC diversity performance of the measured hollow slot cube MEA [7] in a Rayleigh channel with the uniform, uncorrelated incoming wave distribution is presented. This MEA with simultaneous combining (such as MRC) has low mismatch loss, and low correlation coefficients for the uniform Rayleigh scenario [7], but the high mutual coupling loss

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Fig. 7. Scaled singular values of the 12 element hollow slot cube MEA. indexes the equivalent uncorrelated antenna branches.

This example demonstrates how the impact of correlation and MEA efficiency on the MEA diversity performance can be separated. The impact of the correlation is to change the slope of the CDF curve, and the impact of MEA efficiency is to translate the CDF curve. For this example of the hollow slot cube MEA, the mutual coupling loss dominates the reduction in diversity gain and the correlation is low so its impact is small. Other antenna examples may be differently impacted by these factors. This 12 element MEA with MRC has a diversity order of only 6, so it is equivalent to a 6-element idealized (uncorrelated and lossless) diversity antenna. With this, the transmission reliability at 0.5% probability is still improved by a diversity gain of 25 dB. IV. IMPACT OF MEA TOTAL EFFICIENCY ON CAPACITY The MIMO channel capacity [16], [17] (the term capacity is favoured by information theorists, and capacity efficiency by communications engineers; here we also use capacity for brevity) for a static unknown channel can be expressed as (23)

Fig. 8. MRC CDFs for SNR less than the abscissa for ideally uncorrelated and , solid curves), and for the hollow slot cube MEA lossless branches ( when the impact of antenna correlation coefficient is included (circle-dashed curve) and when efficiency is also included (star-dashed curve).

causes a low MEA total efficiency as shown in Fig. 4. The correlation coefficient matrix of the MEA is obtained with the method of embedded element radiation patterns [15] as mentioned in Appendix B. Based on the MEA efficiency and correlation coefficient matrix, the singular values are attained with (20) and depicted in Fig. 7, which represent the different mean power in each equivalent lossless and uncorrelated branch. In Fig. 8, the solid curves are the MRC CDFs of idealized MEAs (uncorrelated and lossless) having 1 to 12 antenna branches, from the left to the right. The circle-dashed curve is for the 12-element slot cube at its resonance with MRC, obtained with (14) and (18) including the impact of antenna correlation coefficient but not including the impact of the MEA total efficiency. It overlaps with the curve for the 11-branch ideal MEA, so the diversity order of this slot cube MEA is slightly reduced (by about one ideal branch), owing to the finite correlation among slot elements. Taking the first left curve for 1 branch antenna as the reference antenna, and a probability of , which is 1 dB less 0.5%, the diversity gain is than the ideal case. With (18)–(20), the impact of the MEA total efficiency is included in the CDF of the MEA (star-dashed curve). It is parallel to the circle-dashed curve, and is near the curve for the 6-branch ideal MEA. Now the diversity gain of the MEA is at the probability of 0.5%. Comparing the star-dashed and circle-dashed curves, it can be seen that the antenna correlation coefficient reduces the MEA diversity order by one ideal is reduced by 1 dB), then the MEA total efficiency branch ( is reduces the diversity order by five more ideal branches ( further reduced by 4 dB).

where is the identity matrix; is the number of is a normalized (instantaneous) the transmit antenna; and channel transfer matrix. The mean capacity is averaged over the . Note that this channel variations, written is different to the capacity of the mean channel. The mean capacity from this formula is known to be close to the upper limit given by the parallel (eigen) channel formulation for known channels [10]. This capacity is an information theoretic form derived from mutual information, and is in bits per channel use. Imperfect antennas, filters, etc., and communications system aspects reduce this drastically to an achievable communications capacity efficiency (in bits/sec/Hz). But it is convenient here to isolate the impact of antenna effects on the information theoretic capacity for an insightful evaluation of MIMO antennas. The Kronecker model [18], [19] is a simplistic method to combine the transmit and receive antenna correlation coefficients into the channel transfer matrix. The accuracy of this approach has been questioned [20], and [21] reports that it is not applicable to the polarimetric case. But in the same spirit as the capacity, the Kronecker model is nevertheless a convenient simplification for comparatively evaluating MEAs. With this model, the channel can be taken as zero mean, unit variance, complex Gaussian i.i.d., and the instantaneous white , is modified with the correlachannel matrix, denoted tion coefficient matrices of the transmit and receive antennas, as (24) where and are the correlation coefficient matrices of the transmit and receive antenna, respectively, in a given propagation channel model. The transmit correlation coefficient matrix is taken to be the same as that from its well defined receive operation. To include the impact of the receive and transmit MEA total efficiencies on the MIMO capacity, the scaled correlation coefficient matrices defined in (19) are used in the same way,

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Fig. 9. MIMO Capacity of the hollow slot cube MEA.

(25) The capacity is now

(26) If an ideal transmit antenna (unity total efficiency for each el, the ement and zero correlation) is used, i.e., impact of the imperfections of the receive antenna can be singled out. Here, the receive MEA efficiency scales the transmis, as sion matrices to (27) or alternatively stated, the SNR is scaled, and the resulting capacity, , is

12-element MEA at the transmitter. The curve has a MIMO capacity order of about 9 when the SNR is higher than 15 dB, and a MIMO capacity order from 7 to 8 for lower SNR. A more significant drop in MIMO capacity is caused by the MEA antenna efficiency. For an SNR of 20 dB, this MEA example is equivalent to an 8.5-branch ideal MEA in terms of MIMO capacity. The cross-dashed curve is for the slot cube MEA example at both transmitter and receiver. It is emphasized that here the transmit and receive total efficiencies are assumed to be the same for simplicity, but this is not a limitation of the formulation. Here, the capacity is computed with (25) and (26), and it is obviously decreased further. From the figure, the pair of slot cube MEAs has the capacity of a pair of 6-branch ideal MEAs for an SNR of 20 dB. Note that diversity gain and MIMO capacity vary differently , and at given SNR for capacity. at given probabilities for Overall, this MEA is essentially equivalent to a 6 branch idealand capacity. ized MEA in terms of both

V. CONCLUSION

(28) Fig. 9 illustrates the impact of MEA total efficiency on the averaged capacity of the slot cube MEA in a Rayleigh channel. Statistical channel information is contained in the correlation coefficient matrix (Appendix C) so the capacity for other propagation scenario models can also be found. The solid curves are the averaged capacity for the unknown, ideal, Rayleigh channels of order of 1 to 12. The dashed curve is for the case when an ideal 12-element transmit antenna is used, and the slot cube MEA example with unity efficiency (in (27) and (28)) is receiving. This curve is between the MIMO capacity order of 11 and 12. In other words, the correlation coefficient between the slot cube elements decreases its MIMO capacity slightly, so this lossless form of the slot cube MEA is equivalent to an ideal MIMO antenna with 11.2 branches at . The circle-dashed curve includes the MEA total efficiency in (27) and (28) for using the slot cube at the receiver and an ideal

In this paper, formulas of MEA efficiencies with fixed diversity combining are developed in the context of MIMO communications performance. The MEA embedded element efficiency is derived for both the transmit and the receive cases. This allows identification of the conditions for the transmit and receive efficiencies to be the same. The total efficiency of the embedded element is also presented. The MEA total efficiency is expressed as a diagonal matrix of the total efficiencies of the embedded elements. This matrix is for calculating the impact of the MEA total efficiency on the communications performance in terms of the diversity gain and capacity in modeled propagation scenarios. The reductions in the diversity gain and capacity, resulting from the finite correlation coefficient and the MEA total loss (ohmic and through mutual coupling) are separated in order to analyze the different performance degradations. The diversity order and MIMO capacity order of an MEA are expressed as an equivalent number of idealized branches, i.e., lossless, equal gain, uncorrelated and uncoupled. This metric allows a performance comparison of different MEA designs. An element-asymmetric MEA example and two element-symmetric MEAs are used as examples to get a feel for the efficiency metrics.

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APPENDIX A DIVERSITY COMBINING Combining can be implemented at either the transmitter or receiver, and it may act to change the terminations of the elements. One class of combining implementation has all the elements connected to fixed loads (viz., the transmitters or receivers), and it is here called simultaneous combining because all the branch signals are used simultaneously. It includes Optimal Combining (OC), Maximum Ratio Combining (MRC), Equal Gain Combining (EGC), and Selection Combining (SC) implementations where all the elements have fixed terminations. With simultaneous combining, power coupled from one MEA element to other elements can be “collected” at the receive loads in the receive case, or radiated by other elements in the transmit case. Such power must be considered “useful”—except in the receive case of SC with fixed terminations because we do not have access to the received power in the unselected terminations. For the case of the re-radiation, the power radiated via mutual coupling is part of the embedded element radiation pattern, and is therefore “useful”. Meanwhile, there is “wasted” power in the form of ohmic loss in all the elements. Another class of combining implementation can be called non-simultaneous combining, in which the signals are not combined simultaneously. It includes Switched Combining (SwC), and the implementation is to have only one element selected (i.e., terminated) at a time and the unused elements open circuited. With this non-simultaneous combining, we can simplistically model the situation as having no mutual coupling since there is no current flowing through the open circuits. In some implementations, there may be physical non-zero currents because the physical “open circuit” termination may in fact be reactive and/or have finite resistances, but the circuit model (with ideal open circuits) is still valid because the elements are considered as embedded. Therefore for MEAs, the efficiency of one element needs to be considered as being embedded in the MEA, i.e., the efficiency must include the presence of the other elements and the supporting structure, as well as the diversity combining scheme in the sense that the embedded efficiency depends on the terminations of the other elements. In this way, the MEA efficiencies are defined for different diversity combining schemes. For simultaneous combining (OC, MRC, EGC, SC etc.), an embedded transmit element is taken to mean that this element is connected to its transmit source while all the other elements are terminated with their transmit source impedances. Likewise, an embedded receive element means that this element is receiving and all the other elements are terminated with their receive load impedances. For non-simultaneous combining (i.e., SwC), an embedded transmit element means that this element, in the circuit model, is connected to its transmit source while all the other unselected elements are open circuited. So an embedded receive element circuit model includes this receiving element, and all the other unselected elements are open circuited. APPENDIX B DIVERSITY GAIN The diversity performance of an MEA is measured by . There are several definitions its diversity gain [10],

for the diversity gain. For example, in digital communications, an error rate can be modeled along the lines of , or plotted on the usual log-log , for scale, log high SNR. The slope of the BER function gives the diversity is a coding gain). But such a slope metric gain (and alone, while simple, is insufficient to capture the complete gain garnered from diversity action. A more complete definition is conveniently read from cumulative density function (CDF) plots of the SNR, but clarification is required for the definition of the CDF quantities. Here, the diversity gain is defined as the improvement in the averaged normalized SNR, here expressed in dB (B-1) is the instantaneous SNR of the combined received where signal. is the mean SNR on one MEA receiving branch. Simiand are respectively the instantaneous and mean larly, SNR received by a single element reference antenna. This shows that the diversity gain is the improvement in receive SNR of the diversity MEA over the SNR of a reference single branch. Note that this definition of diversity gain depends on the choice of the probability and the choice of reference antenna element. There are several options for the reference element. For example, it can be one of the MEA’s elements which is already mounted on the supporting structure or terminal, but with the other elements removed [22]. In this case, the diversity gain gives the SNR improvement from a single element system to a multiple element diversity systems in the same device. Another option is to take the element with the highest average SNR as the reference antenna, while the other elements remain present. Or the reference element can be a separate antenna, such as a dipole, or for analysis or simulation, an idealized element such as one with a lossless, isotropic pattern. The choices of probability and reference antenna need to be specified in a study of diversity performance in order to allow direct comparison of results. and include the propagation channel Factors affecting characteristics, diversity combining method, the MEA total efficiency, and the correlation coefficient between each element. The total efficiency of each element impacts the SNR value of the branch which includes that antenna element. Changing propagation channel characteristics may change the antenna correlations, but do not change the MEA efficiencies. Using the embedded element patterns and modeled propagation scenario statistics, the antenna correlations can be found from the approach of [15] for diversity performance analysis; and likewise for the capacity analysis in different propagation models in the Section IV. can be estimated from the time series In a measurement, samples from real world propagation environments, e.g., urban, indoor, etc. This is the best estimation technique in the sense that the real world behavior is being sampled. But it is a complex and expensive measurement, and care must be taken with the averaging, i.e., the experiment must cover all the propagation environments, with appropriate weightings, for an accurate ensemble estimate. Moreover, the mobile antenna must be moved, e.g., translated, rotated, etc., in a realistic way, and be deployed

YUN AND VAUGHAN: MULTIPLE ELEMENT ANTENNA EFFICIENCY AND ITS IMPACT ON DIVERSITY AND CAPACITY

appropriately—a major exercise for handheld terminals which are held to the head and also operated in the hands, in both cases with many different poses [23]. In such measurements, an observation from one environment may not match well with another observation from a different environment, or with an ensemble average. Another physical measurement method is to create an artificial incoming wave distribution, typically striving for uniform and uncorrelated scattering [24]. This method needs no antenna patterns as required by the approach of [15]. It is useful for measuring the mean effective gain of an antenna when it is not possible to measure the patterns and when the uniform propagation scenario can be assumed present all the time.

APPENDIX C ANTENNA CORRELATION Antenna correlation usually refers to the time series correlation of the received signals (or rather the modulation imposed by the multipath channel on a transmitted carrier signal). This is hard to measure accurately, requiring extensive data collection and time series analysis, and the results from such a measurement can only be repeated in a statistical sense. The accuracy is further complicated since such a measurement features signal plus noise. If the signal cannot be separated from the noise (usually impossible) then the time series measurement is affected by ohmic loss in the antenna, because the SNR is governed by the loss. This is clear from the limiting case of zero efficiency where a measured signal correlation will reflect only the (un)correlation of the noise at the receiver. If the signal can be separated from the noise, then the correlation coefficient of the signals can be calculated and will be independent of the losses, or antenna efficiency. Under certain conditions, this correlation coefficient can be estimated by the normalized inner product of the embedded antenna element patterns, using probability density functions (pdfs) to model the polarized incident waves. This measure is deterministic, and flexibility is possible using the distributions of the incoming waves. The measured pattern correlation coefficient is not strongly affected by the ohmic loss in the antenna (because the pattern measurement requires good SNR, the antenna efficiency cannot be zero), but may well be affected by the changes to the environment (i.e., the pdfs), including the presence of a user. In this paper, we refer to the correlation as the signal correlation, and consider that the pdf-weighted pattern-calculated correlation is a good approximation to this.

REFERENCES [1] “IEEE Standard Test Procedures for Antennas,” in IEEE, Standards. Piscataway, NJ: IEEE, pp. 149–1979. [2] “IEEE standard definitions of terms for antennas,” in IEEE, Standards. Piscataway, NJ: IEEE, pp. 145–1993.

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[3] J. F. Valenzuela-Valdés, M. A. García-Fernández, A. M. MartínezGonzález, and D. A. Sánchez-Hernández, “The influence of efficiency on receive diversity and MIMO capacity for Rayleigh-Fading channels,” IEEE Trans. Antennas Propag., vol. 56, no. 5, pp. 1444–1450, May 2008. [4] K. Karlsson, J. Carlsson, I. Belov, G. Nilsson, and P.-S. Kildal, “Optimization of antenna diversity gain by combining full-wave and circuit simulations,” in Proc. EuCAP 2007, Nov. 2007, pp. 1–5. [5] J. B. Andersen and A. Frandsen, “Absorption efficiency of receiving antennas,” IEEE Trans. Antennas Propag., vol. 53, no. 9, pp. 2843–2849, Sep. 2005. [6] J. B. Andersen and R. G. Vaughan, “Transmitting, receiving and scattering properties of antennas,” IEEE Antennas Propag. Mag., vol. 45, no. 4, pp. 93–98, Aug. 2003. [7] J. X. Yun and R. G. Vaughan, “Slot MIMO cube,” presented at the IEEE Antennas Propag. Soc. Int. Symp., Toronto, ON, Canada, 2010. [8] [Online]. Available: http://www.agilent.com/ [9] [Online]. Available: http://www.satimo.com/ [10] R. G. Vaughan and J. B. Andersen, “Channels, propagation and antennas for mobile communications,” in Inst. Elect. Engr. Electromagnetics Waves Ser.. London, U.K.: , 2003, vol. 50. [11] W. C. Jakes, Microwave Mobile Communications. Piscataway, NJ: IEEE Press, 1993. [12] R. G. Vaughan, “Requirements for dversity/MIMO with some evaluation techniques,” in Antennas for Wireless Systems. New York: Wiley, 2007, ch. 15, pp. 405–445. [13] J. X. Yun, “Design and evaluation of slot multiple element antennas,” Ph.D., Simon Fraser Univ., Burnaby, BC, Canada, 2011. [14] M. Schwartz, W. R. Bennett, and S. Stein, Communication Systems and Techniques. New York: McGraw-Hill, 1966. [15] R. G. Vaughan and J. B. Andersen, “Antenna diversity in mobile communications,” IEEE Trans. Veh. Technol., vol. 36, no. 4, pp. 149–172, Nov. 1987. [16] J. H. Winters, “On the capacity of radio communications systems with diversity in a Rayleigh fading environment,” IEEE J. Sel. Areas Commu., vol. SAC05, no. 5, pp. 871–878, Jun. 1987. [17] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Pers. Commun., vol. 6, pp. 311–335, 1998. [18] A. L. Moustakas, H. U. Baranger, L. Balents, A. M. Sengupta, and S. H. Simon1, “Communication through a diffusive medium: Coherence and capacity,” Science, vol. 287, Jan. 2000. [19] D. Chizhik, F. Rashid-Farrokhi, J. Ling, and A. Lozano, “Effect of antenna separation on the capacity of BLAST in correlated channels,” IEEE Commun. Lett., vol. 4, no. 11, pp. 337–339, Nov. 2000. [20] H. Özcelik, M. Herdin, W. Weichselberger, J. Wallace, and E. Bonek, “Deficiencies of the Kronecker MIMO radio channel model,” Electron. Lett., vol. 39, pp. 1209–1210, Aug. 2003. [21] J. P. Kermoal, L. Schumacher, F. Frederiksen, and P. E. Mogensen, “Polarization diversity in MIMO radio channels: Experimental validation of a stochastic model and performance assessment,” in Proc. 54th IEEE VTS Fall VTC 2001, 2001, vol. 1, pp. 22–26. [22] V. Plicanic, B. K. Lau, A. Derneryd, and Z. Ying, “Actual diversity performance of a multiband diversity antenna with hand and head effects,” IEEE Trans. Antennas Propag, vol. 57, no. 5, pp. 1547–1556, May 2009. [23] M. Pelosi, O. Franek, M. B. Knudsen, M. Christensen, and G. F. Pedersen, “A grip study for talk and data modes in mobile phones,” IEEE Trans. Antennas Propag., vol. 57, no. 4, pp. 856–865, Apr. 2009. [24] P. S. Kildal, K. Rosengren, J. Byun, and J. Lee, “Definition of effective diversity gain and how to measure it in a reverberation chamber,” Microw. Opt. Technol. Lett., vol. 34, no. 1, pp. 56–59, Jul. 2002. J. X. Yun, photograph and biography not available at the time of publication.

R. G. Vaughan, photograph and biography not available at the time of publication.

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On the Accuracy of Equivalent Circuit Models for Multi-Antenna Systems Jon W. Wallace, Member, IEEE, and Rashid Mehmood, Student Member, IEEE

Abstract—The equivalent circuit model of a general PEC antenna array is derived, based on a rigorous method of moments (MOM) formulation, indicating that network analysis is exact from the standpoint of electromagnetic wave theory. It is found that the network parameters (Z, Y, or S-parameters) for the transmit mode can be used for exact prediction of the receive-mode array response. Numerical and experimental examples illustrate the validity of the analytical results. Index Terms—Antenna arrays, equivalent circuits, modeling, moment methods, multiple-input multiple-output (MIMO) systems, mutual coupling.

I. INTRODUCTION

E

QUIVALENT circuit models, also referred to as network models, have gained attention for modeling antenna arrays and multiple-input multiple-output (MIMO) systems, allowing circuit effects such as amplifier noise, matching and reconfigurability to be studied [1]–[5]. Such models are computationally attractive, since the transmit and receive arrays can be represented as equivalent circuits, requiring only a modest number of full-wave simulations or measurements, after which circuits of varying complexity are analyzed with efficient circuit-level simulation. In [6] it was formally proven that antenna arrays in the transmit and receive mode can be modeled with network analysis and that the same impedance matrix (with the exception of a transpose) can be used for both modes. In [7], the effect of mutual coupling on adaptive arrays is studied by considering an equivalent network model, yielding a simple linear relationship between the loaded and open-circuit voltages on a receive array and a beamformer for optimal signal to interference and noise ratio (SINR) is derived. More recently, [8] gives the equivalent circuit of a single receive antenna and [9] provides an equivalent circuit for a receiving array. In contrast to work endorsing simple equivalent circuit models, there is also work that questions the use of such models. For example, [10] suggests that the compensation method in [7] is suboptimal since the network model only assumes a single basis function per antenna and an improved compensation method based on a full moment method model of the array is proposed. In [11] the use of Norton or Thévenin Manuscript received June 15, 2010; revised November 03, 2010; accepted November 15, 2010. Date of publication May 10, 2011; date of current version February 03, 2012. The authors are with the School of Engineering and Science, Jacobs University Bremen, Bremen, Germany (e-mail: [email protected]; r.mehmood@ieee. org). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2152339

equivalent circuits for receiving antennas is challenged, since power absorbed by the internal impedance of the network does not have a strict physical meaning and a different model is proposed based on a constant power source. A physically appealing model is also proposed in [12] that includes the transmit antenna in the equivalent receive model. Recent work [13], [14] also questions the use of array transmit-mode mutual impedances for the receive mode, which is troubling from the standpoint of reciprocity. The purpose of this paper is to provide a straightforward but rigorous analysis of antenna arrays based on method of moments (MOM), illustrating that equivalent circuit models are exact and that receive-mode behavior of an array can be exactly predicted by usual transmit-mode quantities. Although these observations are basically equivalent to those in [6], the MOM analysis here has a number of advantages: the development is simpler and intuitive, the transmit and receive modes do not need to be considered separately and the MOM discretization provides an exact definition for the ports. The analysis provides valuable insight on the operation of equivalent circuit models, such as the connection of transmit and receive mode, the number of basis functions (or degrees of freedom) required to represent currents accurately on an antenna array and potential sources of inaccuracy in network models. Several examples are provided based on full-wave simulations and direct measurement that validate the analytical results. The paper is organized as follows: Section II derives Z, Y and S-parameter equivalent circuit models of antenna arrays in the transmit/receive mode from MOM. Section III provides numerical examples that demonstrate the observations of the MOM analysis, followed by an experimental example in Section IV. Section V provides concluding remarks. II. METHOD OF MOMENTS ANALYSIS OF MULTI-ELEMENT ARRAYS In this section, we rigorously analyze general antenna arrays ports by applying the method of accessible at a finite set of moments. Although we restrict our attention to antennas composed of perfect electric conductor (PEC) surfaces, we do so only for the sake of simplicity and the method can be naturally extended to dielectric and magnetic materials, finite conductivity, etc. This exercise provides valuable intuition on the connection between network analysis and full-wave analysis and the requirements for good agreement. Furthermore, we prove that mutual interactions of the transmit mode, receive mode and combined transmit/receive mode can be captured with a single equivalent model that involves the usual (transmit mode) mutual impedance matrix.

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Fig. 2. Equivalent antenna array circuit model in transmit/receive mode.

Fig. 1. Geometry of (a) a general antenna array and (b) a wire dipole array and example method of moments segmentation.

Appropriately partitioning (4) into elements at the ports (P) and on the PEC antenna array structure (A), (5) (6)

A. Governing Equations Fig. 1 depicts a general antenna array in a free-space medium where signals can be driven and/or measured at ports. An externally applied incident field may also be present, denoted by , which is general (plane wave, spherical wave, etc.). Total field at observation point is given in terms of current density on the antenna according to [15] (1) is the dyadic Green’s function for free space. where MOM discretization is performed using basis expansion , or (2)

followed by the projection onto the weighting functions

where

due to PEC surfaces.

B. General Transmit/Receive Mode The general mode (transmit and receive) of the antenna is considered. From (6) the currents on the antenna array are (7) and plugging into (5) gives the voltages on the ports in terms of the port currents only, or

(8) This resulting system is equivalent to the network model depicted in Fig. 2. Thus, the operation of the array can be comfor all puted exactly if we know the open circuit voltages incident fields of interest as well as the impedance matrix . Radiated fields from the antenna can be computed using (2), yields where the partitioning

(3) (9) which gives the usual linear relationship (4) and to have identical local support We choose , such that and represent the current and voltage on the element, respectively. The basis functions are ordered so that the first correspond to port terminals, where and for are the port currents and voltages. Many choices of the and are possible, but a simple choice is a filament properly connecting the two port terminals, where is the current on the filament and is the contour integral for voltage between the terminals. Note that basis and weighting functions for elements on the PEC structure are chosen to be tangential to these surfaces.

is field scattered by the antenna for (open where circuit) and is interpreted as the radiation pattern of port for polarization for unit input current when the other ports are open-circuited. Typically, we are most interested in far-fields of the array and the expression can be simplified to (10) , and In the transmit mode, so that the radiated fields are just a superposition of the opencircuit embedded patterns weighted by the port currents. For the receive mode (and combined mode) the scattered field term must also be included.

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current . If we use a simple Hertzian dipole for the reference antenna, the field present at the origin is (11)

Fig. 3. Computation of ciprocal equivalent.

for far-field sources (a) direct problem and (b) re-

C. Comparison of Transmit and Receive Mode Our analysis shows that the only difference in using the antenna in transmit versus receive mode is that for the pure transmit case, so that a linear system is obtained, whereas for the receive case. Also, note that is the usual transmit mutual impedance and there is no approximation when using this for the receive case. This is in contrast to the development in [13] that questions the use of transmit mutual impedances for the receive mode. We also compare with the result in [6], where it was shown that the receive mode mutual impedance matrix is the transpose of that for the transmit mode. Although a reciprocal antenna and medium are considered here, the same equivalent circuit as in Fig. 2 would be obtained for non-reciprocal (general bianisotropic) materials. The impedance matrix does not transpose due to or what is connected to the ports, indicating that must be the same for both the transmit and receive mode. To remedy the apparent dilemma, it must be noted that [6] invokes the Lorentz reciprocity theorem, where for non-reciprocal materials the system must be changed to a new system with complementary materials [15]. Given that the original transmit impedance matrix is , we denote the transmit impedance matrix of the complementary system as . In [6] it was actually shown that whereas is used for the transmit case, should be used for the receive case. However, since the original and complementary systems are related by reciprocity, and alone (no transpose) can be used for the receive system. Also, [6] shows that the load matrix is optimal for receive power transfer, but this is the same as a Hermitian match to the original physical transmit impedance, or . For S-parameters with a real normalizing impedance, it can be shown that this condition is the same as , which was proven to provide maximum power transfer in [2]. D. Computation of The exact network model requires knowledge of for all incident fields of interest. In many cases, external sources are far away from the array and only needs to be found for plane-wave incidence. In this case, reciprocity arguments can be used to obtain in terms of the radiated far-fields for the transmit-only mode. Consider the configuration depicted in Fig. 3(a) for finding , which is the open-circuit voltage induced on the array due to a plane wave originating from direction . Here, a transmit reference antenna is placed at coordinate , which is in the far-field of the array near the origin and driven with

where is the orientation and the effective length of the reference antenna and and are the wavenumber and intrinsic impedance of the background medium. Next, consider the reciprocal system in Fig. 3(b), which will give the same value of . The field incident on the reference antenna is (12) The open-circuit voltage on the Hertzian dipole is

(13)

Thus, the receive-mode open-circuit voltages for plane-wave incidence can be computed using the transmit-mode open-circuit embedded radiation patterns. For receive array calibration, the direct arrangement in Fig. 3(a) may be preferred. Terminating the array with load impedance matrix and defining to be the vector of currents flowing into the antenna ports, (14) (15) Proper combination gives (16) indicating that the open-circuit voltage can be computed using . a measurable voltage across known loads E. Degrees of Freedom of an

Port Array

As the number of MOM basis functions used to discretize the antennas grows large, one would expect that an equally large number of parameters would be needed to represent the current distribution on the antennas. Here we illustrate that often a more concise representation is possible. Consider the array in transmit mode where . According to (7), is a weighted sum of at most linearly independent vectors spanned by the columns of , regardless of what is attached to the ports (loads or sources). Therefore, only independent basis functions are needed to completely represent currents on the array. Next consider the receive mode with a fixed . The incident field simply adds one additional basis vector in (7), meaning that can be decomposed into a weighted sum of fixed basis vectors, regardless of port termination.

WALLACE AND MEHMOOD: ON THE ACCURACY OF EQUIVALENT CIRCUIT MODELS FOR MULTI-ANTENNA SYSTEMS

For the receive mode when is not fixed, the number of required basis vectors is at most , where is the number of linearly independent that can exist, which may be large in practice. However, in some special cases, the are linearly dependent. For example, if the array consists of minimally scattering thin-wire dipoles [16] and is a plane wave coming from direction and oriented parallel to the dipoles, for each antenna is a scan angle dependent scalar times a constant vector. According to (7), the current on each antenna requires at most one basis vector in addition to the transmit mode vectors, meaning up to vectors are needed to represent all current distributions on the array. In [10] it is correctly observed that one basis function per antenna is insufficient to represent antenna currents on a dipole array with parallel plane-wave excitation. However, our analysis shows that only two basis functions are needed per antenna, as long as they span the correct subspace. F. Alternative Model Parameterizations Although equivalent, there are times when other network parameterizations are desirable. Multiplying both sides of (8) by results in the admittance formulation (17)

where is the admittance matrix and is the current flowing into the ports due to the incident field when all ports are shortcircuited. Substituting from (17) into expression (9) for radiated fields,

(18) where are the transmit-mode short-circuit embedded patterns where the pattern (column) is obtained by placing a unit voltage source across the port and zero volts (short circuit) across the other ports. The scattering parameter (S-parameter) formulation relates the ingoing waves and outgoing waves on the network ports, which are related to the port voltages and currents according to (19) where and

is an arbitrary normalizing impedance. Substituting from (19) into (8) and rearranging yields

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which substituted into (9) yields

(22) is the scattered field due to incident field with where matched loads on all ports and are the matched circuit patterns. G. Network Analysis of Reconfigurable Antennas Network analysis is an attractive solution for analyzing reconfigurable antennas with a large number of possible states, since the number of required full-wave simulations can be kept to a minimum. In this section, we illustrate that if out of ports are terminated with loads (such as reconfigurable elements), this simply creates a new effective array with ports having modified network parameters and new radiation/reception patterns. Also, we use this framework to show that the impedance matrix of a non-reciprocal system is the same for transmit and receive mode and only the transmit and reception patterns are different. Consider a reconfigurable antenna array with total ports, where ports are terminated with loads (such as reconfigurable elements) and are left accessible to be connected to transmit or receive RF chains. Letting vector ports 1 and 2 correspond to the accessible and reconfigurable terminations, respectively, we have (23) Terminating port 2 with a network having the impedance matrix , we have and solving for

(24) which means that the loaded antenna system forms a new circuit with impedance matrix and open-circuit voltage . The far-field of the array can be computed using (10) where (25) and are radiation pattern matrices for the and accessible and loaded ports, respectively. Eliminating

(20) where is the outward traveling wave due to the incident field for matched circuits (loads with impedance ) connected to all ports and is the transmit S-parameter matrix of array. Substituting (20) into (19), (21)

(26) indicating that the loaded array can be treated as a usual array as before except with modified open-circuit radiation patterns.

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It is instructive to consider the case where the unloaded array and channel are reciprocal , but the loading is not . The unloaded open-circuit voltage can still be computed from (13), or (27) Substituting into (24), (28) (29)

in (26) is Thus, although the radiation pattern different from the reception pattern , the same impedance matrix in (24) is used for both transmit and receive modes. H. Potential Sources of Inaccuracy Although (8) and other network representations are exact, it is instructive to consider how improper application may lead to potential inaccuracy. 1) Isolated vs. Embedded Element Patterns: A common simplifying assumption in equivalent circuit models of antenna arrays is the use of isolated transmit and receive patterns, rather than precise embedded patterns. For an array composed of identical elements, this approach only requires a single pattern to be found followed by pattern multiplication with the array factor. The operation of isolated elements is defined from (5) and (6) by replacing with the block matrix , where otherwise

(30)

maps the basis function index to and the function its associated antenna port . Assuming isolated antennas in the transmit mode, implies that the current on an entire open-circuit antenna is zero. In the receive mode, a similar substitution of is made for in (8), which leads to the observation that when is computed, only the currents induced by for are used and currents on other antennas are treated as zero. Antennas that exhibit negligible current when open-circuited, or , are referred to as minimally scattering antennas [16], where the principle example is thin wire dipoles. Clearly for general antennas, will not be close to , meaning that significant currents can flow on the surface of an open-circuited antenna. Since these currents will affect and , assuming isolated patterns can lead to significant error in network computations. 2) Current Distribution on Loads and Sources: The network model in Fig. 2 allows arbitrary loads and sources to be connected to the ports. However, note that the model is only exact when the current densities on the ports have the same distribution as the basis functions that were chosen for computing . When the current distributions on the ports are significantly altered, the matrices , and are also different, leading to error.

Fig. 4. Current distribution on a single dipole antenna for different loading, where is the predicted value using the transmit-mode current distribution and is from direct receive-mode simulation.

III. NUMERICAL EXAMPLES This section provides numerical examples, not only to validate the previous analytical results, but also to help provide intuition on the behavior of the multi-antenna systems with coupling. A. Single Antenna: Transmission vs. Reception First, we study a simple single-antenna MOM simulation. Although somewhat trivial, this case demonstrates the important principle that the difference in transmit and receive current distributions on an antenna is exactly predicted by the open-circuit current distribution. The Numerical Electromagnetics Code Version 2 (NEC2) [17] was used for simulations of a single -directed dipole with length and radius . The antenna was first simulated in the transmit mode with a 1 V source placed across the terminals and the resulting current on the antenna and -directed far-zone E fields versus azimuth angle were stored. Second, the antenna was simulated in receive mode with a plane wave coming from azimuth angle with for loads giving antenna current . Fig. 4 plots the current distribution on the antenna for different loads obtained in two ways. First, the load current in the receive mode combined with the open-circuit current is used to compute the current everywhere on the antenna, or , where is the load position. In this first case, the current can be computed for any receive load using just two basis functions. Second, the current is taken directly from receive mode simulations . The result indicates nearly perfect agreement in the current distribution for the receive mode simulation for different loads and the value predicted from transmit-mode quantities. This also confirms that for the chosen incident field, the current distribution on the antenna is the sum of only two independent basis functions. B. Two Dipole Simulation Next, we consider the case of two dipoles and show that load voltages in the receive mode are exactly predicted by

WALLACE AND MEHMOOD: ON THE ACCURACY OF EQUIVALENT CIRCUIT MODELS FOR MULTI-ANTENNA SYSTEMS

Fig. 5. Voltage on antenna 1 for simulations of coupled 2-dipole simulations, computed using direct receive (RX) mode simulations, using transmit (TX) simulations with embedded patterns (EP) and TX simulations using isolated patterns (IP).

transmit-mode only quantities, regardless of dipole separation. NEC2 simulations were performed for two -directed dipoles separated by distance with and . First, the array is analyzed in the transmit mode, where the and are found by performing simquantities ulations, where for the simulation, port is driven with a 1 V source across the terminals and short circuits (PEC) are placed across the terminals of the other elements. The , giving resulting vector of terminal currents is denoted the column of the admittance matrix . Far-fields are and the far-field pattern is stored for the azimuthal plane , yielding the column of . After performing a simulation for each port, the impedance matrix is computed with and is found from (18) as . Second, the array is analyzed directly in the receive mode by and running a sepaterminating each antenna with rate simulation for a plane wave arriving in the plane from . azimuthal angle with The load voltage on one of the antennas in the receive mode versus the arrival angle is obtained three different ways. In the first case, the open-circuit voltage of the array for arrival angle is computed using the embedded transmit patterns according to (13), after which the loaded voltage for arbitrary load impedance can be computed. In the second case, we apply the same procedure, except that the open-circuit voltage is computed using the transmit patterns of isolated elements (i.e., one antenna is driven with 1 V and the other is removed). In the third case, the voltages from direct receive-mode simulations are used. Fig. 5(a) and (b) show the amplitude and phase, respectively, and . The result of the voltage on antenna 1 for shows exact agreement between the transmit and receive mode cases when the embedded patterns are used to obtain . Also, since the results are not normalized, the agreement validates the to the embedded open-cirscaling constant in (13) relating cuit transmit patterns. When isolated patterns are used, however, a small amount of error (mainly in the amplitude) is created for , which may or may not be dipoles separated by less than tolerable depending on the application.

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Fig. 6. Directional gain of a 7-element parasitic dipole array (thick line) and fractional deviation of gain when network analysis is used (thin lines), where is the number of fixed-length segments used for the load.

Fig. 7. Load voltages for the terminated 7-element array for plane wave excitation arriving from azimuth angle . Solid lines show voltages computed using transmit-mode quantities with network analysis and points show values from direct receive-mode simulations.

C. Simulation of a Parasitic Array In this section we demonstrate the behavior of a larger array with parasitic loading. We also study the effect of a varying port current distribution that can affect the accuracy of the network analysis computations. Moment method simulations of a 7-element uniform linear array of dipoles were performed using NEC2 identical to the antennas in Sections III-A and III-B, except a fixed inter-element spacing of was used. We also consider the case of a distributed load occupying of the segments at the middle of the antenna, allowing the port current distribution to be changed. First, we demonstrate how the size of the load can affect the accuracy of network computations. Fig. 6 depicts the directive gain of the array for (thick black line) obtained from a single transmit-mode NEC2 simulation when the center element (antenna 4) is driven with an active source, antennas 1–3 are terminated with and antennas 5-7 are terminated with . Next, directional gain was computed with network analysis using and and the results of Section II-G. The fractional error of the network analysis solution compared to the direct solution is shown as thin lines in the plot. For small , network analysis and the direct solution give nearly identical results, whereas for increasing moderate error is obtained. Finally, we illustrate again that transmit-mode quantities can precisely predict the receive-mode response. Fig. 7 plots

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Fig. 8. Photos of the parasitic reconfigurable antenna measured in a compact anechoic chamber: (a) parasitic array where ports 1 and 2 are connected to the receiver and a varactor diode load (b) reference patch antenna used to illuminate the array (c) reconfigurable varactor diode circuit.

the terminal voltage on three of the antennas for a single plane wave, where antennas 1–4 and 5–7 are terminated with and , respectively and . The receive load voltage was computed with network analysis using transmit mode quantities (solid lines) and with direct receive-mode NEC2 simulations for plane waves at specific angles (points). Nearly exact agreement is obtained, indicating that the receive-mode behavior can be computed from the usual transmit-mode quantities. IV. EXPERIMENTAL EXAMPLE This section provides a simple experiment that confirms that transmit-mode quantities can be used to predict receive mode behavior in real antenna systems. The chosen antenna is a reconfigurable parasitic antenna that has application in adaptive matching and pattern synthesis. Fig. 8(a) depicts the antenna system to be analyzed, consisting of one monopole antenna connected to a receiver (Port 1) and a coupled parasitic monopole terminated with a varactor diode having variable 0–5 V reverse bias (Port 2), where the varactor diode circuit is depicted in Fig. 8(c). The monopoles are spaced by 1 cm which is approximately at the operating frequency of 2.2 GHz. Antenna measurements were performed at 2.2 GHz in the anechoic chamber depicted where a low transmit power of 0 dBm was used to ensure linearity of the varactor diode. The reference antenna for the experiment was a patch antenna mounted on a chamber wall, depicted in Fig. 8(b). Measurements were performed with a two-port Rohde&Schwarz VNB20 vector network analyzer outside of the chamber, connected to the antennas with phase-stable cables. To avoid having to reroute cables between the various measurements, three cables were run from the VNA location to the antenna ports inside the chamber, where two 3 m cables were run to the monopole antenna ports and one 6 m cable to the patch antenna. Note that the VNA was calibrated for each configuration to obtain S-parameters with respect to the ends of the cables. First, the receive antenna was characterized directly in the pure receive mode using the arrangement in Fig. 9(a), where for each rotation angle , biases of were successively placed on

Fig. 9. Measurement cases taken in an anechoic chamber to illustrate antenna computations.

the diode and was measured, where is the complex amplitude of the constant incident wave fed to the patch and the superscript “(a)” denotes configuration (a) in Fig. 9. Next, we show that the antenna system can be characterized using pure transmit-mode quantities. Consider the reconfigurable antenna to be a two-port element, where Port 2 is terminated with the varactor diode load having the bias-dependent reflection coefficient . Using (20) and noting that , the outgoing wave from Port 1 of the antenna is (31) Reflection of the varactor circuit with respect to is performed with a 1-port VNA measurement to obtain . S-parameters of the 2-port monopole array are found using the usual transmit-mode configuration in Fig. 9(b), giving the values , and as required in (31). Next, the source waves and must be determined in the presence of the transmitting patch antenna for each illumination angle . The quantity is found using the reciprocal arrangement in Fig. 9(c), where for each angle Monopole 1 is excited with an incident wave having complex amplitude , Monopole 2 is terminated with and the wave received by the patch is measured. This measurement gives (32) indicating that mode quantity used to obtain

can be obtained by just scaling the transmit. Similarly, the arrangement in Fig. 9(d) is . Substituting into (31), (33)

Fig. 10 compares direct receive-mode measurement of and the value computed with network analysis

WALLACE AND MEHMOOD: ON THE ACCURACY OF EQUIVALENT CIRCUIT MODELS FOR MULTI-ANTENNA SYSTEMS

Fig. 10. Received signal on a parasitically controlled reconfigurable antenna obtained by direct measurement in the receive mode (RX) and predicted using network analysis and measured transmit-mode quantities (TX), where is the is the reverse bias placed on the varactor rotation angle of the antenna and diode element.

in (31) using transmit-mode quantities, where cases of both the bias and sweep angle being held constant are shown. Good agreement is obtained and the small discrepancies are to be expected due to separate measurements being performed, where disconnection and reconnection of a single cable caused as much as and variation in measured S-parameters. V. CONCLUSION This paper has analyzed antenna arrays consisting of general PEC surfaces based on a rigorous method of moments (MOM) formulation, showing that equivalent circuit models are exact from the standpoint of electromagnetic wave theory. The results also indicate that receive-mode operation of arrays is exactly predicted by employing the usual transmit-mode network parameters (Z, Y, or S-parameters) and an excitation-dependent source term. For the case of reciprocal antennas and far-field sources, this source term is completely determined by the transmit-mode embedded radiation patterns of the array. Two sources of possible error in equivalent network models were identified, namely using isolated instead of embedded element patterns and modeling the incorrect current mode at the ports. Numerical and experimental examples demonstrated the validity of the analytical results and the effect of the sources of error. REFERENCES [1] C. Waldschmidt, S. Schulteis, and W. Wiesbeck, “Complete RF system model for analysis of compact MIMO arrays,” IEEE Trans. Veh. Technol, vol. 53, pp. 579–586, May 2004. [2] J. W. Wallace and M. A. Jensen, “Mutual coupling in MIMO wireless systems: A rigorous network theory analysis,” IEEE Trans. Wireless Commun, vol. 3, pp. 1317–1325, Jul. 2004. [3] M. L. Morris and M. A. Jensen, “Network model for MIMO systems with coupled antennas and noisy amplifiers,” IEEE Trans. Antennas Propag, vol. 53, pp. 545–552, Feb. 2005.

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[4] B. K. Lau, J. B. Andersen, G. Kristensson, and A. F. Molisch, “Impact of matching network on bandwidth of compact antenna arrays,” IEEE Trans. Antennas Propag, vol. 54, pp. 3225–3238, Nov. 2006. [5] V. Papamichael and C. Soras, “MIMO antenna modelling using the effective length matrices,” Progr. Electromagn. Res. C, vol. 10, pp. 111–127, Oct. 2009. [6] A. T. D. Hoop, “The -port receiving antenna and its equivalent electrical network,” Philips Res. Rep., vol. 30, pp. 302–315, 1975. [7] I. Gupta and A. Ksienski, “Effect of mutual coupling on the performance of adaptive arrays,” IEEE Trans. Antennas Propag, vol. 31, pp. 785–791, Sep. 1983. [8] J. Van Bladel, “On the equivalent circuit of a receiving antenna,” IEEE Antennas Propag. Mag., vol. 44, pp. 164–165, Feb. 2002. [9] P.-S. Kildal, “Equivalent circuits of receive antennas in signal processing arrays,” Microwave Opt. Technol. Lett., vol. 21, pp. 244–246, May 1999. [10] R. S. Adve and T. K. Sarkar, “Compensation for the effects of mutual coupling on direct data domain adaptive algorithms,” IEEE Trans. Antennas Propag, vol. 48, pp. 86–94, Jan. 2000. [11] A. W. Love, “Comment on the equivalent circuit of a receiving antenna,” IEEE Trans. Antennas Propag, vol. 44, pp. 124–125, Oct. 2002. [12] W. Geyi, “Derivation of equivalent circuits for receiving antenna,” IEEE Trans. Antennas Propag, vol. 52, pp. 1620–1623, Jun. 2004. [13] H. T. Hui, “A new definition of mutual impedance for application in dipole receiving antenna arrays,” IEEE Antennas Wireless Propag. Lett, vol. 3, pp. 364–367, Mar. 2004. [14] H.-S. Lui, H. T. Hui, and M. S. Leong, “A note on the mutual-coupling problems in transmitting and receiving antenna arrays,” IEEE Antennas Propag. Mag., vol. 51, pp. 171–176, Oct. 2009. [15] J. A. Kong, Electromagnetic Wave Theory, 2nd ed. New York: Wiley, 1990. [16] W. Wasylkiwskyj and W. Kahn, “Theory of mutual coupling among minimum-scattering antennas,” IEEE Trans. Antennas Propag, vol. 18, pp. 204–216, Mar. 1970. [17] [Online]. Available: http://www.nec2.org

Jon W. Wallace (S’99–M’03) received the B.S. (summa cum laude) and Ph.D. degrees in electrical engineering from Brigham Young University (BYU), Provo, UT, in 1997 and 2002, respectively. He received the National Science Foundation Graduate Fellowship in 1998 and worked as a Graduate Research Assistant at BYU until 2002. From 2002 to 2003, he was with the Mobile Communications Group, Vienna University of Technology, Vienna, Austria. From 2003 to 2006, he was a Research Associate with the BYU Wireless Communications Laboratory. Since 2006, he has been an Assistant Professor of electrical engineering at Jacobs University, Bremen, Germany. His current research interests include MIMO wireless systems, physical-layer security, cognitive radio and UWB systems. Dr. Wallace is serving as an Associate Editor of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION and is a Co-Guest Editor of the Special Issue on Multiple-Input Multiple-Output (MIMO) Technology.

Rashid Mehmood (S’05) received the B.Sc. degree (cum laude) in communication systems engineering from the Institute of Space Technology (IST), Pakistan, in 2007 and the M.Sc. degree in electrical engineering from Jacobs University Bremen (JUB), Bremen, Germany, in 2010. From 2007 to 2008, he worked as a Research Associate at IST and supervised various undergraduate laboratories. From 2008 to 2010, he worked as a Research Assistant in several laboratories at JUB and external companies. His current research interests include reconfigurable aperture antennas, antenna optimization and wireless and optical communications. Mr. Mehmood was a recipient of the 2009 IEEE AP-S Undergraduate Research Award.

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A Low-Cost MIMO Channel Sounder Architecture Without Phase Synchronization Daniele Pinchera, Member, IEEE, and Marco Donald Migliore, Member, IEEE

Abstract—A MIMO channel sounder that does not require phase measurements is proposed. The system is based on parasitic antennas, with a single active element connected to a low expensive amplitude only receiver and a proper phase retrieval algorithm whose computation burden is compatible with today personal computers. Numerical simulations confirm the effectiveness of the approach. Index Terms—Channel estimation, microwave propagation, MIMO, mutual coupling, phase estimation.

I. INTRODUCTION

Fig. 1. Scheme of a standard MIMO sounder.

T

HE effectiveness of a MIMO system is strictly related to the number of orthogonal communication sub-channels that can reliably transmit information. Consequently, the characterization of the MIMO channel is of paramount importance for the evaluation of the performance of the communication system. In order to measure the channel matrix, high-accuracy channel sounders have been developed, for example [1]–[4]. The method usually adopted for the estimation of the -th element of the channel matrix is to measure the ratio between the phasor associated to the harmonic signal received by the -th receiving element and the phasor associated to the harmonic signal transmitted by the -th transmitting element of the MIMO system. A critical point of this strategy is the exact measurement of the difference between the phase of the transmitted and the received signal. The phase noise in a MIMO sounder is indeed an important issue [5], [6]. Low phase noise can be obtained using a very stable time-reference in the transmitter and receiver system, like the use of atomic clocks [1] or GSM [4]. In a different approach the reference is obtained directly by the received signal after a proper demodulation [2]. However, even this solution is complex, since it requires, in practice, the development of a complete MIMO system. In this paper a radically different approach, presented for the first time in [7], is proposed to overcome the problem of phase synchronization using amplitude only measurements. The key point of our solution is the use of parasitic loads instead of RF switches (see Figs. 1 and 2), with three main advantages: first, the strong reduction of the sounder cost, since parasitic loads are cheaper than RF switches; second, since the possible number of combinations of the impedance states can be Manuscript received May 31, 2010; revised March 16, 2011; accepted April 09, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. The authors are with the DAEIMI, University of Cassino, Cassino 03043, Italy (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TAP.2011.2173433

Fig. 2. Scheme of the Parasitic MIMO Channel Sounder (PMCS).

very large we could use these redundant data to improve the reconstruction of the channel; third, we could use a simple scalar detector as a receiver, since it is possible to retrieve the phase information of the signals by means of a proper elaboration of the measurements. Broadly speaking, the idea at the basis of the proposed method is to use the simplest (and cheapest) possible hardware (e.g., parasitic loads and a simple scalar detector), at a cost of a greater computation burden compared to other approaches. For example, a possible hardware consists of a generator, connected to the transmitting parasitic antenna array, and a (scalar) spectrum analyzer connected to the receiving parasitic antenna array. The electronic switches in transmission and reception are controlled by a microcontroller, while a low-cost wireless connection (for example ZigBee or Wi-Fi) is used to control the state of the switches at the transmitter side. It has to be noticed that the cost and complexity of RF switches increase very rapidly with the number of terminations needed; the use of single controllable impedances allows an almost linear increase of the cost and complexity of the measuring system with the number of employed parasitic loads. As it will be shown in the following, the performances of the scheme that we propose are slightly inferior than the performances of existing schemes, but the strong reduction of the

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hardware cost could make our solution attractive in many applications. It is interesting to note that this idea resembles, at least in the basic philosophy, a recent trend in data acquisition and elaboration, characterized by the simplification of the detector at the cost of a more complex data elaboration [8]. The paper is organized in the following Sections. The problem of the measurement of the MIMO channel matrix using vector and amplitude only strategies is discussed in Section II. Section III is devoted to the description of the amplitude only MIMO channel sounder architecture, while the phase-retrieval algorithm is described in Section IV. Numerical simulations in case of measurement of a large MIMO channel matrix (25 25 elements) and small channel matrix (4 4 elements) are reported in Section V. Finally, in Section VI conclusions and observations are reported.

Fig. 3. Graphical representation of the linear mapping

.

II. THE MEASUREMENT OF THE MIMO CHANNEL MATRIX Let us consider a MIMO system constituted by transmitting and receiving elements. In the following harmonic signals at frequency will be considered, and the time-dependence , wherein , will be understood and dropped. The channel matrix of such a system relating the vector of the receiver currents and the vector of the transmitter voltages, can be written as [9]:

Fig. 4. Scheme of the alternate projection algorithm; the solution is the intersection point (if exists) between the two sets and ; in absence of intersection point, the solution is the point which minimizes the distance between the two sets; the non-convexity of the sets causes the presence of local minima in which the algorithm can be trapped.

(1) where and are the impedance matrices of the receiving and transmitting array, is the matrix relating the currents on the transmitting antennas to the currents on the receiving antennas (MIMO propagation matrix in the following), and and are the diagonal matrices of the internal impedances of the generators and the receiver equivalent impedances, respectively. The matrices and are known quantities, that do not depend on the particular channel realization. Our goal is the estimation of the propagation matrix . In standard channel sounders the elements of are measured using a vector (amplitude and phase) receiver. The estimation of requires a simple inversion procedure. Under suitable conditioning of the and matrices, the propagation matrix can be stably recovered. This method requires a number of transmitters and receivers equal to the length of the vectors and respectively, or a proper switching system at both communication sides. Furthermore, it requires phase synchronization, which is a cumbersome problem. In case of short distance the phase reference can be transmitted by cables or optical fibers, but this affects the flexibility of the system. An effective solution is the use of highly stable time reference at both the transmitter and receiver side. A further approach to solve the problem of phase estimation is to completely avoid the measurement of the phase, and to estimate it from some functional relationships in the amplitude only received signals. This approach is used, for instance, in antenna near-field measurement systems, in which the phase is estimated from amplitude only measured data. The basic idea of the phase-retrieval methods in near-field measurements is to

collect a set of amplitude only data, which is (hopefully) compatible with only the true phase distribution, avoiding false solutions [11]. Before introducing the details of the proposed technique, it is useful to clarify the general strategy of the method using a simple geometrical approach. A matrix maps a -dimensional hypersphere having unit radius, into a -dimensional hyperellipsoid. The length of the semi-axes of the hyperellipsoid are equal to the singular values of . Consequently, from a geometrical point of view, the problem is the estimation of its principal axes. This requires the identification of the hyperellipsoid apart from an arbitrary rotation around the origin. For the sake of simplicity and clarity, in the following the matrix channel will be supposed a 2 2 real symmetric matrix having full rank. Extension to complex non-hermitian matrices is straightforward, but less geometrically intuitive. With reference to Fig. 3, the ellipsoid can be identified by varying on the unit-circle of the plane, and observing the output . In particular, standard MIMO sounders choose along the coordinate axes of the system , i.e., and . The values of allow to identify the ellipsoid, and hence the singular values. In order to give an intuitive idea of the problems related to amplitude-only measurements, let us suppose that we measure only the length of the vectors and . The amount of information obtained from the length of the 2 output vectors is only one-half compared to the amount of information associated to . Consequently, only two measurements are not capable to

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uniquely identify the ellipses. In order to increase the number of data, we need to observe the output of under other input vectors . This would require a beamforming at the transmitter, that would increase the complexity and the cost of the sounder. A possible approach to obtain a larger set of vectors is to start with a single vector, let be, and to apply an orthogonal transformation at the transmitter side that rotates the vector . By using different orthogonal transformations , we can obtain different outputs . Let us consider the received vector . In order to simplify the receiver we suppose that we are able to measure only one entry of , for example only the first entry. In order to measure all the components the vector, we can apply a further orthogonal transformation at the receiver side that rotates the vector . By using different orthogonal transformations , we obtain different outputs . Using the above described approach, the system becomes , wherein is an operator that selects only the first entry of . Note that the receiver must know which is used by the transmitter. This requires a form of synchronization between transmitter and receiver. This synchronization is fundamentally different from the phase-synchronization required in other MIMO sounders, and can be implemented in a quite simple way using low-rate wireless systems. The number of measured data depends on the number of and that can be synthesized. Consequently, a key point in the application of the method in amplitude-only measurements is related to the possibility of obtaining a large number of different and in a cheap and fast way. Regarding this point, it is worth stressing that the method works also in case of not-orthogonal and matrices, provided that they are sufficiently well conditioned, of course at the cost of a higher computational complexity. This work proposes a low-cost easily-implementable way to obtain such matrices, and an effective algorithm to estimate the singular values from amplitude-only data. In particular, the identification of an effective strategy to obtain pieces of information large enough to estimate the phase in a stable way will be discussed in the next Section, while the problem of identifying the functional relationships between the measured data, and an effective algorithm to retrieve the phase from the set of measured data is the object of Section IV. III. PARASITIC MIMO CHANNEL SOUNDER (PMCS) ARCHITECTURE Let us consider the data acquisition problem. As discussed in Section II, standard sounder configurations allow to measure independent quantities. This set of data is insufficient for amplitude only measurements. Consequently, we must change the sounder hardware to perform a larger number of measurements. The solution that we have investigated to increase the number of acquired data consists in the use of parasitic antennas [12], [13]; these antennas comprise an active element, connected to the transmitter or the receiver, and a number of parasitic elements placed close to the active element and terminated on controllable loads (Fig. 2). The system uses only one transceiver at

the transmitting and one at the receiving side, and, respectively, and parasitic elements on the transmitting and receiving side. The parasitic elements are loaded with controllable impedances that can assume, for instance, two different values ( and ). Note that the synchronization channel shown in figure is used only to synchronize the switches and, consequently, the value of the loads used at the transmitter and receiver antenna, and not for a phase-synchronization of the transmitter and receiver oscillators. For these reasons, transmitter-receiver synchronization requires a relatively simple hardware. The relationship between the current on the active antenna at the receiver and the voltage on the active antenna at the transmitter is [9]:

(2) is the diagonal where matrix containing the internal impedance of the generator of the transmitting active antenna and the load impedances of the transmitting parasitic antennas in the state defined by the binary vector . This means that the -th parasitic element will be connected to an impedance if and to an impedance if . Similarly we have that is the diagonal matrix containing the internal impedance of the receiver attached to the active antenna and the parasitic load impedances for the receiving parasitic antennas in the state defined by the binary vector , and and are two vectors taking into account the fact that we cannot access to the signals on the parasitic elements. In practice, we have access to a single element of the matrix . However, we have the possibility to modify the matrices and and, consequently, we can observe different outputs associated to different matrices. Let us suppose that the number of parasitic load combinations employed is at the receiver and at the transmitter; in such a way we can define the matrices and wherein and , and and are respectively the -th and -th binary vector defining the combination of the parasitic load impedances for the receiving and the transmitting antenna, obtaining (3) are the ratio between and wherein the elements of for the considered combinations of transmitting and receiving loads. Roughly speaking, we make the control system on the transmitting antenna cycle on the set of parasitic load combinations while we maintain the parasitic load combination at the receiver fixed, then we change the parasitic load combination at the receiver and we cycle through all the parasitic load combination at the transmitter, and so on: in this way the amplitude of the signal received will be proportional to the entries of the matrix read by rows. It is necessary to underline that the acquisition of the matrix has to be done within a coherence

PINCHERA AND MIGLIORE: A LOW-COST MIMO CHANNEL SOUNDER ARCHITECTURE WITHOUT PHASE SYNCHRONIZATION

time of the channel, otherwise the reconstruction of the propagation matrix would be mistaken. Under the hypothesis that the impedance combinations are chosen in order to obtain well-conditioned and matrices, the above equation allows to estimate . Let be the set of complex valued matrices having dimension, the set of complex valued matrices having dimension, the set of matrices compatible with the employed parasitic system (in the following PSM—parasitic system matrices) and the linear operator (4) and are fixed matrices that depend on the wherein choice of the parasitic combinations. is a one-to-one, and hence invertible, mapping under suitable hypotheses on the matrices and . In particular, if and are full rank squared (e.g., ) matrices, the evaluation of is straightforward, being . If we can evaluate the Moore-Penrose pseudo-inverse of and , let and be [10], (5) (6) and consider the linear mapping defined in the following way

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to estimate the propagation matrix and to do so we need to reconstruct the phase of the elements of the matrix . Let us consider the quantity (8) wherein if the Frobenius matrix norm and is the projector operator on the set of matrices compatible with the choice of the parasitic loads, namely:

(9) and the matrix

is obtained as (10)

with a phase matrix, i.e., a matrix in which each element is in the form and “ ” is the Hadamard element by element matrix product. One null of is surely achieved when . The uniqueness of the solution, i.e., that no other phase matrix gives a matrix lying in the set of matrices compatible with the parasitic loads, is still an open problem. Nevertheless, we have undertaken a long numerical investigation, during which no other nulls were found when the following conditions (11)

(7) and , the null space Note that since of will be of dimension . Consequently, the increasing of the number of parasitic configurations increases the number of dimensions of the null space and only a subspace of the complex matrices of elements corresponds to matrices of a parasitic system defined by and . The possibility of redundant measurements by means of a large number of parasitic load combinations opens a further interesting perspective. In fact, use of “redundant” information allows to simplify the hardware required for the sounder avoiding the transmission of the phase information by means of a proper phase retrieval algorithm able to reconstruct the lost information. The algorithm adopted to solve the problem is a mixed alternate projections-random search procedure. The use of such an algorithm, as described in the following, allows to obtain a reasonable convergence speed, and a good robustness with respect to the local minima problem. IV. AMPLITUDE-ONLY MIMO CHANNEL SOUNDER PHASE RETRIEVAL ALGORITHM In the following we will assume, for the sake of simplicity, that we have a perfect knowledge of the system, i.e., there is no uncertainty on the definitions of the matrices and (this assumption will be dropped in the sensitivity analysis of Section V). Furthermore, we suppose that only the amplitude of the elements of the matrix is known; the amplitude only measured data will be collected in the matrix ; our aim is

(12) were satisfied. It is not easy to find a proof of (11) and (12), since non linear equation are involved in the amplitude-only problem. In order to better understand this behavior we could observe that the set of equations we are dealing with consists of non linear real equations in real variables; if the equations were linear we would need at least and in order to achieve an unique solution, but since the equations are non linear we need a slightly larger set of equations, thus giving a rough explanation of the obtained relationships. Numerical evidence of (11) and (12) will be given in Section V.C. Identification of the null of the objective function (8) can be solved in terms of intersections of two sets. The first set is the set of all the matrices compatible with the parasitic loads. The second set is the set of all the matrices compatible with the measured data (e.g., whose elements have amplitude equal to the elements of ), let be this set. The solution is the point . In presence of noise-affected data the intersection point generally does not exist. In this case the condition is substituted by the condition where is a proper threshold that is proportional to the additive Gaussian noise at the receiver (see Appendix). The minimization problem can be solved by means of the alternate-projection algorithm [14], [15]. The alternate-projection algorithm allows to find the intersection point among sets using successive orthogonal projections on the sets or, if the intersection point does not exist, the solution which minimizes the distance between the two sets.

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The projection operator on the space of the set has already been defined in (9); the projection operator on the set is: (13) where operates on the single entries of the matrix M, so that . The operator simply substitutes the amplitude of the elements of the matrix with the measured data, without affecting the phase of the element. The alternate projection algorithm implemented can thus be described by the following steps: 1) Generate a random phase matrix ; 2) Reset iteration-counter; 3) Evaluate ; 4) Increase iteration-counter by 1; 5) Evaluate ; 6) Evaluate ; 7) If go to step 4; 8) If go to step 1 otherwise stop. A brief discussion of the algorithm is now in order. When the two sets are not convex, as in our case, local minima arise, and the alternate-projection algorithm can be trapped in false solutions. Once the counter has reached the maximum number of allowed iterations we can check if the algorithm achieved , otherwise we can start again, generating another random phase matrix. The choice of the threshold will be discussed in the Appendix. It could be possible that the alternate projection algorithm requires hundreds of trials for but, as will be shown in the next section, the phase retrieval algorithm remains perfectly compatible with the computing power available with modern PCs. It has also to be underlined that if we increase the number of parasitic load combinations at the transmitter and receiver so that and we achieve the convergence of the algorithm in typically less than ten trials. Once a correct reconstruction of the phase of is performed, it is trivial to recover the propagation matrix by means of (7).

V. NUMERICAL EXAMPLES In the following a number of numerical examples will be discussed, in order to show the flexibility of the proposed method. In a first set of simulations a 25 25 MIMO system will be used; in a second set of simulations a 4 4 MIMO system will be considered. The numerical test procedure has been the following. A random channel propagation matrix , simulating a rich scattering environment has been simulated; then the measurement matrix has been computed, adding to it a white Gaussian noise matrix ; then the phase of the matrix has been reconstructed by means of the algorithm presented in the previous paragraph, obtaining . Once obtained , the estimated channel matrix is given by: (14)

Fig. 5. Scheme of the 25 element antenna array.

To evaluate the reconstruction capability of our measurement scheme the estimated channel matrix is then compared to the “real” channel matrix by means of the following metric:

(15) Values of most purposes. A. 25

lower than

can be considered good for

25 MIMO System

The 25 elements MIMO antenna is constituted by 25 wire elements displaced on a plane in a regular grid of 5 rows by 5 columns (Fig. 5). The central element (marked 0) is the active one, the remaining 24 elements are parasitic. The inter element distance on the grid is , so that the overall area of the array is . The impedance of the parasitic element has been chosen to be and . This two values have been chosen in order to guarantee a good conditioning of the matrices to be pseudo-inverted (7); it has to be noticed that these values are close to the values obtainable by pin-diode switches we developed in a previous work [16]. It could have been possible to consider impedances with a higher number of states, in order to increase the possible number of parasitic load combinations, but we chose to investigate the performances achievable by means of the simplest parasitic load. Since the MIMO system is perfectly symmetric we choose the same parasitic load combinations at both the transmitter and the receiver. The number of parasitic load combinations for this antenna, even if the load can assume only two values, is very big, more than 16 millions; this means that if we want to use a set of parasitic load combinations at the receiver, the number of possible sets would be really huge , so a brute force search of the best possible set of load combinations is practically impossible. In order to choose the best combinations a proper genetic algorithm (GA) [17] has been implemented. The genetic algorithm tries to find the best set of load combinations in order to reject as much as possible the measurement noise; this is obtained minimizing the condition number of the matrix . The description of the GA employed is in the Appendix.

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Fig. 6. Performance of the parasitic sounder with amplitude only measurements.

Fig. 8. Sensitivity analysis for variable .

and

in the case

B. Sensitivity Analysis The results shown up to this point were obtained supposing a and ; it is thus imporperfect knowledge of the matrices tant to understand the stability of the reconstruction procedure we are proposing with respect to the knowledge of the system. In order to answer this question we have considered a sensibility analysis, where we supposed an imperfect knowledge of the impedance matrices and , needed for the reconstruction of the channel matrix. In particular in the reconstruction of the channel matrix we used parasitic matrices and calculated using the following impedance matrices:

Fig. 7. Performance of the parasitic sounder with vector measurements.

In Fig. 6 the average of on 100 channel snapshots, for a different number of parasitic load combinations, is depicted as a function of the average SNR at the receiver, defined as: (16) where is the matrix of the AWGN noise on the measure of at the receiver. It has to be underlined that each combination of the parasitic loads at the transmitter and at the receiver would result in a different SNR, but for the reconstruction purposes we look at the whole measurement matrix , so combinations related to particularly low or high SNRs do not influence the reconstruction. It is interesting to observe that there is a great improvement when passing from 50 parasitic load combinations to 75, while the improvement is much smaller when passing from 75 to 100 combinations. The performances of the parasitic sounder are worse than that of the standard sounder, i.e., we require a higher SNR in order to achieve the same performances, but we would like to stress the point that the standard sounder requires more expensive hardware. For the sake of comparison, in Fig. 7 we have depicted the performances of the parasitic sounder when vector measurements are employed. It is possible to see that the gap with respect to the standard sounder is reduced, since we do not need anymore to estimate the phase from measures, but this solution is less attractive, since a phase synchronization between the transmitter and the receiver is required.

(17) (18) where and are complex Gaussian variable matrices. The imperfection on the knowledge of and will be modeled by the quantities: (19) (20) For the sake the of simplicity we will suppose . The results of the sensitivity analysis are reported in Fig. 8; according to the reported results, a relative error of is required to achieve a satisfactory reconstruction. This error level is comparable with the error made by VNAs commonly used to measure the impedance matrix of an array; moreover, since this error is deterministic, it could be possible to set up a specific calibration procedure in order to further reduce the error on the knowledge of the system. A similar sensitivity analysis has been done also on the controllable impedances, obtaining similar results; it has not been reported here since the uncertainty on the measure of single impedances is usually smaller than the uncertainty on the measurement of an impedance matrix, so we focused on the impedance matrix to understand the stability of the reconstruction method proposed.

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Fig. 11. Performance of the PMCS for a variable Fig. 9. Number of correct reconstructions for a variable

at the receiver.

.

an average number of 8.3 starting points when , and an average number of 1.5 starting points when . For the sake of completeness, we have to say that the average number of iterations of the alternate projection algorithm, before it is able to detect if it has converged to a good solution, or if it needs to generate another starting point, is approximately 300. D. 4

Fig. 10. Average number of starting points needed for a variable

.

C. Convergence and Computational Considerations In Section VI we have given two “rule of thumb”, (11) and (12), that should guarantee the convergence of the algorithm. In Fig. 9 we provide a numerical evidence of such equations: we have considered the reconstruction of 100 channel snapshots with a variable , and we have depicted the number of reconstructed channel matrices that converged to the exact channel matrices. The graph has a step behavior, with a turning point around , where we achieve the correct result in 57% of the considered cases; for the convergence is guaranteed, and for we have never converged to the exact solution. This result was obtained with an of 50 and perfect knowledge of the parasitic matrices, but similar results, except for the slope of the curve around the turning point, have been obtained in other cases. Another aspect that has to be taken into account is the computational burden of the algorithm. First of all, we need to underline that the reconstruction of the channel matrix can be done off-line once the measured data have been collected, so the computation of the channel matrix can be done on a PC without particular computation concerns. Beside this consideration, we have to observe that one of the key points of the procedure we are proposing is the generation of a random phase matrix in order to provide a starting point for the alternate projection algorithm. In principle nobody can assure us on the number of starting points we need to consider in order to achieve a solution; for this reason in Fig. 10 we have reported the average number of starting points that the algorithm needed to generate in order to reconstruct 100 channel snapshots. It has to be noticed that the number of starting points is pretty high when , but it rapidly decreases, so we need

4 MIMO System

This section has been introduced in order to show that a PMCS could also be implemented in MIMO systems with a relatively low number of antennas. In this case, our transmitting and receiving antenna is constituted by a linear array of 4 wire elements, with spacing between the elements. The active element is one of the inner ones, while the other three are parasitic. The parasitic impedances are equal to those considered in the previous array, thus resulting in a maximum of 8 parasitic load combinations. In Fig. 11 it is possible to see the performances of the PMCS with 8 parasitic load combinations both at the transmitter and at the receiver and non-LOS rich scattering environment. The performances are lower than the ones obtained in the case of the 25 25 MIMO channel sounder, since the number of parasitic load combinations that can be used is smaller, but for a high SNR at the receiver the channel matrix reconstruction is satisfactory. It is important to stress that the increase of the SNR at the receiver requires an increase of the length of the measurements, so it is not very difficult to achieve such a SNR, provided that the entire set of 8 8 channel measurement is performed within the coherence time of the channel. VI. CONCLUSION A novel MIMO sounder, based on the use of parasitic elements, has been discussed. The sounder is low cost and, according to our simulations, allows to obtain a good estimate of the channel using phaseless measurements. The basic idea is to use parasitic MIMO antennas with a single active element connected to an amplitude only receiver and a proper phase retrieval algorithm. The system requires a very simple hardware (sinusoidal tone generator, controllable impedances, and a scalar detector), and a computational burden that is compatible with current personal computers. The building and testing of a prototype PMCS is in progress. The actual implementation of the sounder will be presented in a future paper, as a part of a much larger investigation on the

PINCHERA AND MIGLIORE: A LOW-COST MIMO CHANNEL SOUNDER ARCHITECTURE WITHOUT PHASE SYNCHRONIZATION

MIMO channel sounding topic; we plan to study also the use of more complex loads, in order to improve the performances in terms of noise rejection and stability. As last observation, the decreasing of the cost of elaboration makes the use of strongly different measurement strategies possible, accepting the acquisition of data indirectly related to the quantity of interest, provided that the acquired data contain enough information on the quantity of interest. Along this track, the connections between information theory and electromagnetics could play an important role for the next generation electromagnetic measurement systems.

APPENDIX A. On the Noise Threshold In order to derive a simple expression for the threshold as a function of the receiver noise, let us suppose that we have obtained the optimal phase matrix , such that . If we consider now the measurement matrix reconstructed with such a phase, we would have: (21) where N is the matrix of the AWGN at the PMCS receiver; so when we compute (8) we would obtain

(22) where is the variance of the noise at the receiver and we have used the property , valid for any projection. The threshold could thus be chosen to be equal to . B. The Genetic Algorithm Employed The genetic algorithm used for the selection of the set of parasitic load combinations considers “individuals” described a the vector of discrete values, in the range . The population is made of 150 individuals and the selection is by tournament; overlapping of generations is also implemented. The crossover operator works by joining the vector of two selected individuals into a single vector of discrete values; a new individual is then created randomly extracting a set of discrete values from joined vectors (“Join and Extraction” scheme). A mutation can occur on an element of the new vector, that is changed to a random one in the range , with a probability . In order to prevent stagnation of the algorithm, some new random individuals are also added at each iteration (“Migration scheme”). The algorithm is then terminated after a fixed number of iterations, usually in the range 1000–10000.

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ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers and editor for their helpful corrections and suggestions, that have allowed a significant improvement of the quality of the paper. REFERENCES [1] J. W. Wallace, M. A. Jensen, A. L. Swindlehurst, and B. D. Jeffs, “Experimental characterization of the MIMO wireless channel: Data acquisition and analysis,” IEEE Trans. Wireless Commun., vol. 2, no. 2, pp. 335–343, Mar. 2003. [2] V. M. Kolmonen, J. Kivinen, L. Vuokko, and P. Vainikainen, “5.3-GHz MIMO radio channel sounder,” IEEE Trans. Instrum. Meas., vol. 55, no. 8, pp. 1263–1269, Aug. 2006. [3] V. M. Kolmonen, P. Almers, J. Salmi, J. Koivunen, K. Haneda, A. Richter, F. Tufvesson, A. F. Molisch, and P. Vainikainen, “A dynamic dual-link wideband MIMO channel sounder for 5.3 GHz,” IEEE Trans. Instrum. Meas., vol. 59, no. 4, pp. 873–883, 2010. [4] J. M. Molina-Garcia-Pardo, J. V. Rodriguez, and L. Juan-Llacer, “MIMO channel sounder based on two network analyzers,” IEEE Trans. Instrum. Meas., vol. 57, no. 9, pp. 2052–2058, 2008. [5] A. Taparugssanagorn and J. Ylitalo, “Characteristics of short-term phase noise of MIMO channel sounding and its effect on capacity estimation,” IEEE Trans. Instrum. Meas., vol. 58, no. 1, pp. 196–201, 2009. [6] A. A. Aboudaand, H. M. El-Sallabi, and S. G. Haggman, “Reducing impact of phase noise on accuracy of measured MIMO channel capacity,” IEEE Antennas Wireless Propag. Lett., vol. 6, pp. 419–422, 2007. [7] D. Pinchera and M. D. Migliore, “A phaseless parasitic MIMO-channel sounder,” in Proc. IEEE Antennas and Propagation Society Int. Symp., 2008, pp. 1–4. [8] D. Takhar, V. Bansal, M. Wakin, M. Duarte, D. Baron, J. Laska, K. F. Kelly, and R. G. Baraniuk, “A compressed sensing camera: New theory and an implementation using digital micromirrows,” presented at the Comp. Imaging, IV SPIE Electronic Imaging, San Jose, Jan. 2006. [9] M. D. Migliore, D. Pinchera, and F. Schettino, “Improving channel capacity using adaptive MIMO antennas,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pt. 2, pp. 3481–3489, Nov. 2006. [10] G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore, MD: The Johns Hopkins Univ. Publishers, 1983. [11] M. D. Migliore, F. Soldovieri, and R. Pierri, “Far-field antenna pattern estimation from near-field data using a low-cost amplitude-only measurement setup,” IEEE Trans. Instrum. Meas., vol. 49, no. 1, pp. 71–76, 2000. [12] M. Wennstrom and T. Svantesson, “An antenna solution for MIMO channels: The switched parasitic antenna,” in Proc. 12th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Commun., Sept. 2001, vol. 1, pp. 159–163. [13] M. D. Migliore, D. Pinchera, and F. Schettino, “A simple and robust adaptive parasitic antenna,” IEEE Trans. Antennas Propag., vol. 53, no. 10, pp. 3262–3272, Oct. 2005. [14] A. Levi and H. Stark, “Image restoration by the method of generalised projections with application to restoration from magnitude,” J. Opt. Soc. Am. A, vol. 1, no. 9, pp. 932–943, 1984. [15] O. M. Bucci, G. D’Elia, G. Mazzarella, and G. Panariello, “Antenna pattern synthesis: A new general approach,” Proc. IEEE, vol. 82, no. 3, pp. 358–371, Nov. 1994. [16] D. Pinchera, J. W. Wallace, M. D. Migliore, and M. A. Jensen, “Experimental analysis of a wideband adaptive-MIMO antenna,” IEEE Trans. Antennas Propag., vol. 56, no. 3, pp. 908–913, Mar. 2008. [17] A. Fraser and D. Burnel, Computer Models in Genetics. New York: McGraw-Hill, 1970. Daniele Pinchera (S’05–M’08) received the Dr. Eng. degree (summa cum laude) in telecommunication engineering and the Ph.D. degree in information and electronic engineering from the University of Cassino, Italy, in 2004 and 2008, respectively. He is currently working as a Postdoctoral Researcher in the Faculty of Engineering, University of Cassino. His current research is in the fields of smart antennas and MIMO systems, large array synthesis, compressed sensing, sensor networks and industrial and medical applications of microwaves.

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Marco Donald Migliore (M’04) received the Laurea degree (honours) in electronic engineering and the Ph.D. in electronic engineering from the University of Naples, Naples, Italy. He is currently an Associate Professor at University of Cassino, where he teaches electromagnetic fields, propagation in urban area and microwave measurements. His research interests are adaptive and MIMO antennas, antenna measurement techniques, studies of connection between electromagnetic theory and information theory, industrial

and medical applications of microwaves. He is author or coauthor of more than 100 papers in books, journals or international conferences. He was a Visiting Professor at the University of San Diego in California in 2007 and 2008, and a speaker at the summer research lecture series of the UCSD CALIT2 Advanced Network Science (ANS) in 2008. Prof. Migliore is a member of SiEm (Societ Italiana di Elettromagnetismo) and the Electromagnetics Academy.

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Impact of Incomplete and Inaccurate Data Models on High Resolution Parameter Estimation in Multidimensional Channel Sounding Markus Landmann, Martin Käske, and Reiner S. Thomä, Fellow, IEEE

Abstract—Multidimensional channel sounding aims to estimate the geometrical structure of multi-path wave propagation in terms of directions of arrival/departure, Doppler shift, time delay, and complex polarimetric path weights. Maximum likelihood parameter estimation based upon an underlying data model is used to achieve high-resolution of the path parameters and, thus, renders possible an antenna independent channel characterization. However, any mismatch of the underlying data model to physical reality imposes limits to accuracy and reliability of the estimation. To cope with the limited resolution capability of the setup we are using a propagation data model that does not only contain discrete deterministic components but also a non-resolvable stochastic part. Joint estimation of both components considerably enhances the estimation quality and finally allows the interpretation as specular and diffuse contribution of multi-path propagation respectively. However, besides of noise influence, the achievable resolution is further limited by the accuracy of the data model that describes the measurement setup. Since the antenna characteristics are very susceptible to calibration and modeling errors, the directional estimates are most error-prone. We refer to the antenna array calibration procedure and discuss common pitfalls in highresolution multi-path direction estimation that are related to inaccurate and/or incomplete device data model. Depending on the type of the antenna array (linear, circular) this will inherently produce biased and artificially spread angular estimates. Only with precise knowledge of the model errors the stochastic part can be identified as diffuse propagation component vs. modeling error. Index Terms—Antenna array calibration, direction of arrival (DoA) estimation, high resolution parameter estimation, multi-path channel characterization, multi-path cluster, multiple-input multiple-output (MIMO) channel sounding, polarimetry.

I. INTRODUCTION

M

ULTIDIMENSIONAL channel sounding is the key technology for experimental analysis of electromagnetic wave propagation in mobile radio [1], [2]. Measurement campaigns are conducted in representative deployment scenarios [3]. The results help to understand the physical propa-

Manuscript received August 05, 2010; revised March 28, 2011; accepted September 14, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG), Bundesministerium für Bildung und Forschung (BMBF) and in part by the European Union (EU). M. Landmann is with the Fraunhofer Institute for Integrated Circuits IIS Helmholtzplatz 2, 98693 Ilmenau, Germany. M. Käske and R. Thomä and are with Ilmenau University of Technology, 98693 Ilmenau, Germany (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173446

gation mechanisms and to recognize fundamental information theoretic limitations of multiple-input multiple-output (MIMO) channels in real propagation environments. The data is further used to deduce and parameterize channel models, and to evaluate transmit and receiver signal processing schemes. Once the channel response has been recorded in its multiple dimensions (spatial, temporal, and frequency) by the measurement system, the data undergoes extensive analysis. Gaining explicit knowledge of the geometric structure of wave propagation in terms of direction of arrival (DoA), direction of departure (DoD), time of arrival (ToA), Doppler shift, and complex polarimetric path weights is a prerequisite for most of the propagation study and data analysis procedures. A wide variety of high resolution parameter estimation (HRPE) is available [4] to estimate these structural parameters by fitting an appropriate data model to the recorded data. Only if we can assume the underlying data model to be physically correct, complete, and precise, the achievable estimation accuracy and resolution is given by the Cramér-Rao lower bound (CRLB), which defines the fundamental limitations on the parameter variance in case of noise influence. In practice however, the model will never be perfect. There are various reasons for this deficiency. Although the data model has to be accurate enough to represent the essential effects of electromagnetic wave propagation and the influence of the measurement system it must be simplified in order to make it tractable by the HRPE. Regarding the propagation data model, in most cases a finite number of discrete narrow-band plane waves is assumed describing the specular components of propagation or the “propagation paths.” For example, the same data model is applied by the subspace based estimation of signal parameters via rotational invariance techniques (ESPRIT) method which becomes even more stringent in this case since ESPRIT additionally presumes identical antenna responses and shift invariant array structures. Very often omnidirectional antennas are presumed and the influence of polarization is not considered [5]. Also whole dimensions such as elevation or DoD are frequently neglected. In general, maximum likelihood (ML) HRPE estimation based upon iterative search procedures such as SAGE are more flexible which allows defining more sophisticated data models. Nevertheless, the same simplifications of the propagation data model are often applied also with ML HRPE estimation (see, e.g., [6]–[8]). Since the real propagation environment is not finite discrete but rather a continuum of structures and materials, a purely discrete data model will not suffice. Moreover, polarization cannot be neglected since it is strongly related to the antenna char-

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acteristics and influenced by scattering and reflection. Therefore, in this paper we are using a hybrid polarimetric propagation data model which is composed of a superposition of a finite number of discrete deterministic contributions that are attributed as specular components (SC) and statistically distributed dense multipath components (DMC) mainly resulting from non-resolved diffuse scattering. It was shown that this hybrid propagation model matches the received data much better than the SC-only model [9]. Depending on the propagation environment the diffuse propagation may carry a considerable part of the received power which can be in the same order of magnitude as the specular components. Both the SC and the DMC parts are jointly estimated by the iterative ML HRPE estimation framework RIMAX which uses a combination of space alternating and gradient search for parameter optimization [10]. In addition to the propagation phenomena the data model has to include precise knowledge of the measurement device in all the relevant dimensions to separate its influence from the measured data. We call this part the device data model. Since device calibration data are determined by measurements, there are many practical issues that limit its accuracy. These are mainly related to the complexity and repeatability of the measurements. Accuracy may be limited by the available time and effort, by a lack of precise references, and by noise and phase drift during the calibration measurement procedure. Determination of the antenna characteristics (the array manifold respectively) is probably the weakest point in this respect which makes directional estimates most error prone. One reason for that is the lack of a precise echo-free calibration environment. Any “anechoic chamber” will give rise to parasitic reflections which will especially be generated by the installed calibration equipment itself, namely the antenna positioner. Even if the equipment is carefully covered by absorbing material, the accuracy of the measured radiation patterns is clearly limited which also precludes the antenna frequency response to be included into the total frequency response calibration. In this paper we will describe the effective aperture distribution function (EADF) method which is not only a memory-efficient description of the radiation patterns but easily allows interpolation and gradient calculation for data model parameter optimization as well. Moreover, due to its compactness in the spatial domain it additionally allows detection and reduction of calibration errors from parasitic reflections by spatial gating (which is comparable to time domain gating). However, the practical situation as reflected by the available literature seems to be even more severe. It is often observed that inadequate calibration is performed which will seriously affect the performance. The common pitfall is to use incomplete antenna responses which implicitly result from ignoring orthogonal polarization and/or full solid angle characterization of the antenna elements. For example, single linear polarimetric and azimuth-only responses are often considered despite of the true spread of impinging waves in polarization and elevation and irrespective of the real antenna characteristic. Elevation characteristics are often neglected since “only azimuth is of interest” or only azimuth and elevation cuts of the full solid angle antenna radiation characteristic are used for simplicity. Polarization is often reduced to single linear if only single port antennas

(such as dipoles) are available. This, however, completely ignores that any real antenna is sensitive to both orthogonal polarizations which severely limits the polarization discrimination ratio especially for off-main radiation direction. Only a few publications are found trying to avoid these insufficient assumptions when estimating the radio channel parameters [11]–[13]. In this paper we will show that in cases of such a serious data model mismatch the parameter estimator will yield completely wrong results since it tries to match the wrong (reduced) data model to the received data. The estimated results will approximate the avoidable model error by spurious components, thus pretending multi-path components that are non existing in reality [14]. Obviously, this is primarily a problem of the data model and widely independent of the actual estimation procedure applied. The practical consequences are far reaching. If the estimated propagation parameters are used for further analysis such as clustering algorithms, channel capacity calculations, and parameterization of geometry-based stochastic channel models (GBSCM) especially in the angular domain (e.g., in [15]–[17]) we have to make sure that a full solid angle polarimetric data model is used since otherwise the results may be rendered useless. Moreover, the limited accuracy of the antenna array (AA) calibration measurements has to be considered to define the available dynamic range with respect to the reliability level of the estimated paths. This is of crucial importance also for the estimation and interpretation of the hybrid data model described. Only the precise knowledge and control of the modeling error level allows for identifying the estimated DMC as either a result of diffuse propagation or just as a mere approximation of the modeling error. In the following we will at first describe the hybrid propagation data model and give an overview of the RIMAX parameter estimation framework. Then we will introduce the antenna data model based on the EADF and describe how it is determined by a calibration measurement in a well defined anechoic environment. We will discuss the influence of unavoidable calibration errors resulting from parasitic reflections and give an idea about the achievable model accuracy in a practical situation. Moreover, we will discuss the decisive factors to evaluate the resulting DoA estimation performance. Then we will discuss the common pitfalls resulting from using only subsets of the full solid angle polarimetric antenna response, show the severe estimation errors that will arise in this case, and explain the reasons of their occurrence. Since practical antennas are involved, we follow an experimental approach based on measurements and simulations. All the parasitic antenna effects such as mutual coupling, antenna element position error, gain and phase errors are considered as systematic effects and do not need a separate discussion since they are already included in the measured antenna calibration vector. Hence, a further statistical analysis of these effects, e.g., as given in [18] is not adequate and also not tractable since all those effects cannot be handled by a closed form analytical model. On the other hand, the results given here are strictly valid only for the specific system used. The aim of the paper is toward emphasizing the physical understanding of propagation and device model mismatch, pointing out the resulting estimation error mechanisms and explaining the methods of error reduction and mitigation. Hence the road will be paved to enhance model design and device calibration

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and end up with reliable high resolution parameter estimation results.

(2)

II. RIMAX CHANNEL PARAMETER ESTIMATION FRAMEWORK The ultimate goal of Channel Parameter Estimation is to deduce a parametric model of the MIMO propagation channel from the recorded data that is independent from the antennas used during the measurement. This offers the possibility to emulate the MIMO transfer properties of arbitrary antenna arrays by reconstructing the output of the dedicated antenna array from the estimated directional channel parameters which will be weighted by the dedicated antenna’s radiation characteristic [19]. The key techniques to estimate the individual path parameters are HRPE and precise device calibration which includes the antenna array response. From the variety of estimation methods (see, e.g., [4] for an overview) mostly subspace methods like ESPRIT and iterative ML procedures like space alternating generalized expectation maximization (SAGE) have been applied to multidimensional sounding data [5], [6], [8], [20], [21]. We have developed a mixed SAGE and gradient based iterative ML approach for parameter optimization that clearly outperforms the pure SAGE based procedure with respect to local convergence, especially in case of closely spaced correlated paths ([10], [22]). In the following, we will describe the resulting RIMAX ML estimation framework and give details of the underlying hybrid propagation data model that contains both resolved specular and non-resolved stochastic components. A. The Propagation Data Model As indicated in the introduction the most widely accepted data model for HRPE in propagation measurement consists of a discrete multidimensional function. Essentially the same underlying model is used in electromagnetic wave propagation modelling such as ray-tracing [23]–[25]. It is based on a ray optical understanding of the propagation phenomena [26]. Consequently, propagation paths are modeled by the sum of frequency independent planar wave fronts in the equivalent base band. Each path is described by nonlinear structural parameters: DoD , (azimuth and co-elevation), ToA , Doppler-shift , and DoA , , and 4 linear parameters which are the complex polarimetric path weights: , , , . The - and -polarization are defined with respect to the unit vectors and of the local spherical coordinate system of the respective antenna array. Only in the equatorial plane (co-elevation 90 ) the -polarization is identical to horizontal-polarization and the -polarization is identical to vertical polarization. For notational convenience the parameters of the ’th path are arranged in the parameter vector (1) In the discrete angular-delay-doppler parameter domain an individual path is described by an -dimensional Dirac function, weighted by a 2 2 complex polarimetric path weight matrix

The Fourier transform reveals a set of multidimensional harmonic functions in a spatial-frequency-temporal aperture domain which indicates that the estimation problem could be handled as a harmonic retrieval procedure:

(3) is

hereby

a

function of the six parameters with frequency being the Fourier transform of the ToA and time being the Fourier transform of the Doppler-shift . As far as the directional part is concerned, a reasonable physical interpretation in the spatial domain can only be achieved if an additional geometric transformation similar to near/far-field transformation is included that depends on the antenna array structure. As will be shown later on, this is not explicitly needed for the estimation since the RIMAX procedure relies on measured (“calibrated”) far-field radiation patterns. B. Extension to a Hybrid Propagation Data Model Since specular reflection presumes wave interaction at plane surfaces that are at least as large as some wavelengths it is well known that the discrete-only (SC) approach is not sufficient to describe the full reality of wave propagation. Although using a vast number of weak discrete paths could help to approximate the microscopic structure of wave interaction with a real propagation environment, the situation in parameter estimation is different. Because of noise and with the limited calibration accuracy (as discussed already in the introduction) the resolution capability of any sounder is somewhat limited. Or in other words there is not enough information available from the measurement to resolve all those micro-paths and assign them to a deterministic parameter set . Overburdening the estimator would obviously create unreliable results. There are some proposals to model non-resolvable paths by an appropriate statistical distribution. One approach considers a concentrated von-Mises distribution in the angular domain to model a plurality of non-resolvable paths gathered in a small angular region [27]. In [28] the product of the von-Mises and the exponential distribution is used to model the delay-angular distribution. We are following the DMC approach as described in [29] which is motivated by the request to describe the observed diffuse scattering in addition to the resolvable specular reflection. While the electromagnetic background of diffuse scattering is already well understood [30] and various attempts are made to include diffuse scattering in ray tracing propagation modeling [23]–[25], [31], its influence was widely neglected in HRPE from sounding measurements. The first joint estimator for deterministic specular and distributed diffuse multipath components was published in [29]. Recent results have shown that the contribution of the latter varies depending on the complexity of the

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propagation environment [32]–[34]. Diffuse scattered components may be weak in macro-cell line of sight (LoS) scenarios (around 20% of the total received power), but they are considerably stronger in densely build urban areas and can even dominate in complicated scenarios such as factory halls [35] (up to 80%). For this reason the hybrid data model proposed in [29] comprises one deterministic and two stochastic parts that are jointly estimated by the RIMAX procedure. The total observed signal vector in (4) (also called snapshot or observation at a fixed time stamp) contains the superposition of a limited and resolvable number of deterministic components . This part corresponds to (1) and is also called the structural part of the propagation data model since it has a clear geometric interpretation. The second component represents the observed dense multipath part (DMC) that cannot be resolved further and assigned reliably to SC components by the estimation procedure. This part can be interpreted as the resulting global contribution of diffuse scattering as observed at both the transmitter and receiver antennas if and only if model mismatch and estimation errors can be excluded. The third part is the stationary noise related to the measurement equipment. Moreover, it turns out that joint estimation of the stochastic parts together with the SC components will considerably enhance the estimation quality of SC part

(4) C. Mapping of the Structural Propagation Data Model to Channel Observation In Section II-A the data model of the radio channel was introduced using a multidimensional Dirac function or harmonic function respectively. While the two parameters and are directly accessible by the channel sounder this is not true for the angular parameters or their respective Fourier transform. Therefore, we need to explicitly define the mapping of the angular parameters to the individual antenna array elements of the sounder. The contribution of any single specular propagation path to the total channel observation is described as follows:

(5) operator denotes the Kronecker product. The comThe plex harmonics in this equation directly correspond to (2), denote the steering vectors at the receiver and

transmitter respectively. The radiation patterns of the respective antenna elements are in general not uniform for the individual antenna elements of the array. They are also different for all of the four polarization components in (5). The device frequency response can be presumed to be uniform if a back-to-back calibration is carried out. However, this data model is still not directly applicable to parameter estimation, since it still lacks the systems limited bandwidth and temporal characteristics.1 Furthermore, in (5) the mapping of the angular parameters appears to be different from the mapping of the ToA and Doppler shift. We can, however, restore a unified mapping of all parameters and incorporate bandlimitation by using the EADF and introducing a concise vector/matrix notation

(6) The samples in the multidimensional aperture space are arranged in vectors as: (7) where are sampled versions of the complex exponenare the normalized structural path tials in (2) and (5) and parameters, which are related to their physical counterparts by unique projections , , , , , and a proper normalization to the respective aperture size, e.g., frequency bandwidth in case of . The linear projector matrices (for transmit polarization and receive polarization respectively) describe how the individual propagation paths are perceived by the measurement device in the spatial, temporal, and frequency aperture domain in terms of a multidimensional linear transfer function. is the weighting of the Doppler frequencies, is the frequency response,2 and and are the EADF matrices of the individual antenna array elements (related to Tx or Rx respectively). Each spatial response or is a transformed two dimensional function of the complex steering vectors and is of size . and denote the number of samples of the EADF, see Sections III-B and III-C for a discussion about the size of the EADF. For simplicity it is assumed that the total projector matrix is composed of the Kronecker products of to . to are pairwise independent This is only valid if which already implies some basic simplifications of the following data model. 1) Delay and Doppler are considered independent although nonzero Doppler shift requires changing of delay. 2) Doppler is considered frequency independent although Doppler in general causes a frequency dependent shift of frequency. 3) In the Doppler domain reduces to an identity matrix and linear uniform movement and propagating wave directions 1The 2If

finite size of the antenna arrays is accounted for by the steering vectors.

back-to-back calibration is used will be the identity matrix. If the is a diagonal systems frequency response is to be included in the model matrix with the systems frequency response as the main diagonal elements.

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that do not change within the temporal observation interval are assumed. 4) Antenna array responses are considered as frequency independent although spatial antenna separation transforms to frequency dependent phase and radiation patterns will have frequency responses which, in general, change with direction. 5) or are considered independent on distance (respectively time delay) which assumes plane wavefronts and, hence, distant scatterers (far field). 6) Further separation of the spatial responses and into Kronecker products of two vectors and would imply independent azimuth and elevation characteristics (“cuts”). In general this is not adequate as will be discussed later. Many of these simplifying assumptions will gradually lose their justification with increasing bandwidth and array size.

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of the stochastic part in the frequency covariance matrix domain is hereby given as

.. .

..

.

(9) being the number of samples in the frequency domain With and the spacing between the samples. This model still does not represent any spatial or rather angular distribution. That is because of the lack of knowledge about the spatial and temporal structure of the observed global diffuse scattering in complex environments. The reason is a lack of measurements with reliable angular resolution of diffuse components. First results from measurements are described in [36]–[38]. E. The Parameter Estimation Process

D. Mapping of the Stochastic Part As described above, the stochastic part of the observation (4) is composed of two components. The part is attributed to the stationary measurement noise. Therefore, it is not a part of the Channel Impulse Response (CIR) since it does not contribute to power transfer from transmitter (Tx) to receiver (Rx). This part has to be interpreted separately and must be omitted when a channel transfer matrix is resynthesized from the estimated parameters. Nevertheless, it is of advantage to include it into the propagation data model since it give us an estimate of the noise level. Note that the measurement signal-to-noise-ratio (SNR) is different and (preferably higher) than the SNR of some transceiver system that might be simulated using the measured CIR. Moreover, the estimation of the deterministic path parameters effectively results in some measurement noise reduction because of correlation gain. The second stochastic part, on the other hand, is clearly related to the impulse response since it is an exponential decaying function which relates to the expected of the non-resolved DMC in power delay profile is the corresponding correlation functhe delay domain. tion in the frequency domain. The describing parameter vector of this simple model is composed of the parameters , , , which are the coherence bandwidth, base delay and maximum power respectively:

(8) In the same manner as the initial SC model in (5) this model also implies infinite bandwidth whereas the data is observed within the finite bandwidth of the measurement system. This is actually a very important issue since it causes the DMC contribution at any delay-bin to be a superposition of a reasonable number of diffuse components which warrants its stochastic behavior. That can be justified only by a finite bandwidth. The resulting

With the unknown (hence random) parameters the observed signal vector (4) shows a conditional probability density of

(10) The related log-likelihood function is

(11) The resulting estimation problem requires a joint solution for two separate parameter sets, and respectively. Equation (11) contains the (total) covariance matrix of the DMC. is assumed to be decomposable into the Kronecker-product of four individual matrices (12) being the variance of the measurement noise. With the With propagation data model described in II-D the DMC influences the part only. The other covariance matrices are assumed to be identity matrices which results in a uniform distribution of the DMC in both spatial and Doppler domains. The Kronecker structure of the DMC part (although not really relevant for this paper) seems to be valid if the correlation in the different domains is independent. Since the influence of the DMC is not white in the delay domain according to (8), it acts as a “whitening” function for estimating SC. The knowledge of the covariance matrix will have considerable influence on the estimation of SC and enhance its quality. However, the covariance matrix depends on the estimated DMC. Therefore, both problems are related and joint estimation is required for the SC and DMC parameter. Due to the Gaussian nature of the probability density, the maximization of (11) with respect to the specular components is essentially a non-linear weighted least squares problem. Since an exhaustive search in the multidimensional parameter space is not feasible, an iterative search framework is used

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which is based on both sequential parameter update (SAGE) and the gradient based Levenberg-Marquardt algorithm. The latter enhances the convergence performance considerably in case of coherent paths that are closely co-located (and, hence, coupled in its influence to ) in the aperture limited multidimensional parameter space. Although the search procedure could work independently snapshot by snapshot, it is better initialized with the parameters of the previous snapshot. Since paths parameters are often persistent and slowly changing, Kalman tracking can further reduce the search effort per snapshot [12]. The number of paths is adaptively controlled by a birth and death process which discards disappearing paths and searches snapshot per snapshot for emerging paths. Paths are discarded if they appear as unreliable. This is indicated by the variance of the estimated path-weights calculated from the estimated Fisher Information Matrix (FIM) which is available from the gradient estimation [10]. A path is discarded if its relative variance is above a certain threshold. In general can be used as the threshold which means that the variance (or uncertainty) of the path-weight must be less than halve of the power of the path. This procedure continuously adjusts the model order according to the evolution of the propagation environment. Since the variance of the estimates is related to the variance of the stochastic part and thus to the DMC distribution, exaggerated deterministic approximation of dense components is avoided. This also avoids possible path splitting that may result from model order overestimation. Path splitting occurs when the estimator is forced to estimate e.g., two paths where in fact only a single path is present. The estimated paths will be very strong and closely spaced having nearly equal magnitude and opposite phase. Although the two estimated paths will approximate the single path with high accuracy they are physically incorrect. This case, however, can be detected due to the high variance of the parameters that will be reduced to the usual value by discarding one path. The parameter vectors and are estimated by an alternating search procedure. The DMC model search uses a Gauss-Newton procedure that performs parameter update using estimates from previous snapshot. The update rate (step-size of the Gauss-Newton algorithm) of the DMC model parameters can be chosen smaller than that of the SC parameters since the resulting diffuse scattering seems to change more slowly with the “average environment.” The DMC model parameters are estimated based on (13) that is equalized only with the frequency response calibration vector retaining any influence of the antenna arrays to the estimated DMC parameters. F. Interpretation of the DMC-Part Despite the deficiencies the DMC data model still has, it already considerably enhances the estimation performance of the deterministic SC from the observed data by maximizing (11) as will be demonstrated in Section V. The advantage comes from the influence of the covariance matrix which causes

a “whitening” of the DMC in the delay domain which considerably enhances the dynamic range of the SC. Without the covariance whitening the SC estimator would not detect the weaker components at larger delay. Moreover, without the knowledge about the covariance matrix it is also not possible to validate the quality of the estimates, thus, disturbing the control of the model order as described in Section II-E Instead the estimator would be trying to approximate the non-resolvable strong DMC with unreliable SC which are better described by the stochastic DMC distribution. Furthermore, the DMC model allows the parameter estimator to reallocate some error from the SC model mismatch to the DMC. From the viewpoint of SC parameter estimation this is a clear advantage since it helps to avoid model error approximation by SC. However, this might jeopardize the interpretation of the estimated DMC as a result of distributed diffuse scattering. Therefore, we will quantify the most important model error mechanisms in Section III. It should be noticed that the described advantages of the hybrid data model can only be realized if both the deterministic and the stochastic part of the model are estimated jointly. Just estimating the deterministic part, removing it and then trying to interpret the remainder is not enough. III. ANTENNA ARRAY CALIBRATION AND EVALUATION OF ESTIMATION RESULTS A. System Calibration In the following we solely assume that the frequency response of the measurement device is calibrated. This is accomplished by connecting the receiver and transmitter directly (without antennas) and measuring the frequency response. However, this already may include some potential pitfalls which are partly related to the time domain switching principle of the sounder system used [39], [40]. Time domain switching has the inherent advantage of a common up- and down-converter channel responses for all antenna elements at the transmitter and receiver side respectively. The limitations comes from the frequency response of the antennas and antenna switches. This problem is partly solved by calibrating the antenna array together with the switching circuit. This makes sure that the different electrical lengths of the cabling of the antenna ports to the switch are included in the antenna calibration. A rigid construction of the antenna module is thereby required in order to guarantee perfect phase stability throughout the period of usage. Concerning the antennas itself we assume frequency independent responses as discussed already in Section II-C Consideration of frequency dependent spatial response would require overthe-air frequency response measurements which would make antenna calibration even more challenging and would also increase the complexity of the parameter estimator. Another problem at the receiver side results from the Automatic Gain Control (AGC) which is required to match the input signal level to the ADC range. Especially in case of nonlinear antenna arrays (e.g., circular) and directive elements, the AGC attenuator will adjust the signal power when switching from one antenna port to another since the received signal strength changes according to the antenna orientation. So, in general,

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the AGC switches during one snapshot which will cause phase variation because of the changing electrical length of the AGC circuit and, hence, severely distorting the DoA estimation. A primitive solution is to fix the AGC within one snapshot but that would be appropriate only in case of linear or planar antenna arrays. In the RUSK sounder system the AGC induced phase variation is compensated by using an AGC dependent calibration vector. That means for each of the different AGC settings a calibration measurement is performed. The time domain switching is also often suspected to be highly sensitive to phase noise. Our investigations have shown that for the results given here, phase noise was not the limiting factor since its influence was smaller than the available model accuracy [9]. Similar assessment is given in [41], [42]. Nevertheless, in chapter V we will include realistic correlated phase noise in our simulations. B. Antenna Array Calibration Using EADF As explained in the previous section the spatial dimension of the channel response of the AA is described by and . Precise knowledge of the AA radiation patterns in magnitude and phase is required in order to avoid estimation artifacts and to achieve the anticipated resolution and accuracy. The AA calibration measurement is performed by far field measurements in an anechoic chamber using a precise polarimetric reference horn antenna and the sounder system. As reference we have used a dual slot coupled horn antenna with polarization decoupling better than 40 dB in the far field in the main-beam direction. This is adequate since the reference antenna is always aligned towards the AA. AA calibration using the broadband channel sounder system saves a lot of time compared to vector network analyzer (VNA) but long term phase drift can occur because of separate phase locked loop (PLL)s at Tx and Rx even with 10 MHz reference synchronization. This phase drift is in general not disturbing field measurements with fast antenna switching since the required coherence time interval is short (e.g., around a ms). But it may have a detrimental influence in calibration measurements which can last over hours. Therefore calibration measurements must be corrected either by recording the phase drift of an additional RF reference channel or by estimating the phase drift using ML methods as proposed in [43]. The AA element radiation patterns are described by their two dimensional (2D) discrete Fourier transformation. For each antenna element and for each polarimetric input/output combination in (6) we need a separate EADF. Since the transformation of the far field radiation pattern can be interpreted as a distorted inverse 2D near-field to far-field transform [44] we call it the effective aperture distribution function EADF [1], [45]. Note that we are using the EADF as an efficient radiation pattern descriptor and we are not interested in the physically correct field distribution. The same radiation pattern description (although not named as EADF), was used in [46] for one-dimensional (1D) and in [47] for 2D. Compared to the alternative vector spherical harmonics (VSH) descriptor [48], the EADF is not rotational invariant and the number of required aperture samples

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may be larger and dependent on the alignment of the antenna element. Nevertheless due to the use of fast Fourier transformation (FFT) algorithms the EADF is preferable since it is computational more attractive [9] and rotational invariance is not of importance. Application of FFT to sampled radiation pattern is straightforward and does not give rise to any leakage error because the patterns are naturally periodic with respect to the azimuth and co-elevation angles. This is especially true since FFT processing is also applied for radiation pattern interpolation and derivation w.r.t. azimuth and elevation which are required by the gradient based parameter search of the RIMAX algorithm. This way the EADF descriptor can be directly applied to construct the linear projector matrices at Tx and at Rx. Moreover, EADF is an efficient means to calculate the CRLB of DoA/DoD estimates in case of single and coherent multipath situations [45]. Since it can be determined based on measured as well as simulated radiation patterns (e.g., by using full wave EM solvers) it is a very powerful tool for evaluating the resolution potential of real AAs. C. Error Mitigation Using EADF The EADF turns out to be not only an efficient tool to handle the spatial array response. It can also be applied to detect and minimize some calibration errors. Although AA calibration measurement is conducted in an anechoic chamber, parasitic reflections can still occur especially from scattering at the positioning system which are expected to be attenuated by 10 dB to 40 dB w.r.t. the direct wave for frequencies between 4 GHz and 6 GHz depending on the angle of the incoming wave and the absorbing material [49]. Since the EADF is related to the electrical near-field distribution of a corresponding hypothetical antenna element, it should be confined to a compact support area in 2D space. The EADF will loose its spatial compactness as a result of parasitic reflections from the positioning device. So the EADF method indicates parasitic reflections and to some extend also allows for enhancement of calibration response by spatial tapering which may be considered as equivalent to temporal gating. Spatial tapering has to be handled with sure instinct since EADF blurring also occurs as a result of mutual antenna element coupling and if the radiation solid angle due pattern can not be measured over the full to the impact of the positioning system which causes tapering in the radiation pattern domain and, hence EADF leakage. Furthermore, the EADF will be somehow blurred if the radiation pattern is not measured with respect to its phase center which will always occur since we are rotating the whole array during calibration. So it is important to use the optimum pivot point in the center of the array which causes minimum EADF blurring. To demonstrate the effect of EADF distortion by parasitic reflections we have carried out simulations and measurements. Both are related to a polarimetric uniform circular array (PUCA) with 24 dual-polarized elements. The ideal dual polarimetric radiation response was calculated using the simulation software WIPL-D [50] with 7 adjacent antenna elements. The influence

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Fig. 2. Estimated mean angular power distribution versus deviation from true angle in azimuth as function of co-elevation applying (a) CEADFs; deviation of angular estimates using CEADF and (b) TEADFs for single path excitation and a simulated PUCPA with 24 elements (deviation of angular estimates using TEADF).

Fig. 1. (a),(b) Normalized EADFs of a single antenna for vertical excitation of a simulated and (c) measured PUCPA 24, magnitude in [dB]. [(a) Simulated undistorted EADF, (b) simulated distorted EADF, (c) measured EADF].

of parasitic reflections from the positioning device was simulated by a ray tracing approach. The strongest parasitic influence obviously results from a circular absorber plate which was mounted below the foot of the AA to shield the positioner. Depending on the elevation angle of the impinging LOS reference waveform the plate causes scattering, diffraction, and even LOS shadowing. In the simulation 10 spatially distributed parasitic waves with 25 dB attenuation w.r.t. the LOS wave and identical distributed polarization were assumed. Fig. 1 shows the resulting EADFs of a single simulated antenna and matched polarization without and with distortion in comparison to a measured antenna element. From comparison of Fig. 1(a) and (b) it can be concluded that EADF spreading occurs for spatial freand as a consequence of the quencies radiation pattern distortion due to parasitic reflections. The measured EADF shows similar behavior. Consequently, distortion can be reduced by spatial truncation of the measured EADF in both dimensions. Note that these reflections can not be removed

by time gating since they are closer than the Rayleigh resolution of 2.5 m which results from the measurement bandwidth of 120 MHz. In the following analysis, the performance of DoA parameter estimation is investigated for two different AA models: • The distorted and complete EADF (CEADF) with and ; • The distorted but truncated EADF (TEADF) with and . The parameter estimation results are shown in Fig. 2 for a simulated single-path excitation which acts as a known reference. The direction of the impinging wave is tuned over the full solid angle. In case of the undistorted antenna data model the parameter estimator RIMAX perfectly returns only one path from the true directions (which is not shown in the picture). Contrary, spurious paths appear in the distorted case since the model deviates from reality and the spurious are required to approximate the model error. Up to 9 spurious paths show up for each simulated arrival direction with a considerable spread in azimuth. Relative to the true paths the spurious are about lower in power. Stronger artifacts are estimated closer to the poles of the spherical coordinate system since in this region the AA model shows a lower accuracy. This is related to the reduced magnitude of the radiation patterns toward these directions which gives artifacts a stronger relative influence. Spatial truncation of the EADF reduces the level of the artifacts by about 10 to 15 dB. The advantage of the TEADF model becomes most obvious for co-elevation angles of incidence around where the remaining artifacts are almost negligible.

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D. Measure of Antenna Array Calibration Accuracy The mean square model accuracy is related to the Signal-toRemainder-Ratio (SRR) which is defined by (14) as the ratio between the power of the estimated specular paths and the remaining signal power which is left after subtraction of the estifrom the measured data : mated specular paths (14) where denotes the estimated noise power which is also removed since by definition it is not a part of the data model. If we force the parameter estimator to estimate only one single path which we know is the true model order in the reference case, the SRR is equal to the mean model accuracy of the data model. However, if we do not fix the model order in this way (since in general we do not know the true model order!) the contribution of the spurious paths actually reduces the SRR thus pretending a higher accuracy. Consequently, a better approximation of the received waveform must not be interpreted as a better result if the data model is wrong! In our example the resulting mean model ) is around accuracy (estimated from the SRR with 25 to 33 dB in case of the TEADF which is approximately 8 dB higher than with the CEADF AA model. This means that the TEADF AA model is a better match to the “real” (undistorted) model from which the reference data were deduced. Finally, the model accuracy is lowest for directions close to the zeros of the radiation patterns as discussed above. IV. ESTIMATION ERRORS DUE TO THE APPLICATION INCOMPLETE ANTENNA DATA MODELS

OF

The major effect used in direction estimation ought to be the phase response of the antenna elements which changes with incident angle in azimuth and elevation depending on the antenna array architecture. But any antenna element is somehow directive in the full solid angle domain. This causes radiation pattern magnitude to be an additional feature which must be taken into account by the estimation procedure. There are also many secondary effects that may result in distortion of the radiation patterns. Reasons are manufacturing inaccuracy, influence of array mounting brackets, and, most of all, mutual element coupling. All these effects have influence to the measured antenna response in amplitude and phase. The measured full solid angle polarimetric antenna response of the complete array (the “calibration pattern” or the measured steering vector in (5)) is directly exploited by the parameter estimator to match the received array response for every path. However, there is a common misuse of the calibration response which results from an inappropriate simplification. The consequences of reducing the model to 1D (e.g., by taking only azimuth cuts) is discussed in Section IV-A In Section IV-B we discuss the adverse effect of using only a single-polarimetric antenna data model instead of a full, dual-polarimetric one. A. Effect of Using Only 1D Antenna Data Models For an ideal Uniform Linear Array (ULA), the phase response along the array is inherently linear for each individual impinging

Fig. 3. DoA ambiguity ideal ULA and Phase over 16 element UCA for incidence at different co-elevations . (a) Ambiguity-cone of an ULA, array elements are placed along -axis, (b) phase distribution of UCA for different co-elshows highest variation, the curve for evation angles, the curve for shows no variation (const. phase for all elements (the curves in between are ordered according to the legend).

plane wave. Since the angle of incidence is defined with respect to the array axis in end-fire direction, the phase response shows a rotational symmetry around this axis. This means that any impinging wave with solid angle of incidence on a cone around a ULA end-fire direction will impose the same phase gradient over the array, as shown in Fig. 3(a). There is no way of telling from the array response which is the correct angle of incidence in the azimuth plane. So we have to accept an unknown bias in azimuth depending on co-elevation. More specifically, due to the lack of aperture in the plane perpendicular to the line through the array, estimation of the co-elevation angles of incidence with linear arrays is not possible. So if we don’t have any idea about the true co-elevation angle of the impinging wave we have no other chance than using one azimuthal cut of the 3D radiation pattern at an arbitrary co-elevation angle and we have to accept an unknown bias error in azimuth. It should be noted that the problem stated here is an inherent problem of ULAs that cannot be solved. For practical array the situation turns out to be a little bit more complicated as discussed below. For an Uniform Circular Array (UCA) the situation is different. In this case, the phase changes with varying angles of incidence along the array are not linear but sinusoidal (see Fig. 3(b)) with phase deflection depending on co-elevation. This constitutes additional information (compared to the ULA case) that can be used to estimate the co-elevation of the impinging wave. However, if we deliberately use only an azimuthal cut (e.g., for 90 of co-elevation which corresponds to the highest phase amplitude in Fig. 3(b)) of the antenna data model, matching of a lower gradient phase distribution (e.g.,

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Fig. 4. Estimated angular power distribution azimuth deviation from the true path 1D data model of the PULA.

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versus the and co-elevation using the

) by a single path is not possible. Therefore, the parameter estimator will be forced to provide spurious paths to match the incoming field with the applied AA azimuth-only model and, hence, pretending angular spread. 1) Measurement Example for an ULA: The consequences of the ULA’s ambiguity for direction estimation with a measured Polarimetric Uniform Linear Array (PULA) will be illustrated in the following example. In contrast to the ideal isotropic ULA, the real PULA has directional polarized patch antennas with nonuniform radiation patterns. Because of the secondary effects mentioned above the phase slope is not exactly linear and the magnitude response is similar but not uniform for a single planar wave. Most important, this non-uniformity changes with co-elevation. One could even try to deliberately exploit this feature to estimate the co-elevation angle. In general, for a reasonable array design the available information is not sufficient to achieve reliable elevation estimates but the same effect may be strong enough to seriously degrade the dynamic range of the estimator if the co-elevation angle of the impinging wave differs from that angle at which the azimuth pattern is measured during calibration (typically: ). In Fig. 4 the results are shown for a single -polarized wave (estimated with ). The true angle of incidence is in azimuth with co-elevation ranging from 20 to 160 . The distribution in the figure is clipped at amplitude which corresponds to the known relative model accuracy (as discussed in Section III). The effect of elevation on bias and variance of the azimuth angle estimation is obvious (both are zero only for ). The spread at other elevation angles results from the above mentioned pattern mismatch that depends on elevation if only azimuth patterns for elevation ) are used. This effect could only be avoided if the true elevation angle would be available and used to select the correct azimuth pattern. 2) Measurement Example for an UCA: In this example a 16 element UCA was used. Again, the array was illuminated by a single wave (always matched in polarization) with the incidence angle ranging over full azimuth and elevation. The estimation was performed using the reduced 1D ( , azimuth only) pattern. The results in terms of the mean model accuracy (corresponding to SRR with in (14)) are shown in Fig. 5(a). The mean model accuracy of the 1D data model drastically decreases for co-elevation angles toward the

Fig. 5. (a) Mean model accuracy (SRR with ) and (b) estimated for measured UCA, using 1D data angular power distributions model.

poles of the spherical coordinate system whereas the full 2D data model shows almost uniform accuracy resembling the expected behavior from the discussion in previous sections. The variation of the curves is related to the circular non-uniformity of the array in azimuth. In Fig. 5(b) the estimated angular power spectrum with paths at each true azimuthal DoA is depicted for the 1D data model. It shows that a single received SC renders a number of estimated SC which are widely spread around the true azimuthal angle of arrival except close to 90 co-elevation where the data model is correct. This detrimental effect is generic for circular arrays and is caused by the fundamental dissimilarity between the antenna response measured in the azimuthal plane and the antenna responses for co-elevation incidence . For comparison the estimation was also performed using the full 2D data model. The result (not shown here) was almost perfect. So compared to the ULA case, the circular array performs clearly worse if the elevation dimension was ignored. But on the other hand, the circular array offers the desired degree of freedom to estimate co-elevation which allows using elevation dependent azimuth patterns and, hence, solving the problem. B. Effect of Using Only Single Polarization Characteristics Despite the fact that radio waves are of vectorial nature which means they are composed of two orthogonal polarized components perpendicular to the propagation direction, often only a

LANDMANN et al.: IMPACT OF INCOMPLETE AND INACCURATE DATA MODELS ON HRPE

Fig. 6. Radiation pattern magnitude of the first element of the UCA for -polarized and -polarized excitation (at 90 co-elevation).

single polarization is considered. This simplification is motivated by the assumption that an antenna element may be sensitive to only one polarization. However, this is not true for a physically realizable antenna especially if the full solid angle of incidence is considered. So waves with the “wrong” polarization orientation may deliver a considerable contribution to the output. But the associate radiation response characteristics will be widely different for the - and -polarized fields. That causes a serious model mismatch and results in extensive estimation error if we try to estimate the DoA for one of the two polarization components with data model for the other one. This is again illustrated by the measured example of the 16 element UCA. Although the UCA array was designed from supposedly -polarized antennas (monopoles), the cross polarization discrimination (XPD), which is the power scaled ratio between the radiation patterns for co-polarized and cross-polarized excitation, is strongly varying with the angle of incident. Both azimuthal radiation patterns of the first element of the UCA for a constant co-elevation of 90 and - and -polarized excitation is depicted in Fig. 6. The XPD is low (between 0 dB and 10 dB) except for the azimuthal directions . This strong variation in azimuth maybe somewhat surprising for vertical monopoles. But it seems that the XPD of the antenna element is adversely influenced by mutual coupling in the array configuration. Nevertheless, many publications neglect this strong cross-polar sensitivity of real antenna elements when estimating propagation directions. Simple single polarimetric AA models are rather applied which may have catastrophic influence to the quality of the parameter estimation results. In the next example only the -polarized AA model was used. That is, only the radiation pattern which was measured from -excitation during calibration was applied for parameter estimation. On the other hand, the incident field in the evaluation experiment was chosen to be either a pure - or -polarized single wave front with its angle of incidence ranging again over full azimuth and elevation. In case of the -excitation (which perfectly matches the antenna data model) a single path can be perfectly estimated within the array model accuracy of 20 dB to 25 dB. But for the mismatching -excitation, the mean model accuracy (SRR) drops to only 5 dB since the radiation pattern for -polarization does not match. Fig. 7 shows the resulting mean angular power distribution (averaged over azimuth) relative to true azimuth direction only for the latter case. The

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Fig. 7. Estimated angular power distribution for a reduced antenna data model comprising only -polarized response in case of reception of a single -polarized SC.

magnitude was clipped again at to suppress the spurious components that may result from the limited calibration accuracy. Displaying the mean in azimuth is reasonable as the variation in estimation errors over the absolute azimuth angle is small due to the rather homogeneous response of the UCA in azimuth. The distribution in the Fig. 7 shows both a strong bias in azimuth (at the true azimuthal angle almost no power is located) and an asymmetric bias in co-elevation. This asymmetry stems from the asymmetric mechanical structure of the UCA in vertical direction. The apparent angular spread caused by using the oversimplified data model is considerable (be reminded that only a single discrete component was received in reality). Although the particular shapes of the distributions in Fig. 7 are specific for the array, the problem of a significant loss of accuracy in comparison with using a complete data model is generic. One simply does not have control over the polarization direction of incoming waves during measurements and with data models using only single linear polarization estimation of components with the other polarization is bound to yield errors of similar type as described here. So in general, a full polarimetric data model (consisting of the two radiation patterns for both orthogonal polarized excitation) must be used also in case of supposedly linear polarized (single port) antennas. Only under very restrictive conditions such estimation errors could be small. That happens e.g., when the array in fact only receives a single linear polarization, either because the impinging field has only a pure linear polarization (matching the calibration data model) or because the XPD of the antenna elements is extremely high. The former is not so likely in a real propagation environment [13] and the latter is only true for very few antenna designs within a small range of angles of incidence. Otherwise large spurious angular spread has to be expected. The conclusion is that ULA or antennas arrays with otherwise reduced calibration dimension can only be used if impinging waves from those directions are avoided. That has to be guaranteed already during data recording. There is no way to correct the resulting ambiguity and variance by a “better” estimator as long as no additional calibration data information is available. So, e.g., ULA could only be used in place of an elevated base station site where we can assume that azimuthal angle range is limited to a reasonable broadside range in azimuth and low elevation spread. The latter also means that the ULA must be given a down tilt to approximate (at least) the main elevation angle or

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we use this azimuthal cross section from the calibration pattern that corresponds to the expected elevation angle. V. ESTIMATION QUALITY IN COMPLEX ENVIRONMENTS This section deals with the overall influence of the real measurement system including the antenna arrays on the HRPE results in complicated multipath propagation environments. Based upon simulations we will demonstrate the impact of imperfect calibration. We explain the beneficial influence of DMC to the accuracy of the estimated SC if both components are jointly estimated and we discuss the balance in interpretation of the DMC as a result of non-resolved (“diffuse”) components vs. approximation of the model error. A. Simulation Setup According to the discussion in Section IV we assume that the complete (full solid angle polarimetric) 2D AA data model is applied which already excludes the serious mistakes described there. Here, we intend to include the influence of errors that in essence cannot be avoided under practical circumstances. These are remaining inaccuracies in calibration and also receiver noise. For the latter we consider additive independent and identically distributed (i.i.d.) complex Gaussian noise and phase noise. We will discuss the influence of correlated phase noise because this is a critical issue if the sounder uses the time division multiplexing (TDM) principle [39], [40]. TDM is suspected to be error-prone in terms of phase variation during the snapshot since the snapshot duration is extended in time by sequential antenna switching. The total snapshot length is given by the number of all CIRs that build the MIMO measurement matrix times the length of a single CIR. At the same time this mostly limits the time interval in which coherent signal processing takes place. Therefore, as long as phase coherence time is longer than the snapshot time the impact should be small. In [41] it was shown that the effect of long-term phase noise (random walk phase) can be neglected. The situation will change if phase noise correlation distance becomes smaller. The impact of correlated short-term phase noise was discussed in [42], [51], [52]. Thus, we have included the TDM frame into the simulations and the phase noise statistics used in the simulation was estimated from the sounding device at hand. In Sections III and IV we used a single path scenario as a reference to show the error effects. In a complicated multipath environment this comparison of measured responses to reference seems not possible since the “true” channel parameters are never known. Therefore, we follow the simulation approach. The CIR raw data are generated by applying a state of the art three dimensional (3D) ray-tracer developed at the Karlsruhe [24]. This gives us the desired access to the true angular distribution of the rays. The 3D ray-tracing model consists of two major parts: a realistic model of the propagation environment and a model to calculate the multi-path wave propagation between Tx and Rx. The propagation phenomena taken into account by the ray-tracer are single reflections, combinations of multiple reflections and multiple diffractions (up to five interactions), and diffuse scattering (single interaction). The power ratio between the strongest and the weakest path is limited to 50 dB. This results in total number of paths between 500 and 6000. This large number of paths is

related to the attempt of modeling diffuse scattering, which is a superposition of a large number of non-resolvable weak paths (weak in terms of power). The vast number of paths is necessary to demonstrate the resolution limits of the parameter estimator for the SC paths which will attribute the remaining part to DMC. From our observation of measured results and also supported by discussion in [23], [25] it becomes clear that this approach of simulating diffuse scattering by ray-tracing still underestimates the non-resolvable part. But, for the intended demonstration this seems not to be of highest concern. B. Impact of Distorted Antenna Array Calibration Based upon the ray-tracing results used as a reference we can directly compare the true path parameters to the parameters which are estimated by the HRPE algorithm. The simulated propagation environment was of a district of Karlsruhe City, Germany, as shown in Fig. 8. A LoS simulation route of 250 m length was chosen. The Tx array, a PULA with 8 polarimetric elements, was placed at a height of 38 m above street level. The Rx array, a Stacked PUCA (SPUCA) with 24 polarimetric elements for each ring, is placed at a height of 2 m above street level. The noise free channel realization is generated based upon the true path parameters and weighted with the undistorted true AA data model. For DoA estimation at the Rx simulated completely undistorted and distorted, but improved by means of TEADF, radiation patterns are applied as described in Section III. This allows for comparison of the results of the HRPE algorithm in case of ideal calibration (perfect knowledge of the radiation patterns, indicated by the term NoDist) with the real case with remaining calibration inaccuracy (indicated by the term FullDist). The TDM switching scheme with an CIR length of 3.2 is applied for all the simulations. • NoDist : In this ideal case infinite model accuracy is assumed and only additive i.i.d. complex Gaussian noise is added to the undistorted response , which results in the observation (15) • FullDist : In this case which resembles real measurements, observations are generated that are affected both by additive i.i.d. complex Gaussian noise and correlated shortterm phase noise

(16) with the diagonal matrix embossing the phase noise characteristic of a TDM sounder. The phase noise variance and the phase noise covariance matrix are estimated from the RUSK channel sounder available at Ilmenau University of Technology (IUT) and finally applied to generate the correlated phase noise samples in the diagonal elements of matrix . The distorted AA data model that will be used for the DoA estimation, is given in terms of the TEADF (which includes the remaining effect of parasitic reflections during AA calibration) that cannot be further reduced. The resulting overall

LANDMANN et al.: IMPACT OF INCOMPLETE AND INACCURATE DATA MODELS ON HRPE

Fig. 8. Visualization of raytracer environment.

TABLE I DATA MODELS USED FOR CHANNEL REALIZATION AND ESTIMATION

accuracy of the estimation model of the SC (respectively ) is thus around 25 to 30 dB, which is related to the accuracy of the AA model and the impact of the phase noise. The differences between the two models NoDist and FullDist are summarized in Table I. In the following two basic estimation approaches are applied to the two data models, NoDist and FullDist respectively, as defined above. With joint SC and DMC estimation (indicated by ), we will show whether the estimated DMC result mainly from unresolved SC or from model error. By further comparing to the case of SC-only estimation we will demonstrate the advantage of incorporating the DMC estimation in the HRPE algorithm. To emphasize the relevance of estimating DMC in the presence of model error let us reconsider (4). In the case of the ideal undistorted data model for (and, hence, unbiased estimation of ), we are able to subtract all resolvable paths from the observation . This allows for attributing all the remaining power of the unresolved DMC part to diffuse propagation. Using a distorted data model instead, the estimated allows less power to be subtracted with each path and more power is allocated to DMC. The power difference of the estimated DMC between the NoDist and the FullDist case indicates how much of the DMC results from the measurement procedure or model error respectively. For this end, let us define the parameter which in general is the ratio between the mean peak power of an impulse response and the mean noise power. and are defined as the ratio between the mean peak power of the SC or the DMC part in the estimated impulse responses relative to the mean estimated noise power . The is calculated from the band-limited, but still antenna dependent response for all resolved specular paths . This means the antenna response is not de-embedded in order to allow comparison with the diffuse part that cannot be de-embedded because of the missing angular model. is calculated from the estimated

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Fig. 9. Estimated of SC and DMC for the chosen LoS simulation and route in case of the estimation setups .

DMC peak power which is antenna dependent. As a consequence, the following observations can be made. 1) In case of , of the estimated DMC expresses the of unresolved SC since there is no AA modeling error. If is close to 0 dB the estimated DMC represent mainly the measurement noise, whereas for a higher than 0 dB the estimated DMC can be considered a feature of the radio channel. 2) If the in case of is higher than the of , then the estimated DMC of are partially related to model error. Consequently, they may not properly describe the propagation in the radio channel. Let us now analyze the illustrated in Fig. 9 for the SC and DMC in case of and for the chosen simulation route. The legend can be read as follows: In front of the colon the component of interest is specified and after the colon the simulation case NoDist or FullDist respectively is indicated. Apparently, the for both estimation setups are almost overlapping. The in case of is always close to 0 dB with only a few exceptions. This means that almost all received SC are resolved. For , the is approximately 5 dB to 20 dB higher. Thus, most of the estimated DMC power is related to model error only. Fig. 9 indicates some correlation between the and the in case of the result. If the ratio between the and is almost equal to the overall model accuracy of about 25 dB to 30 dB, we can conclude that the DMC in case of are mainly related to model error. This allows for an evaluation of the estimated DMC in terms of mere model error approximation vs. true propagation contribution without the need to compare to a Reference which is not available in a practical situation (see, also, analysis of measurements presented in [9] and [53]). C. Impact of DMC on Estimated SC Until now we have analyzed only the relevance of the estimated DMC, but we have got no evidence about the reli-

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simulation cases with the Reference spectrum, the estimated artifacts around the “true” paths give information about the quality of the discussed estimation approaches. With narrower spreads around the “true” paths the estimation result is said to be “better”. Analyzing Fig. 10 and taking the results of the previous discussion about the reliability of the estimated DMC into account, the following conclusions can be made: • The artificial spreads that can be observed in case of are caused by the array model error, phase noise, and additive Gaussian noise. Due to the model error, the estimated SC contribution is not sufficient to describe the received response. The remaining difference is approximated by additional specular paths that are physically nonexistent. • Joint estimation of SC and DMC can considerable improve the estimation result of the SC. For the artifacts due to model error contribute to the estimated DMC and, hence, do not cause additional paths pretending resolvable SC. The estimation results of shown in Fig. 10(b) are the best results that we can achieve in a real measurement. Again, if the ratio between the of the estimated SC and DMC is higher or equal to the overall model accuracy (here between 25 dB and 30 dB), the estimated DMC of must be considered to be not a feature of the radio channel and vice versa if the ratio is lower. It turns out that the estimation of the SC becomes more reliable if the DMC model is included in the estimation framework. VI. CONCLUSION

Fig. 10. Rx azimuth power spectra as a function of Rx position , for (a) the ray-tracer (Reference), (b) the estimated spectra considering all unavoidable , and (c) only. model errors (FullDist) estimating

ability of the estimated SC. For this purpose the Rx azimuth power spectrum of the ray-tracing results—used as a Reference (Fig. 10(a)) will be compared to the estimated spectra of the (Fig. 10(b)) and (Fig. 10(c)) cases that are deemed closest to the condition of a measurement. The amplitudes are clipped 50 dB below the maximum as the ray-tracing calculations were a-priori limited to 50 dB dynamic range between the strongest and the weakest path. Comparing the estimated angular power spectra of the two

Precise HRPE estimation of the structural parameters of multipath wave propagation (which has to include joint estimation of the directions of propagation at both Tx and Rx and full solid angle polarimetric processing) is the prerequisite for antenna de-embedding and, hence, for flexible antenna-independent channel characterization which is the ambitious aim of channel sounding. In this paper we have presented the decisive influence the data model imposes to the quality of HRPE in multidimensional channel sounding. The data model comprises both wave propagation aspects as well as the influence of the measurement device. It is affected by simplifications and limited calibration accuracy. Oversimplified data models that do not use the full dual polarimetric solid angle antenna response will result in serious estimation artifacts in complex multipath environments. This further results in artificial spread of paths in the angular domain which may be strong enough to render any subsequent propagation analysis useless. This error mechanism is solely caused by the data model applied and, hence can not be compensated by a “better” estimator, although, of course, the specific parameter estimator chosen defines which data model can be applied. Model mismatch, in essence, cannot be completely avoided but somehow controlled by sophisticated device data models and careful calibration procedures. This is especially true for the AA influence. We have described the EADF method as a very powerful tool to handle full solid angle polarimeric antenna calibration data that also allows some reduction of the remaining calibration errors.

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In this paper the RIMAX framework is applied for parameter estimation. This iterative estimation framework includes a hybrid data model that consists of a deterministic part describing the geometric structure of the SC components and a so called DMC part which is stochastic in nature. This part shall describe as much as possible the diffuse part of multipath propagation. We have shown that this is only true if we use the full solid angle dual polarimetric AA data model. Remaining model mismatch, however, still increases the amount of power that is estimated for the DMC. So for a reliable interpretation of the estimation results we must have knowledge about the remaining calibration error to make sure that the channel model distortion is small enough. The DMC model part has another advantage for parameter estimation since it can be used to approximate/compensate the remaining calibration model error. This may considerably enhance the quality of the SC estimation since it helps to avoid model overestimation by unreliable (and hence wrong) SC. Moreover, if one has precise knowledge about the calibration data model error, the DMC part that has to be attributed to the data model error can be removed from the estimation result which allows for additional enhancement of estimation quality. It must be emphasized, however, that most of this advantage becomes true only if the SC and DMC parts are jointly estimated. Finally, it should be noted that it was not the goal of this paper to refine the hybrid DMC propagation model. There might be various approaches to achieve that [27], [36]–[38]. Rather it was the goal to show how inaccurate and incomplete device and propagation data models can severely affect estimation accuracy and reliability which may have significant influence to the interpretation of estimated model parameters. So any refinement of the propagation data model must make sure that the pitfalls analyzed in this paper are carefully avoided. ACKNOWLEDGMENT The authors would like to thank G. Sommerkorn for cooperation and assistance during measurement campaigns and antenna calibration as well as Dr. W. Kotterman for valuable discussions. The cooperation with the University of Karlsruhe (IHE, Prof. Wiesbeck) which allowed access to their ray tracing simulator is also gratefully acknowledged. Special thanks go to the MEDAV company for excellent support and cooperation. REFERENCES [1] R. S. Thomä, M. Landmann, A. Richter, and U. Trautwein, “Multidimensional high-resolution channel sounding,” in Smart Antennas in Europe State of the Art, EURASIP Book Series on SP &C, T. Kaiser, Ed. Cairo, Egypt: Hindawi Publishing, 2005, vol. 3. [2] M. Landmann and R. S. Thomä, “Resolution limits and antenna array calibration of real arrays,” in Mobile Broadband Multimedia Networks: Techniques, Models and Tools for 4G Techniques, COST 273, L. M. Correia, Ed. Waltham, MA: Academic Press, 2006, pp. 165–167. [3] C. Schneider, G. Sommerkorn, M. Narandzic, M. Käske, A. Hong, V. Algeier, W. Kotterman, R. S. Thomä, and C. Jandura, “Multi-user MIMO channel reference data for channel modelling and system evaluation from measurements,” presented at the Int. IEEE Workshop on Smart Antennas (WSA 2009), Berlin, Germany, Feb. 2009. [4] M. Viberg and H. Krim, “Two decades of array signal processing research: The parametric approach,” IEEE Signal Processing Mag., vol. 13, pp. 67–94, Jul. 1996.

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[5] M. Kwakkernaat, Y. Jong, R. Bultitude, and M. Herben, “High-resolution angle-of-Arrival measurements on physically-nonstationary mobile radio channels,” IEEE Trans. Antennas Propag., vol. 56, no. 8, 2008. [6] B. H. Fleury, M. Tschudin, R. Heddergott, D. Dahlhaus, and P. K. Ingeman, “Channel parameter estimation in mobile radio environments using the SAGE algorithm,” IEEE J. Sel. Areas Communi., vol. 17, pp. 434–450, 1999. [7] M. Tschudin, C. Brunner, T. Kurpjuhn, M. Haardt, and J. A. Nossek, “Comparison between unitary ESPRIT and SAGE for 3-D channel sounding,” in Proc. IEEE 49th Vehicular Technology Conf., May 16–20, 1999, vol. 2, pp. 1324–1329. [8] M. Haardt, R. S. Thomä, and A. Richter, “Multidimensional high-resolution parameter estimation with applications to channel sounding,” in High-Resolution and Robust Signal Processing, Y. Hua, Ed. et al. New York: Marcel Dekker, 2003, pp. 253–337. [9] M. Landmann, “Limitations of Experimental Channel Characterisation,” Ph.D. dissertation, Technische Universität Ilmenau, Ilmenau, Germany, 2008. [10] A. Richter, “On the Estimation of Radio Channel Parameters: Models and Algorithms (RIMAX),” Ph.D. dissertation, Technische Universität Ilmenau, Ilmenau, Germany, 2005. [11] J. Medbo, M. Riback, H. Asplund, and J. Berg, “MIMO channel characteristics in a small macrocell measured at 5.25 GHz and 200 MHz bandwidth,” in Proc. IEEE 62nd Vehicular Technology Conf., Sep. 2005, vol. 1, pp. 372–376. [12] J. Salmi, A. Richter, and V. Koivunen, “Detection and tracking of MIMO propagation path parameters using state-space approach,” IEEE Trans. Signal Processing,, vol. 57, no. 4, pp. 1538–1550, Apr. 2009. [13] M. Landmann, K. Sivasondhivat, J.-I. Takada, I. Ida, and R. S. Thomä, “Polarization behavior of discrete multipath and diffuse scattering in urban environments at 4.5 GHz,” EURASIP J. Wireless Commun. Network., Special Issue on Space-Time Channel Model. Wireless Commun. Network., 2007. [14] M. Landmann, W. Kotterman, and R. S. Thomä, “On the influence of incomplete data models on estimated angular distributions in channel characterisation,” presented at the 2nd Eur. Conf. on Antennas Propag. (EuCAP 2007), 2007. [15] A. Pal, C. M. Tan, and M. A. Beach, “Comparison of MIMO channels from multipath parameter extraction and direct channel measurements,” in Proc. 15th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Communications, Sep. 2004, vol. 3, pp. 1574–1578. [16] S. Wyne, N. Czink, J. Karedal, P. Almers, F. Tufvesson, and A. F. Molisch, “A cluster-based analysis of outdoor-to-Indoor office MIMO measurements at 5.2 GHz,” in Proc. IEEE 64th Vehicular Technology Conf., Montreal, QC, Canada, Sep. 2006, pp. 1–5. [17] N. Czink, X. Yin, H. Ozcelik, M. Herdin, E. Bonek, and B. H. Fleury, “Cluster characteristics in a MIMO indoor propagation environment,” IEEE Trans. Wireless Commun., vol. 6, pp. 1465–1475, Apr. 2007. [18] A. Ferreol, P. Larzabal, and M. Viberg, “Performance prediction of maximum-likelihood direction-of-Arrival estimation in the presence of modeling errors,” IEEE Trans. Signal Processing, vol. 56, no. 10, pp. 4785–4793, 2008. [19] R. S. Thomä, D. Hampicke, M. Landmann, A. Richter, and G. Sommerkorn, “Measurement-based channel modelling (MBPCM),” presented at the Proc. Int. Conf. on Electromagnetics in Advanced Applications (ICEAA03), Torino, Italy, Sep. 2003. [20] A. Richter, D. Hampicke, G. Sommerkorn, and R. S. Thomä, “MIMO measurement and joint M-D parameter estimation of mobile radio channels,” in Proc. IEEE 63rd Vehicular Technology Conf., May 2001, vol. 1, pp. 214–218. [21] I. Ziskind and M. Wax, “Maximum likelihood localization of multiple sources by alternating projection,” IEEE Trans. Acoust. Speech Signal Process., vol. 36, no. 10, pp. 1553–1560, Oct. 1988. [22] A. Richter, M. Landmann, and R. S. Thomä, “A gradient based method for maximum likelihood channel parameter estimation from multidimensional channel sounding measurement,” presented at the XXVIIth URSI General Assembly, Maastricht, NL, Aug. 2002. [23] V. Degli-Esposti, D. Guiducci, A. de’Marsi, P. Azzi, and F. Fuschini, “An advanced field prediction model including diffuse scattering,” IEEE Trans. Antennas Propag., vol. 52, no. 7, pp. 1717–1728, Jul. 2004. [24] T. Fügen, J. Maurer, T. Kayser, and W. Wiesbeck, “Capability of 3D ray tracing for defining parameter sets for the specification of future mobile communications systems,” IEEE Trans. Antennas Propag., Special Issue Wireless Commun., vol. 54, no. 11, pp. 3125–3137, Nov. 2006.

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[25] V. Degli-Esposti, F. Fuschini, E. Vitucci, and G. Falciasecca, “Measurement and modelling of scattering from buildings,” IEEE Trans. Antennas Propag., vol. 52, no. 1, pp. 143–153, Jan. 2007. [26] M. F. Iskander and Z. Yun, “Propagation prediction models for wireless communication systems,” IEEE Trans. Microwave Theory Tech., vol. 50, no. 3, pp. 662–673, 2002. [27] X. Yin, L. Liu, D. K. Nielsen, T. Pedersen, and B. H. Fleury, “A SAGE algorithm for estimation of the direction power spectrum of individual path components,” in Proc. IEEE Global Telecommunications Conf., 2007, pp. 3024–3028. [28] C. B. Ribeiro, A. Richter, and V. Koivunen, “Joint angular-and delaydomain MIMO propagation parameter estimation using approximate ML method,” IEEE Trans. Signal Process., vol. 55, pp. 4775–4790, Oct. 2007. [29] R. S. Thomä, M. Landmann, and A. Richter, “RIMAX-a maximum likelihood framework channel parameter estimation in multidimensional channel sounding,” in Proc. Int. Symp. on Antennas and Propag., Sendai, Japan, Aug. 2004, pp. 53–56. [30] R. Vaughan and J. B. Andersen, “Channel propagation and antennas for mobile communications,” Inst. Elect. Eng. Electromagn. Waves Series London, no. 50, 2003. [31] V. Degli-Esposti, F. Fuschini, and E. Vitucci, “A fast model for distributed scattering from buildings,” presented at the 3rd Eur. Conf. on Antennas Propag., Mar. 2009. [32] A. Richter and R. S. Thomä, “Joint maximum likelihood estimation of specular paths and distributed diffuse scattering,” in Proc. IEEE 61st Vehicular Technology Conf., Stockholm, Sweden, May 30–Jun. 1 2005. [33] N. Czink, A. Richter, E. Bonek, J.-P. Nuutinen, and J. Ylitalo, “Including diffuse multipath parameters in MIMO channel models,” in Proc. IEEE 66th Vehicular Technology Conf., Baltimore, Sep. 30–Oct. 3 2007. [34] J. Poutanen, J. Salmi, K. Haneda, V. Kolmonen, F. Tufvesson, and P. Vainikainen, “Propagation characteristics of dense multipath components,” IEEE Antennas Wireless Propag. Lett., vol. 9, pp. 791–794, 2010. [35] W. Kotterman, M. Landmann, G. Sommerkorn, and R. S. Thomä, “On diffuse and non-resolved multipath components in directional channel characterisation,” presented at the XXVIIIth General Assembly URSI, New Delhi, India, Oct. 2005. [36] J. Salmi, J. Poutanen, K. Haneda, A. Richter, V.-M. Kolmonen, P. Vainikainen, and A. F. Molisch, “Incorporating diffuse scattering in geometry-based stochastic MIMO channel models,” in Proc. 4th Eur. Conf. on Antennas Propag. (EuCAP), 2010, pp. 1–5. [37] F. Quitin, C. Oestges, F. Horlin, and P. De Doncker, “Diffuse multipath component characterization for indoor MIMO channels,” in Proc. 4th Eur. Conf. on Antennas Propag. (EuCAP), 2010, pp. 1–5. [38] M. Käske, M. Landmann, and R. S. Thomä, “Modelling and synthesis of dense multipath propagation components in the angular domain,” presented at the 3rd Eur. Conf. on Antennas Propag., Mar. 2009. [39] R. S. Thomä, D. Hampicke, A. Richter, G. Sommerkorn, A. Schneider, U. Trautwein, and W. Wiesbeck, “Identification of time-variant directional mobile radio channels,” IEEE Trans. Instrum. Meas., vol. 49, no. 2, pp. 357–364, 2000. [40] R. S. Thomä, D. Hampicke, A. Richter, G. Sommerkorn, and U. Trautwein, “MIMO vector channel sounder measurement for smart antenna system evaluation,” Eur. Trans. Telecommun. ETT, Special Issue Smart Antennas, vol. 12, no. 5, pp. 427–438, Sep./Oct. 2001. [41] P. Almers, S. Wyne, F. Tufvesson, and A. F. Molisch, “Effect of random walk phase noise on MIMO measurements,” in Proc. IEEE 61st Vehicular Technology Conf., Jun. 2005, vol. 1, pp. 141–145. [42] A. Taparugssanagorn, X. Yin, J. Ylitalo, and B. H. Fleury, “Phase noise mitigation in channel parameter estimation for TDM switched MIMO channel sounding,” presented at the Asilomar Conference on Signals, Systems and Computers, 2007. [43] M. Landmann and R. S. Thomä, “Estimation of phase drift during calibration measurements for efficient beam pattern modelling,” presented at the NEWCOM-ACORN Workshop, Wien, Austria, Sep. 2006. [44] C. A. Balanis, Near Field/Far Field Methods, ser. Numerical Analysis. New York: Wiley, 1997, pp. 852–858. [45] M. Landmann, A. Richter, and R. S. Thomä, “DoA resolution limits in MIMO channel sounding,” presented at the Int. Symp. on Antennas Propag. and USNC/URSI National Radio Science Meeting, Monterey, CA, Jun. 2004. [46] M. A. Doron and E. Doron, “Wavefield modeling and array processing—I: Spatial sampling,” IEEE Trans. Signal Process., vol. 42, no. 10, pp. 2549–2559, 1994.

[47] J. E. Hansen, Spherical Near-Field Antenna Measurements, ser. Numerical Analysis. London, U.K.: Peter Peregrinus, 1988, pp. 387–387. [48] G. Del Galdo, J. Lotze, M. Landmann, and M. Haardt, “Modelling and manipulation of polarimetric antenna beam patterns via spherical harmonics,” presented at the 14th Eur. Signal Processing Conf. (EUSIPCO), Florence, Italy, Sep. 2006. [49] Pyramiden-Absorber DATENBLATT 390-1, Noppen-Absorber DATENBLATT 390-7 Emc-Technik & Consulting, 2007. [50] Electromagnetic Modeling of Composite Metalic and Dielectric Structures [Online]. Available: http://www.wipl-d.com/. [51] A. Taparugssanagorn, M. Alatossava, V. M. Holappa, and J. Ylitalo, “Impact of channel sounder phase noise on directional channel estimation by space-alternating generalised expectation maximisation,” IET Microw. Antennas Propag., vol. 1, no. 3, pp. 803–808, 2007. [52] A. Taparugssanagorn and J. Ylitalo, “Characteristics of short-term phase noise of MIMO channel sounding and its effect on capacity estimation,” IEEE Trans. Intrum. Meas., vol. 58, no. 1, pp. 196–201, Jan. 2009. [53] M. Käske , C. Schneider, G. Sommerkorn, and R. S. Thomä, PART II: Reference campaign—quality check for channel sounding measurements COST 2100 Temporary Document TD(09)777, 2009.

Markus Landmann was born in Zeitz, Germany, in 1977. He received the Dipl.-Ing. (M.S.E.E.) and Dr.-Ing. (Ph.D.E.E.) degrees in electrical engineering and information technology from Ilmenau University of Technology, Germany, in 2001 and 2008, respectively. From 2001 to 2003, he was working as a Research Assistant and Instructor at Ilmenau University of Technology. In 2004, he was developing advanced antenna array calibration methods and high resolution parameter estimation algorithm (RIMAX) for propagation studies at MEDAV Company. In 2005, he was Visiting Researcher and Instructor at Tokyo Institute of Technology (Takada Laboratory) in the field of channel measurement and estimation techniques. From 2006 to 2008, he was finalizing his doctoral thesis (Dr.-Ing) as a Research Associate at Ilmenau University of Technology. He is currently with the Project Group Wireless Distribution Systems/Digital Broadcasting, Fraunhofer Institute for Integrated Circuits IIS Helmholtzplatz, Ilmenau, Germany. His current interests are wireless propagation, channel modeling, and array signal processing.

Martin Käske received the Dipl.-Ing. (M.S.E.E.) degree in electrical engineering (information technology) from Ilmenau University of Technology, Germany, in 2008. He is currently working as a Research Assistant at the Electronic Research Measurement Lab, Ilmenau University of Technology. He is focusing on diffuse scattering—its modeling and estimation—as well as advanced antenna array calibration methods.

Reiner S. Thomä (F’07) received the Dipl.-Ing. (M.S.E.E.), Dr.-Ing. (Ph.D.E.E.), and the Dr.-Ing. habil. degrees in electrical engineering and information technology from Technische Hochschule Ilmenau, Germany, in 1975, 1983, and 1989, respectively. From 1975 to 1988, he was a Research Associate in the fields of electronic circuits, measurement engineering, and digital signal processing at the same university. From 1988 to 1990, he was a Research Engineer at the Akademie der Wissenschaften der DDR (Zentrum für Wissenschaftlichen Gerätebau). During this period, he was working in the field of radio surveillance. In 1991, he spent a three-month sabbatical leave at the University of Erlangen-Nürnberg (Lehrstuhl für Nachrichtentechnik). Since 1992, he has been a Professor of electrical engineering (electronic measurement) at TU Ilmenau where he was

LANDMANN et al.: IMPACT OF INCOMPLETE AND INACCURATE DATA MODELS ON HRPE

the Director of the Institute of Communications and Measurement Engineering from 1999 until 2005. Currently, he is Vice Speaker at the Intl. Graduate School on Mobile Communication, TU Ilmenau and Speaker of the nationwide DFG-focus project UKoLOS, ultrawideband radio technologies for communications, localization and sensor applications (SPP 1202). His research interests include measurement and digital signal processing methods (correlation and spectral analysis, system identification, array methods, time-frequency and cyclostationary signal analysis), their application in mobile radio and radar

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systems (multidimensional channel sounding, propagation measurement and parameter estimation, ultrawideband radar), measurement-based performance evaluation of MIMO transmission systems, and UWB sensor systems for object detection and imaging. Prof. Thomä has been serving as Chair of the IEEE-IM TC-13 on Measurement in Wireless and Telecommunications since 1999. In 2007, he was awarded the grade of IEEE Fellow for his “contributions to high-resolution multidimensional channel sounding.”

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A General Coupling-Based Model Framework for Wideband MIMO Channels Yan Zhang, Member, IEEE, Ove Edfors, Member, IEEE, Peter Hammarberg, Member, IEEE, Tommy Hult, Member, IEEE, Xiang Chen, Member, IEEE, Shidong Zhou, Member, IEEE, Limin Xiao, Member, IEEE, and Jing Wang, Member, IEEE

Abstract—A general coupling-based model framework for wideband multiple-input multiple-output (MIMO) channels is presented in this paper. Under this framework, the channel state information (CSI) tensor can be expressed by the product of a coupling tensor, a complex Gaussian tensor and three unitary matrices. The unitary matrices can be either eigenbases or steering matrices in different domains. The coupling tensor reflects the relationship between the column vectors of these unitary matrices. The complex Gaussian tensor is used to describe the small-scale fading. Several realizations of this framework are introduced, including the wideband Kronecker-based (WKB) model, the wideband eigenvalue-decomposition-based (WEB) model, the wideband virtual presentation (WVP) model and the wideband hybrid (WHY) model. To evaluate the performance of these models, channel measurements were carried out in different indoor scenarios both at Tsinghua University and Lund University. The results show that these models have good agreement with the measured data. Furthermore, we can see that the WHY model can provide a tradeoff between complexity and accuracy in channel synthesis. Index Terms—Channel capacity, channel measurement, coupling-based, multiple-input multiple-output (MIMO), wideband channel model.

I. INTRODUCTION

F

OR next-generation wireless communication systems, several new key technologies have been proposed to support high transmit rates. Multiple-input multiple-output (MIMO) systems, which can lead to large capacity gains [1], have drawn considerable interest. Accurate MIMO channel models, which can mimic real wireless channels, is very important for the MIMO system design and evaluation.

Manuscript received June 01, 2010; revised May 28, 2011; accepted September 02, 2011. Date of publication October 26, 2011; date of current version February 03, 2012. This work was partially supported by National Basic Research Program of China (2012CB316002), Tsinghua University Initiative Scientific Research Program (20111081025), China’s Major Project (2009ZX03007-003-02), China’s 863 Project (2009AA011501), PCSIRT, Tsinghua-Qualcomm Joint Research Program, and China Postdoctoral Science Foundation. Support has also been received from the Swedish government agency VINNOVA through the Sino-Swedish Strategic Cooperative Programme on Next Generation Networks (2008-00962). Y. Zhang is with the Department of Electronic Engineering, Tsinghua University, Beijing, 100084 China (e-mail: [email protected]). O. Edfors, P. Hammarberg, and T. Hult are with the Department of Electrical and Information Technology, LTH, Lund University, 221 00 Lund, Sweden. X. Chen, S. Zhou, L. Xiao, and J. Wang are with the Department of Electronic Engineering, Research Institute of Information Technology, Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, 100084 Beijing, China. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173436

Fig. 1. The differences between (a) physical model and (b) analytical model. The physical models are independent of the antenna arrays while the analytical MIMO models consider the impact of the antenna arrays.

In recent years, many MIMO channel models have been developed [2], [3]. They can be classified into physical models and analytical models [2], [4]. Physical models describe the electromagnetic wave propagation environment between the transmitter (Tx) and receiver (Rx) locations. As illustrated in Fig. 1(a), physical models are independent of the antenna array configuration. Typical physical models include the geometry-based stochastic models (GSCM) [5], the Zwick model [6] and the Saleh–Valenzuela model [7]. Analytical models, on the other hand, describe the channel impulse response (CIR) matrix and are often used for channel synthesis and algorithm developments. As Fig. 1(b) shows, the analytical MIMO models consider the impact of the antenna arrays in both ends as parts of the channel response. Amongst the analytical models, the independent identically distributed (i.i.d.) channel model [1] is the simplest one. It is widely used for the calculation of ergodic MIMO capacity. The full-correlation model [4], which characterizes the channel by the complex correlations between all channel matrix element pairs, requires a vast number of parameters to be specified. In order to simplify the full-correlation model, a narrowband MIMO model based on the Kronecker product is presented in [8]. Weichselberger proposes an eigenvalue decomposition (EVD)-based model in [9] and [10], and Sayeed develops a virtual presentation model in [11]. The finite scatterer model [12] constitutes the coupling relationship through linking different scatterers in the propagation environment. The keyhole and max-entropy models are established in [13] and [14], respectively. In [15], a general unitary-independent-unitary (UIU) model is proposed to encompass most of the zero-mean channel models. Future wireless communication systems need wider frequency bands to achieve higher throughput. However, the models mentioned above are all designed for the narrowband channels. Therefore, it is necessary to investigate the wideband

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ZHANG et al.: A GENERAL COUPLING-BASED MODEL FRAMEWORK FOR WIDEBAND MIMO CHANNELS

MIMO channel modeling. Until now, the basic modeling idea is to apply the narrowband models for each delay tap. For example, Yu extends the Kronecker model to the wideband case by calculating the channel correlation matrix tap by tap [16]. In [17], Costa establishes a novel structured model based on the EVDs of the delay, transmit, and receive correlation matrices. This model describes the correlations between different taps and is capable of generating the wideband CIR tensor. Our goal with this paper is to provide additional wideband models to be used for channel synthesis and algorithm developments. A general coupling-based model framework is proposed, and using this framework, we present several models for wideband MIMO channels. The specific contributions of this paper are as follows. • The wideband MIMO channel is described by a three-dimensional (3-D) channel state information (CSI) tensor in the transmitter, receiver, and frequency domains. We divide the wideband MIMO CSI tensor into a deterministic part and a stochastic part. The deterministic part corresponds to the line-of-sight (LOS) component. The stochastic part, which is used to describe the diffuse components, is decomposed into the product of a coupling tensor, a complex Gaussian tensor and three unitary matrices. This decomposition is defined as the coupling-based model framework. • Under this framework, five wideband analytical models are presented, including the wideband i.i.d. model, the wideband Kronecker-based (WKB) model, the wideband eigenvalue-decomposition-based (WEB) model, the wideband virtual presentation (WVP) model, and the wideband hybrid (WHY) model. The physical mechanisms and transform meanings of these models are also explained. • Using the coupling-based framework, the wideband i.i.d., WKB, WEB, and WVP models can be viewed as the extensions of the corresponding narrowband models. A novel WHY model is proposed to provide a tradeoff between the modeling complexity and accuracy. • To evaluate the performance of these wideband coupling-based models, we carried out measurements both at Tsinghua University (THU) and at Lund University. The results show that the models derived from the coupling-based framework are in good agreement with the measured channels. The rest of this paper is organized as follows. In Section II, several popular narrowband analytical models are reviewed. The coupling-based model framework and its several realizations are given in Section III. In Section IV, we describe the measurements carried out at THU and Lund University. In Section V, the performance evaluation metrics are introduced. Measured data and simulation results are shown in Section VI to evaluate the performance of the proposed wideband coupling-based models. Finally, our conclusions are presented in Section VII. The following notation conventions will be adhered to: Lower case letters are scalars and bold lower case letters are vectors. Bold upper case letters are matrices, while upper case script letters are tensors in . is the trace of a matrix, is the expectation operator, stands for the Schur–Hadamard product and stands for the Kronecker product.

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II. NARROWBAND ANALYTICAL MIMO MODEL In this section, we will review several popular analytical models of the narrowband MIMO channel. These models are the basis of our work and we will later show how these can be extended to the wideband cases using the proposed wideband coupling-based framework. Now, Let us consider a narrowband MIMO system that employs transmit antennas and receive antennas. The relationship between the transmitted and received signals can then be expressed as (1) received signal, is the where is the signal, and is the noise. The CSI matrix .. .

..

.

.. .

transmitted

(2)

matrix whose entry is the scalar valued freis an quency response between the th transmit antenna and the th receive antenna. For a Rician fading case, the channel matrix (3) and the stochastic can be divided into the deterministic part part [4]. Here, , a phase-shift-only MIMO matrix, reflects the contribution of the LOS component [4]. is a zero-mean stochastic part and is corresponding to the effect of the diffuse components. is the Rician factor. which represents the ratio of the LOS component power to the total power in the diffuse non line-of-sight (NLOS) components. In the following sections, we only consider the stochastic part , i.e., . Then, and corresponds to a Rayleigh fading channel. A. The i.i.d. Model The i.i.d. model is the simplest model and is commonly used for information theoretical analysis. The matrix entries in this model obey zero-mean circularly symmetric complex Gaussian (ZMCSCG) distribution. It assumes a rich scattering environment where numerous independent multipath components (MPCs) depart and arrive in all directions. B. The Kronecker Model In the Kronecker model [8], the channel matrix is given by (4) where (5) are the transmit and receive correlation matrices. is an random matrix with i.i.d. ZMCSCG entries. The Kronecker model relies on the assumption that direction of departures (DoDs) and direction of arrivals (DoAs) in the

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MIMO channel can be separated. This means that each DoD is linked to all DoAs with the same pattern and that the joint DoA-DoD spectrum can be expressed as the product of the DoA spectrum and the DoD spectrum. Obviously, the separability condition is not met in general [4]. C. The Weichselberger Model In the Weichselberger model [9], the EVDs are applied to the transmit and receive correlation matrices. Then, the channel matrix can be synthesized as (6) and are eigenbases at the Here, the unitary matrices receiver and transmitter domains and given by (7) is used to deIn (7), the amplitude coupling matrix scribe the links between transmit eigenmodes and receive eigenmodes. The Weichselberger model has been shown to agree closely with measured data [4], [10]. Its disadvantages, as compared to the Kronecker model, are the increased number of parameters that need to be specified and the increased complexity in obtaining those parameters from the measured data [17].

be used to generate MIMO CSI tensors. Notation and relevant tensor calculus in this paper follow those defined in [19] and [20]. A. The Wideband MIMO CSI Tensor Let us consider a wideband MIMO system with transmit antennas, receive antennas and a bandwidth of . The CSI matrix at frequency bin can be written as .. .

..

.

.. .

(11)

is the complex frequency response beHere, the entry tween transmit antenna , receive antenna , and frequency bin . The frequency bins are numbered and divide the total bandwidth into equidistant intervals (subcarriers) of width . Compared with the traditional tap-delay model, the wideband MIMO channel response is modeled in frequency domain instead of delay domain. We do not build the CIR matrix tap by tap, but synthesize the CSI tensor in the frequency domain. By changing , we can get a 3-D CSI tensor , which can be divided into two parts: (12)

D. The Virtual Presentation Model The virtual presentation model [10] is designed for uniform linear arrays (ULAs). In this model, the channel matrix (8) is modeled by describing the amplitude coupling between the virtual angles at transmitter and receiver. is the amplitude coupling matrix and

(9)

(10) are the steering matrices into the virtual angles at transmitter and receiver. Here is the normalized antenna spacing and is the wavelength. is the th virtual DoA and is the th virtual DoD, respectively. III. A GENERAL COUPLING-BASED WIDEBAND MIMO MODEL FRAMEWORK The analytical models in Section II are all designed for the narrowband MIMO channel. With an increase of transmission bandwidths in future communication systems, it is important to develop accurate models for the wideband MIMO channel. In this section, a general coupling-based framework is proposed for the wideband MIMO channel. Under this framework, several wideband channel models are proposed. These models can

where still means the Rician factor, representing the ratio of the LOS component power to the total diffuse components’ power. The deterministic tensor denotes the LOS component and the stochastic part represents the diffuse components. Again, we let , i.e., . Only the stochastic part will be considered in the following analysis. Based on the Raleigh-fading assumption, the entry of the MIMO tensor satisfies the joint multivariate ZMCSCG distribution. The wideband MIMO tensor can be fully characterized by an full-correlation matrix (13) Here, is the vector operator [17], [19]. characterizes the correlations between all transmit antennas, receive antennas and frequency bins. The MIMO CSI tensor can then be synthesized by (14) i.i.d. ZMCSCG random tensor. where is an This model can be defined as the full-correlation model of the wideband MIMO channel [17]. Similar to the narrowband case, the full-correlation model can entirely capture the channel tensor’s spatial and delay property, so it can be used as a bench mark to evaluate other models. The drawback of this full-correlation model is its high complexity. In order to synthesize , we need to specify with complex parameters. In general the full-correlation matrix size is too large for channel synthesis. In the following sections, several simpler models will be presented.

ZHANG et al.: A GENERAL COUPLING-BASED MODEL FRAMEWORK FOR WIDEBAND MIMO CHANNELS

B. Coupling-Based Model Framework A coupling-based framework is proposed for the wideband MIMO channel. The wideband CSI tensor can be described by the following coupling-based structure (15) is an amplitude coupling tensor and is where used to describe the gain between the column vectors of , and . , a complex Gaussian tensor, reflects the small-scale fading in the propagation environment. are unitary matrices in the different domains. means multiplication in the th tensor dimension [19]. Under this framework, several wideband models, i.e., the wideband i.i.d., WKB, WEB, WVP, and WHY models, can be established based on different propagation assumptions. 1) Wideband i.i.d. Model: If , , and , equals to . The coupling-based framework characterizes a simple wideband i.i.d. model, which can be used for analyzing the closed-form solution of wideband channel capacity. This wideband i.i.d. channel model satisfies the rich-scattering assumption that a large number of independent multipath components superimpose at the receiver. 2) Wideband Kronecker-Based Model: If , , and the coupling tensor (16)

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any pair of transmit antennas should be independent of the receive antenna index and the frequency bin index. Analogously, the frequency correlation between each pair of frequency bins should also be independent of the receive antenna index and the transmit antenna index. The interpretation of the WKB model is as follows: The joint DoA-DoD-delay spectrum is the Kronecker product of the delay spectrum, the DoD spectrum, and the DoA spectrum. All DoAs, all DoDs, and all delays are linked together in the same pattern. All delays show the same AoA/AoD spectrum. Similar to the narrowband Kronecker model, these assumptions are in general too strict for realistic propagation channel. This WKB model needs the knowledge of , and to rebuild the CSI tensor. Hereby, there are coefficients to be specified. It should be mentioned that this WKB model is different from the model in [16], which is also based on the Kronecker structure. The WKB model does not build the channel response tap by tap as in [16], but considers the correlation in frequency domain together with the correlation in the spatial domain. 3) Wideband EVD-Based Model: In this WEB model, the coupling relationship between the receive, transmit, and frequency eigenmodes are considered. The EVDs of receiver, transmitter, and frequency correlation matrices are given by (23) (24) (25)

the coupling-based framework will describe a wideband Kronecker-based model: (17) The receiver, transmitter and frequency correlation matrices are defined as

, , and are the eigenbases in the receiver, where transmitter, and frequency domain, respectively. , , and are the diagonal eigenvalue matrices. If , , and , the coupling-based framework will describe the coupling relationship between the eigenvectors. The CSI tensor can be synthesized by the following wideband EVD-based (WEB) model

(18) (19) (20) where ,

means the th unfolding of and satisfy

[19]. The traces of

(26) is an amplitude coupling tensor, Here, where the entries correspond to the coupling amplitude between the th receiver eigenmode , the th transmitter eigenmode , and the th frequency eigenmode . The coupling power can be given by

(21) In this WKB model, the wideband full-correlation channel matrix (22) is constructed by the Kronecker product of the three correlation matrices. The WKB model implies the following assumptions. The receive antenna correlation between any pair of receive antennas has to be independent of the transmit antenna index and the frequency bin index. The transmit antenna correlation between

(27) The WEB model can be viewed as an extension of the narrowband Weichselberger model, where also the eigenmodes in the frequency domain are taken account in the CSI tensor modeling. Furthermore, , and are all Karhunen–Loeve transform (KLT) matrices [15]. Thereby the WEB CSI tensor and the tensor is actually a 3-D KLT pair. In other words, the coupling tensor can be transformed to the CSI tensor through three KLTs in the receive, transmit and frequency domains.

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Furthermore, we can see that the WKB model is a special case of this WEB model. If the amplitude coupling tensor

(28) the WEB model will degrade to the WKB model. In the WEB model, , , , and need to be specified to generate , so there are total unknown parameters. 4) Wideband Virtual Presentation Model: The coupling relationships between the steering vectors in the receiver, transmitter and frequency domains are considered in this model. If steering matrices are used in (15), i.e., , , and , the coupling-based framework can extend the narrowband virtual presentation model to the wideband case. The wideband MIMO CSI tensor can be expressed as the coupling relationship between steering vectors (29) where , , and are the steering vectors in the receiver, transmitter and frequency domains, respectively. and are defined in (12) and (13), and

(30) is the steering matrix in the frequency domain. Similar to the virtual angle definition in the narrowband virtual presentation model, can be defined as the virtual delays. divides the max delay range uniformly. In (29), is the amplitude coupling tensor. Its entries represent the coupling amplitudes between the th receive steering vector , the th transmit steering vector , and the th frequency steering vector . This model can be viewed as the extension of the narrowband virtual presentation model in [11]. Thereby, we call it the wideband virtual presentation model. The physical meaning of this WVP model can be explained as follows. The wideband MIMO channel is modeled by using the predefined orthogonal DoAs, DoDs and delays (virtual DoAs, DoDs, and delays). If there exists a path at a unique pair of the virtual DoA, DoD, and delay, the corresponding entry of is equal to the fading gain of this path. For example, if there are two scatterers in the propagation environment and only a single spectral reflection occurs, as Fig. 2 shows, each scatterer causes an individual path. The DoAs, DoDs, and delays of these two paths are , and . The power coupling coefficients and are equal to the power of the first and the second path, respectively. The WVP model can be viewed as “virtual” tap-delay models. However the exact delay values are not required for the WVP model. Similar to the virtual angles, these virtual delays are selected to divide the delay domain uniformly due to the DFT

Fig. 2. Physical mechanism of virtual presentation model. The entry of equals to the amplitude of the virtual path.

property. For example, in Fig. 2, if is not one of the virtual delays, then the first path’s power will be “dispersed” to different virtual tap delays. The spatial resolution of the WVP model depends on the antenna array size. For example, receive (transmit) antennas can only provide virtual DoAs (DoDs). The number of frequency bins specifies the number of the virtual delays, i.e., the delay resolution is determined by the bandwidth. For this model, , , and are the discrete Fourier transform (DFT) matrices. The WVP channel tensor and the coupling tensor are therefore a 3-D DFT transform pair, i.e., the coupling relationships between the virtual DoAs, DoDs, and delays can be transferred to the frequency response in the transmitter-receiver-frequency domain by these DFT matrices. The WVP model is only available for ULAs. In this model, only the amplitude coupling matrix with parameters needs to be specified. 5) Wideband Hybrid Model: In practical MIMO systems, the number of antennas is often limited by cost, power restriction, and terminal size. Thus, the spatial resolutions are limited at both ends, especially at a mobile station. At the same time, the system bandwidth (corresponding to the number of frequency bins) is usually large enough to provide high delay resolution. In this case, the complexity of the WEB model will be quite high because of the increase in the size of the frequency correlation matrix. The WVP model needs only a few parameters and no EVD operation, while its spatial performance degrades quickly if the array size is limited. Furthermore, the WVP model can only be applied in the systems with ULAs. Considering these limitations, we propose a novel wideband hybrid coupling-based model, which combines the advantages of the WEB and WVP models. If , and , the CSI tensor (31) can be modeled by the coupling relationships between the transmit eigenmodes, the receive eigenmodes, and the frequency steering vectors. In this WHY model, the spatial characteristics are still described in the eigendomains while the delay characteristics are presented by the steering vectors. Then, the WHY model can keep the performance in the spatial domain without losing too much delay resolution. Furthermore, the computation complexity in the frequency domain, which plays a major role in the synthesis and simulation process, will be reduced.

ZHANG et al.: A GENERAL COUPLING-BASED MODEL FRAMEWORK FOR WIDEBAND MIMO CHANNELS

TABLE I THE DIFFERENCES BETWEEN PROPOSED COUPLING-BASED MODELS

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TABLE II THE CONFIGURATION OF THU MIMO CHANNEL SOUNDER

In this WHY model, the coupling tensor, and the eigenbases in the transmitter and receiver domain need to be specified. The number of unknown parameters is therefore . C. Discussion The wideband i.i.d., WKB, WEB, WVP, and WHY models are all realizations of the proposed coupling-based model framework. As mentioned above, the wideband i.i.d. model and the WKB model are based on the rich-scattering assumption and separability assumption, respectively. In general, these assumptions are too strict for realistic channels. Therefore, only the WEB, WVP and WHY model will be discussed in the following sections. The differences between these three models are the selection of the unitary matrices, as shown in Table I. In (15), can be either selected as an eigenbase or a steering matrix . The selection can be determined by the antenna array configurations and the system bandwidth. Using an eigenbase can provide higher resolution but more complexity. Employing a steering matrix will lead to less complexity. However, the performance of the model will decrease if the array size, or the system bandwidth, is limited. The complexity and accuracy requirement for the system simulation should be considered when selecting the unitary matrices. This coupling-based wideband model framework can be interpreted in two ways. On one hand, the amplitude coupling tensor reflects the coupling relationship between the receiver, transmitter and frequency domains. Its entries are corresponding to the coupling amplitudes between the columns of the unitary matrices. On the other hand, the wideband MIMO CSI tensor in the transmitter–receiver–frequency domain and the coupling tensor in the DoA-DoD-delay domain are a 3-D transform pair. Here, the transform can be either KLT or DFT. Under this coupling-based framework, other narrowband models could also be extended to the wideband case. Nevertheless, there are still several models that can not be derived from this coupling-based framework, e.g., the wideband keyhole channel model. IV. MEASUREMENT DESCRIPTION To evaluate the performance of the proposed coupling-based models, we carried out measurement campaigns both at Tsinghua and Lund University. A. Measurements at THU At THU, the measurements were carried out by the THU MIMO channel sounder [21]. Some important parameters were shown in Table II. At the transmitter of the THU channel sounder, a signal generator periodically outputed the test signal at the center frequency of 3.52 GHz with 16 MHz bandwidth. The transmitted RF signal was fed to each transmit antenna by

a fast time-division multiplexed switching (TDMS) scheme. Fast switching was also employed at the receiver. The test signal length was 12.8 s. A guard interval of length was inserted between adjacent transmissions. The snapshot interval was 1254.4 s. The synchronization between the transmitter and the receiver was achieved by using well-adjusted Rubidium-based frequency references. ULAs with half wavelength inter-element spacing were employed at both Tx and Rx. The maximum antenna configuration was 7 7, while only the responses of 5 5 antenna pairs were used in the following analysis. The antennas on the array edges were viewed as dummy elements and their responses were discarded. The Tx and Rx antenna arrays were placed at heights of 0.9 m and 1.3 m above the floor. Campaigns were carried out in the Future Internet Technology (FIT) building, Tsinghua University, Beijing, China. Two typical indoor scenarios were chosen, including a office scenario and a corridor-to-office scenario. Because the receiver was too large to move during the measurements, the position of the receiver was fixed and the transmitter was moved to different positions. The office scenario was selected to be in a small lab. The area of this office was 8.8 m 16.3 m. The receiver was fixed on a desk in the center of the office, and the transmitter was mounted on a trolley and moved to different positions. The main scatterers in this office were concrete walls, wooden tables, plastic chairs and metal cabinets. There was a concrete pillar in the center of the office, which could obstruct the LOS propagation between the transmitter and receiver. In the corridor-to-office scenario, the position of the receiver position was the same as that in the office scenario. The transmitter was moved to different positions in the neighboring corridor. Fig. 3(a) and (b) shows photographs of this scenario. The corridor was 105 m long and 2.5 m wide. Fig. 4 illustrates the site map of the measurement campaign. A total of 29 positions were measured. The distance between adjacent positions was 3.6 m. There was no LOS propagation between Tx and Rx. During the measurements, the doors of rooms 4–509 and 4–510 were kept open. B. Lund Measurement Campaign The commercial RUSK Lund channel sounder1 [22], was used to collect the channel data at Lund University. Measurements were performed at 2.6 GHz with a bandwidth of 200 MHz, using a transmit power of 27 dBm. The TDMS 1[Online]

Available: http://www.channelsounder.de/

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Fig. 3. Photos of the corridor-to-office scenario including (a) the transmitter and (b) the receiver.

Fig. 5. Site map of the corridor-to-office scenario at Lund University. The transmitter (the black arrow) was placed at the end of the corridor. The receiver (the red circles) was placed in 22 positions in 20 different small offices. The directions of arrows are the reference directions of the antenna arrays. Fig. 4. Site map of the corridor-to-office scenario at THU. The receiver (red arrow) was fixed in the office and the transmitter was placed in the different positions in the corridor.

TABLE III THE CONFIGURATION OF RUSK LUND CHANNEL SOUNDER

the rectangular array, while that of the Rx antenna array is the direction between the first and sixteenth patches. In the corridor-to-corridor scenario, the transmitter was still fixed at the end of the corridor on the second floor. The receiver was placed in 13 positions in the different corridors without LOS propagations on the same floor. In the lobby-to-corridor scenario, the transmitter was placed in one side of the lobby on the first floor. The receiver was moved to 15 positions in the different corridors on the same floor. V. PERFORMANCE EVALUATION METRICS

schemes were also employed to sequentially connect antenna elements to a single RF chain at both the Tx and Rx side. The length of the Tx signal was 1.6 s. The interval between two consecutive snapshots was 3.4 ms. The main parameters of the RUSK Lund channel sounder are shown in Table III. The transmit antenna was a 2 8 rectangular array with half-wavelength spacing. The receive antenna was a 16-element uniform circular array (UCA) with an element spacing of . All elements are vertical polarized patch antennas. The heights of Tx and Rx antenna arrays were 2.08 and 1.43 m, respectively. The measurement site was the E-building, LTH, Lund University. Three scenarios including corridor-to-office, corridor-to-corridor and lobby-to-corridor were measured. In our analysis, only the positions without LOS propagation are considered. As shown in Fig. 5, for the corridor-to-office scenario the transmitter was fixed at the end of the corridor and the receiver was moved to 22 different positions in 20 offices. The directions of arrows are the reference directions of the antenna arrays. The reference direction of the Tx antenna array is the broadside of

When we evaluate the performance of a wideband channel model, both the modeling accuracy and complexity should be taken into account. On one hand, the channel model should be simple enough to synthesize. On the other hand, a good channel model should characterize the propagation environment accurately. Both the spatial property and the delay property should be reproduced by the proposed channel model. A. Joint DoA-DoD-Delay Power Spectrum Two metrics, the joint DoA-DoD-delay power spectrum and the channel capacity, will be employed to evaluate the accuracies of these analytical models [4]. The joint DoA-DoD-delay power spectrum can be expressed using the Bartlett beamformer [10]:

(32) with normalized steering vectors at DoD and at DoA of the full-correlation matrix.

.

at delay , is the estimation

ZHANG et al.: A GENERAL COUPLING-BASED MODEL FRAMEWORK FOR WIDEBAND MIMO CHANNELS

The computed DoA-DoD-delay power spectrum is an tensor. It can reflect the spatial and delay characteristics of the wideband MIMO channel. In the following analysis, the joint DoA-DoD angular power spectrums (APS) of the strongest tap is used to characterize the spatial structure. Furthermore, the DoA-delay spectrum with the strongest departure direction will be illustrated to describe the delay and receive angular characteristics. Because of Bartlett beamformer will lead a leakage between tap delays, the power spectrum comparison may be unfairly in favor of the WVP model. But considering the validity behind using a Fourier base for the transform, the Bartlett beamformer is sufficient for a quantitative comparison. B. Capacity Let us consider a channel unknown at the transmitter. The capacity of a wideband MIMO channel with equally allocated transmit powers can be calculated as [17] (33) is an identify matrix, SNR is the average rewhere ceive signal power to noise power ratio, and is the normalized CSI matrix at frequency bin . VI. RESULTS The performance of the WEB, WVP, and WHY models will be evaluated in the following section. Because the assumption of the WKB model is obviously too strict for the realistic channel, The WKB will fail completely when comparing the measurement results. In this section the results of the WKB model are not illustrated. For comparison, the traditional channel model in [16], which builds the Kronecker structure tap by tap, is also simulated for comparison. This model will be referred to as the “Kronecker model” in the rest of the paper. The results from the presented models will be shown in this section. For the WEB, WVP, WHY, and Kronecker models, CSI tensors are generated by Monte Carlo simulations. Firstly, the model parameters are extracted from the measured data, and using these the CSI tensors are generated. The generated CSI tensors are then compared with the original measurement data. For the Kronecker model, we first synthesize a narrowband channel matrix for each delay, then transform the CIR to the frequency domain using a DFT. A. Complexity The number of parameters needed in the different models are given in Table IV. An example is also provided when . For the Kronecker model, refers to the tap number, while is the number of frequency bins for the proposed coupling-based models. The full-correlation model can completely characterize the Rayleigh fading channel. However, in this model the full-correlation matrix with parameters need to be specified. In three coupling-based models, the WEB model needs the most parameters because the coupling tensor and three correlation matrices need to be

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TABLE IV THE NUMBER OF PARAMETERS AND EVD OPERATIONS NEEDED IN THE DIFFERENT MODELS

specified. Three EVD operations are also required in the WEB model. With the increase in the number of the frequency bins, the WEB model will become more difficult for synthesis. The WVP model needs the fewest parameters to synthesize and does not require any EVD operation. The WHY model omits the correlation matrix computation and the EVD operation in the frequency domain. Because the number of frequency bins is usually larger than the number of antennas, the WHY model’s complexity is close to the WVP model’s. B. Joint DoA-DoD-Delay Power Spectrum For the measurements at Lund University, the Tx and Rx antenna patterns have not been measured yet. Thus, the DoADoD-delay power spectrum cannot be estimated using the data measured at Lund University. Therefore, only the THU measurements will be presented. 1) THU Office Scenario: Figs. 6 and Fig. 7 show the results from the measured data in the office scenario at THU. Fig. 6 illustrates the APSs of the strongest tap. In this scenario, the transmitter and the receiver were placed in the same office without LOS propagation. There are a lot of scatterers in this position. It can be seen that the strongest path is close to DoD DoA 22 23 and other paths appear at 50 27 , 10 32 , 21 78 , and 12 24 . The Kronecker model forces the joint DoA-DoD spectrum to be the product of two separate DoA and DoD spectrums. This will lead to some artifact paths at the intersection of the DoD and DoA peaks, e.g., the path at 22 30 . The WEB model can reflect the spatial structure more accurately. Nevertheless, the WEB model still fails to model some details of the cluster arriving at about 27 . The WHY model performs identically to the WEB model because they have the same spatial structure. The performance of the WVP model is limited by the array size. In this scenario, the WVP model performs well because most real MPCs depart and arrive at the "virtual" angles. In order to quantify the power spectrum differences, we use the Kullback-Leibler divergence (KLD) to describe the differences. The KLD is defined as follows [25], [26]:

(34)

Here, is the normalized . with equality iff . In Fig. 6, let and represent DoA and DoD, respectively. Then KLDs from the modeled APSs to the measured APS can be

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TABLE V THE KLDS BETWEEN MODELED AND MEASURED APSS

TABLE VI THE KLDS BETWEEN MODELED AND MEASURED DOA-DELAY SPECTRUMS

Fig. 6. MIMO APSs of the strongest tap from: (a) measured data, (b) WEB model, (c) WVP model, (d) WHY model, and (e) Kronecker model in the office scenario at THU.

Fig. 7. Joint DoA-Delay spectrum when DoD from: (a) measured data, (b) WEB model, (c) WVP model, and (d) WHY model in the office scenario at THU.

calculated. The results are shown in the first row of Table V. In this scenario, it can be seen that the KLDs between the measured

APS and the WEB, WHY, and WVP models’ are very small. The Kronecker model defined in [16] has larger KLDs because it generates some artifact paths. Furthermore, the KLD between the WEB and the WHY models’ APSs is 0.0149, near to zero. That is because these two models have similar spatial structure. Fig. 7 shows the joint DoA-delay spectrums at the DoD 22.2 . It can be seen that there are two main taps in the delay domain. The first tap has stronger power and larger angular spread than the second one. The KLDs from the modeled DoA-delay spectrums to the measure one are shown in the first row of Table VI. As shown in Table VI and Fig. 7, the performance of the WEB model is still the best when it is used to characterize the delay-DoA structure. The WHY and WVP models are also close to the measured data in this scenario. For the WHY and WVP models, two delay taps are overlapped, which may be caused by the limited measurement bandwidth of the THU sounder. The measurement bandwidth is 16 MHz, so the delay resolution is around 0.0626 us. Larger measurement bandwidth will lead to better performance for the WHY model. 2) THU Corridor-to-Office Scenario: Fig. 8 illustrates the APSs of the position 1 in the corridor-to-office scenario. Several paths arrive around 10 , which is the direction of the door 4–510. There is another path arriving at 67 , which is corresponding to the door 4–509. In this scenario, because most paths travel through doors opening, the joint APS can be considered as separable. Thus, the performance of the Kronecker model is acceptable while it still produces some artifact paths, e.g., at 31 24 and 24 64 . The KLD results from the modeled APSs to the measured APS in this scenario are illustrated in the second row of Table V. The WEB model and the WHY model still performs better than the Kronecker and WVP models. The WVP model mixes several paths together because of the limited spatial resolution. Thus, its KLD from the measured data is large. Because the Kronecker structure is coincide with the realistic channel, the KLD of the Kronecker model is small. The DoA-delay spectrums when DoD 26.7 in this scenario are plotted in Fig. 9. It is shown that the second tap is the strongest tap in this scenario. The KLDs between modeled and measured spectrums in Fig. 9 are shown in the second row of Table VI. Again, the WEB model captures the spatial and delay characteristics of this channel best. The WVP model cannot distinguish the paths arriving from different directions. The WHY model provides acceptable resolutions both in delay and receive

ZHANG et al.: A GENERAL COUPLING-BASED MODEL FRAMEWORK FOR WIDEBAND MIMO CHANNELS

CAPACITY ERROR

OF

TABLE VII DIFFERENT WIDEBAND MODELS IN THE CORRIDOR-TO-OFFICE SCENARIO THE DIAGONAL DASHED LINE DENOTES NO MODEL ERROR

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AT

THU.

Fig. 9. Joint DoA-delay spectrum when DoD from: (a) measured data, (b) WEB model, (c) WVP model, and (d) WHY model in the corridor-tooffice scenario at THU.

channel capacity analysis. The measured data from the THU office scenarios are not enough to get reliable statistical results, so they are not illustrated here. The evaluation SNR in (33) is selected as 20 dB and the capacity error of wideband models is defined as Fig. 8. MIMO APSs of the strongest tap from: (a) measured data, (b) WEB model, (c) WVP model, (d) WHY model, and (e) Kronecker model in the corridor-to-office scenario at THU.

angular domains. Limited by the bandwidth, a small overlapping in delay domain can be seen in the WHY model. C. Capacity The data from the corridor-to-office scenario at THU and three scenarios from the Lund measurements are used for the

Error

(35)

are the modeled capacity. is the measured Here, capacity. A positive error value means the overestimation of real capacity, while a negative value means underestimation. 1) THU Corridor-to-Office Scenario: Table VII shows the average capacity error of different models when . The average capacity error in the last row is computed by averaging absolute error values at all positions. It is illustrated that the WEB model has the smallest estimation error

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Fig. 10. Modeled capacity error using all data sets and all positions in the corridor-to-office scenario at THU.

Fig. 11. Capacity CDF for all data sets and all positions in the corridor-to-office scenario at Lund University.

and the error of the WHY model is very close to that of WEB model. Fig. 10 illustrates the modeled versus synthesized capacity at all 29 positions. The diagonal dashed line represents no model error. Generally the WHY model beats the WVP model, but for a few positions, the WVP model is better than the WVP model. This may be caused by the propagation environment around these positions. In general, if the number of scatterers is small and the DoAs and DoDs are close to the virtual angles, the WVP model will have good agreement with real channel. Otherwise its performance may degrade quickly. 2) Lund Scenarios: Figs. 11, 12, and 13 show the capacity results of the different scenarios at Lund University. Although the receive cylindrical array response could be transformed to a ULA response by parameter extraction and resynthesization, the WVP capacity have not been calculated because the antenna calibration files are unavailable. Thus, only the results of the WEB, WHY and Kronecker models are illustrated. Similar to the results in the THU scenario, the WEB and WHY models outperform the Kronecker model. The WHY model describes a continuous-time reality better and better with increased sampling rate (bandwidth). Then

Fig. 12. Capacity CDF for all data sets and all positions in the corridor-tocorridor scenario at Lund University.

Fig. 13. Capacity CDF for all data sets and all positions in the lobby-to-corridor scenario at Lund University.

with higher bandwidth, the WHY model will perform better with significant complexity reductions. During the Lund measurements, the measured bandwidth is 200 MHz which leads a higher delay resolution. As a result, the WHY model’s capacity estimation error is smaller in the scenarios at Lund University than that at Tsinghua. For example, in Lund corridor-to-office scenario, the averaging absolute capacity errors of the WEB, WHY and Kronecker models are 2.67%, 2.45%, and 7.89%, respectively. The WHY model’s performance approximately equal to the WEB model’s. At the same time, the WHY model requires much smaller computation and memory loads than the WEB model. D. Summary Above all, the performance of these models is related to the propagation environment. In general, the WEB model has the best performance but also the highest complexity. The WVP model decreases the computation load but it cannot describe the spatial channel properties as well as the WEP model. The WHY model can provide a tradeoff between the modeling complexity and accuracy. Once again, we mention that the selection

ZHANG et al.: A GENERAL COUPLING-BASED MODEL FRAMEWORK FOR WIDEBAND MIMO CHANNELS

of models should be decided by the simulation requirements on accuracy and complexity.

VII. CONCLUSION In this paper, we presented a general coupling-based model framework for wideband MIMO channels. We reviewed several narrowband analytical models, and introduced the CSI tensor expression and full-correlation model for the wideband MIMO channel. A general coupling-based framework was proposed by building the relationship between transmitter, receiver and frequency domains. Several models were established under this framework, including the wideband i.i.d. channel, the WKB model, the WEB model, the WVP model, and the WHY model. The WKB, WEB, and WVP models can be viewed as extensions of the corresponding narrowband models. The novel WHY model employed the steering matrix in the frequency domain and eigenbases in the transmitter and receiver domains. In order to evaluate the performance of these models, measurement campaigns were carried out in different indoor scenarios both at Tsinghua and Lund Universities. The joint DoA-DoD-delay power spectrum and capacity were selected as the evaluation metrics. Using data sets gathered in different scenarios, we compared the performance of different models. The results showed that the WEB model outperformed other models, but with the highest complexity. The WHY model was shown to provide a good tradeoff between the complexity and the performance.

REFERENCES [1] E. Telatar, “Capacity of multi-antenna Gaussian channels,” Eur. Trans. Telecommun., vol. 10, no. 6, pp. 585–595, Nov./Dec. 1999. [2] P. Almers, E. Bonek, and A. Burr et al., “Survey of channel and radio propagation models for wireless MIMO systems,” EURASIP J. Wireless Commun. Netw., vol. 2007, 2007, 10.1155/2007/19070, Article ID 19070. [3] K. Yu and B. Ottersten, “Models for MIMO propagation channels—A review,” Wireless Commun. Mobile Comput., vol. 2, no. 7, pp. 1211–1226, Nov. 2002. [4] H. Özcelik, “Indoor MIMO channel models,” Ph.D. dissertation, Institut für Nachrichtentechnik und Hochfrequenztechnik, Technische Universität Wien, Vienna, Austria, Dec. 2004 [Online]. Available: http://www.nt.tuwien.ac.at/mobile/theses [5] P. Petrus, J. H. Reed, and T. S. Rappaport, “Geometrical-based statistical mocrocell channel model for mobile environment,” IIEEE Trans. Commun., vol. 50, no. 3, pp. 495–502, Mar. 2002. [6] T. Zwick, C. Fischer, and W. Wiesbeck, “A stochastic multipath channel model including path directions for indoor environments,” IEEE J. Sel. Areas Commun., vol. 20, no. 6, pp. 1178–1192, Aug. 2002. [7] A. A. M. Saleh and R. R. Valenzuela, “A statistical model for indoor multipath propagation,” IEEE J. Sel. Areas Commun., vol. 52, no. 1, pp. 128–137, Feb. 1987. [8] J. P. Kermoal, L. Schumacher, K. I. Pedersen, and P. E. Mogensen, “A stochastic MIMO radio channel model with experimental validation,” IEEE J. Sel. Areas Commun., vol. 20, pp. 1211–1226, Aug. 2002. [9] W. Weichselberger, M. Herdin, H. Özcelik, and E. Bonek, “A stochastic MIMO channel model with joint correlation of both link ends,” IEEE Trans. Wireless Commun., vol. 5, pp. 90–100, Jan. 2006. [10] W. Weichselberger, “Spatial structure of multiple antenna radio channels,” Ph.D. dissertation, Vienna Univ. of Technology, Vienna, Austria, 2003 [Online]. Available: http://www.nt.tuwien.ac.at/mobile/theses

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[11] A. M. Sayeed, “Deconstructing multiantenna fading channels,” IEEE Trans. Signal Process., vol. 50, pp. 2563–2579, Oct. 2002. [12] A. Burr, “Capacity bounds and estimates for the finite scatterers MIMO wireless channels,” IEEE J. Sel. Areas Commun., vol. 21, no. 5, pp. 812–818, Jun. 2003. [13] A. Sibile, “Keyholes and MIMO channel modeling,” Tech. Rep. COST 273 TD (01) 017, Bologna, Italy, 2001 [Online]. Available: http://www. ensta-paristech.fr/~sibille/TD(01)017.pdf [14] M. Debbah and R. R. Müller, “MIMO channel modeling and the principle of maximum entropy,” IEEE Trans. Inf. Theory, vol. 51, no. 5, pp. 1667–1690, May 2005. [15] A. M. Tulino, A. Lozano, and S. Verdü, “Impact of antenna correlation on the capacity of the multiantenna channels,” IEEE Trans. Inf. Theory, vol. 51, no. 7, pp. 2491–2509, Jul. 2005. [16] K. Yu, M. Bengtsson, B. Ottersten, D. McNamara, and P. Karlsson, “Modeling of wideband MIMO radio channels based on NLoS indoor measurements,” IEEE Trans. Veh. Technol., vol. 50, pp. 655–665, Jul. 2002. [17] N. Costa and S. Haykin, “A novel wideband MIMO channel model and experimental validation,” IEEE Trans. Antennas Propag., vol. 56, pp. 550–562, Feb. 2008. [18] Y. Zhang, X. W. Hu, Y. Z. Jia, S. D. Zhou, X. Chen, and J. Wang, “A novel coupling-based model for wideband MIMO channel,” in Proc. IEEE Globalcom, Nov. 2009, pp. 1–6. [19] M. Milojevic, G. Del Galdo, and M. Haardt, “Tensor-based framework for the prediction of frequency-selective time-variant MIMO channels,” in Proc. IEEE Int. ITG Workshop Smart Antennas, Feb. 2008, pp. 147–152. [20] M. Weis, G. Del Galdo, and M. Haardt, “A correlation tensor Cbased model for time variant frequency selective MIMO channels,” in Proc. IEEE Int. ITG Workshop Smart Antennas, Feb. 2008, pp. 147–152. [21] Y. H. Rui, Y. Zhang, S. J. Liu, and S. D. Zhou, “3.52-GHz MIMO radio channel sounder,” in Proc. IEEE Int. Conf. Commun., Circuits, Syst. (ICCCAS), May 2008, pp. 79–83. [22] S. Wyne, A. F. Molisch, P. Almers, G. Eriksson, J. Karedal, and F. Tufvesson, “Outdoor-to-indoor office MIMO measurements and analysis at 5.2 GHz,” IEEE Trans. Veh. Technol., vol. 57, no. 3, pp. 1374–1386, May 2008. [23] IST-WINNER II Deliverable D1.1.2, WINNER II Channel Models, Sep. 2007 [Online]. Available: https://www.ist-winner.org/deliverables.html [24] P. Almers, F. Tufvesson, and A. F. Molisch, “Keyhole effect in MIMO wireless channels: Measurement and theory,” IEEE Trans. Wireless Commun., vol. 5, no. 12, pp. 3596–3604, Dec. 2006. [25] G. Matz, “Characterization and analysis of doubly dispersive MIMO channels,” in Proc. 40th Asilomar Conf. Signals, Syst., Comput., Pacific Grove, CA, Oct. 2006, p. 946C950. [26] T. T. Georgiou, “Distances and Riemannian metrics for spectral density functions,” IEEE Trans. Signal Process., vol. 55, no. 8, pp. 3995–4003, Aug. 2007. [27] L. Bernadö, T. Zemen, A. Paier, G. Matz, J. Karedal, N. Czink, C. Dumard, F. Tufvesson, M. Hagenauer, A. F. Molisch, and C. F. Mecklenbräuker, “Non-WSSUS vehicular channel characterization in highway and urban scenarios at 5.2 GHz using the local scattering function,” in Proc. Int. ITG Workshop Smart Antennas, Darmstadt, Germany, Feb. 2008, pp. 9–15.

Yan Zhang (S’06–M’10) received the B.E. degree in information engineering from the Beijing Institute of Technology, Beijing, China, in 2005 and the Ph.D. degree in communication and information systems from Tsinghua University, China, in 2010. He is currently an Assistant Researcher in the State Key Laboratory on Microwave and Digital Communications, Department of Electronic Engineering, Tsinghua University, Beijing, China. His research interests include the areas of wireless communications and channel modeling.

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Ove Edfors (S’92–A’96–M’00) was born in Örnsköldsvik, Sweden, in 1966. He received the M.Sc. degree in computer science and electrical engineering and the Ph.D. degree in signal processing, both from the Luleå University of Technology, Sweden, in 1990 and 1996, respectively. In spring 1997, he worked as a Researcher at the Division of Signal Processing at the same university, and in July 1997, he joined the staff at the Department of Electrical and Information Technology, Lund University, Sweden, where he is currently a Professor of radio systems. His research interests include radio systems, statistical signal processing, and low-complexity algorithms with applications in telecommunication.

Peter Hammarberg (S’07–M’11) received the M.S. degree in engineering physics from Uppsala University, Sweden, in 2005 . He is currently working towards the Ph.D. degree at the Department of Electrical and Information Technology, Lund University, Sweden. His research interests include channel estimation and receiver algorithm design, mainly for MIMO-OFDM systems.

Tommy Hult (M’11) received the M.Sc. degree in electrical engineering with emphasize on telecommunication and the Ph.D. degree, both from Blekinge Institute of Technology, Sweden, in 2002 and 2008, respectively. Since 2009, he has been working as a Research Fellow attached to the communications group of the Department of Electrical and Information Technology at Lund University, Sweden. His research interests are in space-time processing (especially MIMO), radio channel modeling, radio channel measurement, and radio wave propagation.

Xiang Chen (M’08) was born in Hunan, China, on March 24, 1980. He received the B.E. and Ph.D. degrees, both from the Department of Electronic Engineering, Tsinghua University, Beijing, China, in 2002 and 2008, respectively. He is currently an Assistant Researcher in the Wireless and Mobile Communication Technology R&D Center, Research Institute of Information Technology, Tsinghua University, Beijing, China. His research interests include statistical signal processing, digital signal processing, and wireless communications.

Shidong Zhou (M’98) received the B.S. and M.S. degrees in wireless communications from Southeast University, Nanjing, China, in 1991 and 1994, respectively, and the Ph.D. degree in communication and information systems from Tsinghua University, Beijing, China, in 1998. He is currently a Professor at Tsinghua University. From 1999 to 2001, he was in charge of several projects in China 3G Mobile Communication R&D Project. He is now a member of the China FuTURE Project. His research interests are in the area of wireless and mobile communications.

Limin Xiao (M’00) received the B.S. and M.S. degrees in wireless communication engineering from the Harbin Institute of Technology, Harbin, in 1992 and 1995, respectively, and the Ph.D. degree in communication and information systems from Tsinghua University, Beijing, China, in 2000. From 2000 to 2003, he was a Lecturer in the Department of Electronic Engineering at Tsinghua University, China, where he is currently a Vice-Researcher.

Jing Wang (M’99) received the B.S. and M.S. degrees in electronic engineering from Tsinghua University, Beijing, China, in 1983 and 1986, respectively. Since 1986, he has been on the faculty of Tsinghua University, Beijing, China, where he currently is a Professor and the Vice Dean of the Tsinghua National Laboratory for Information Science and Technology. His research interests are in the area of wireless digital communications, including modulation, channel coding, multi-user detection, and 2-D RAKE receivers.

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Multi-Link MIMO Channel Modeling Using Geometry-Based Approach Juho Poutanen, Fredrik Tufvesson, Senior Member, IEEE, Katsuyuki Haneda, Member, IEEE, Veli-Matti Kolmonen, and Pertti Vainikainen

Abstract—Geometry-based stochastic channel models (GSCMs) are extended to support multi-link simulations by applying the concept of common clusters. This novel approach aims to control the correlation between different links, inter-link correlation, by adjusting the amount of power simultaneously propagating via the same clusters in the different links. The behavior of common clusters is analyzed based on dual-link channel measurements, and a multi-link GSCM is developed based on common clusters. In addition, the effects that the common clusters have on inter-link correlation and on sum rate capacity are investigated based on simulations. Finally, comparison between simulations and measurements is done in order to indicate the validity of the proposed multi-link GSCM. Index Terms—Geometry-based channel modeling, multi-link channel modeling, multi user MIMO, radio channel modeling.

I. INTRODUCTION

G

EOMETRY-BASED stochastic channel models (GSCMs) have attained much attention in MIMO channel modeling during the past decade. This is due to their inherent capability of modeling spatial and temporal correlation properties in a straightforward manner. The basic idea behind the GSCMs is to emulate the double-directional radio channel by placing clusters in the simulation environment to act as physical scattering objects. The clusters consist of groups of closely located multipath propagation components (MPCs), and the directions, delays, and complex amplitudes of each MPC are directly computed based on the geometry of the simulation environment. Examples of GSCMs, which all rely on the cluster approach, are the COST 259 [1], COST 273 [2], and WINNER [3] channel models.

Manuscript received May 27, 2010; revised September 13, 2010; accepted October 09, 2010. Date of publication March 03, 2011; date of current version February 03, 2012. This paper has been written within the framework of WILATI+ which is a joint project between three Scandinavian universities and a part of the NORDITE research program funded by the Finnish, Swedish and Norwegian national research institutes Tekes, Vinnova and RCN, respectively. The work was supported in part by the Jenny and Antti Wihuri Foundation and the post-doctoral research project of the Academy of Finland, Helsinki, Finland. J. Poutanen, K. Haneda, V.-M. Kolmonen, and P. Vainikainen are with the Department of Radio Science and Engineering, Aalto University School of Science and Technology, FI-00076 Aalto, Finland (e-mail: [email protected]). F. Tufvesson is with the Department of Electrical and Information Technology, Lund University, SE-221 00 Lund, Sweden. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2122296

A. Motivation Even though the state-of-the art GSCMs are extremely sophisticated, the capability of the current implementations to simulate multi-link scenarios has up to now remained an open question. In principle, the cluster-based structure of the GSCMs supports multi-link simulations just by dropping multiple mobile stations (MSs) and/or base stations (BSs) into the environment. However, the major open question has so far been how to control the correlation between different links, the inter-link correlation. Since clusters are generated randomly and independently for each link, there is no guarantee that the different links result in having proper correlation with respect to each other. Based on previously reported work, however, it has been realized that different links may encounter remarkable inter-link correlation when the units are in close proximity to each other [4], but also when they are largely separated in distance [5]–[8]. Two links may also have very different inter-link correlation even if they are in the same environment (e.g., in the same room) [9]. Those experimental findings indicate a true need for multilink MIMO channel models being able to reflect those properties. Furthermore, since the trend in novel radio communication systems is going more and more towards applications that utilize links between multiple nodes in the network for their operation, the need for realistic multi-link channel model increases accordingly. Examples of such systems where it would be very beneficial to have realistic multi-link channel models include cooperative communication systems, and indoor localization applications. Underestimating or neglecting the inter-link correlation would usually lead to too optimistic performance results in system simulations [4]. To the authors’ best knowledge, previous works on multilink MIMO channel modeling are restricted to the analytical dual-link model proposed in [10]; no contributions on multi-link GSCMs are available in the open literature. B. Contributions In this paper we propose an approach for extending a general GSCM to fully support multi-link simulations by applying the concept of common clusters (CCs). In short, the idea behind the proposed method is to control the correlation between different links by allowing a certain proportion of the energy in different links to propagate through the same clusters. The idea to use CCs as a means to develop a multi-link GSCM is based on observations made in measurements that significant amounts of energy can indeed propagate through the same scatterers in different MIMO links in certain types of environments [6].

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At first, CCs are analyzed based on measured dual-link MIMO data. Then, to reflect the characteristics of the measured dual-link channels, a multi-link GSCM is implemented based on the concept of CCs. The implemented simulation model is used to study the effect of the CCs on channel characteristics and system performance from two perspectives: first, it is shown that CCs are a suitable way of adjusting the correlation between different links, and, second, the effect of the CCs on channel capacity is investigated. It is also shown that the developed multi-link GSCM is able to accurately predict the channel behavior in comparison with the measurement data. Even though the GSCM developed in this paper is rather simple, the modeling concepts are fully applicable to more sophisticated GSCM implementations (such as [1]–[3]), as well and it should be straightforward to extend those models to handle the multi-link scenario. C. Organization The remainder of the paper is organized as follows. In Section II, CCs are extracted from dual-link channel measurement data. In Section III, the modeling philosophy of the multi-link GSCMs is discussed, followed by a detailed description of the model implemented in this work. Section IV is dedicated to the analyses of the effect of the CCs on inter-link correlation and dual-link capacity based on simulations. In Section V, the relationships between the significance of common clusters, inter-link correlation, and sum rate capacity are studied based on measurement data. A comparison between the developed model and measurement data in made in terms of the dual-link channel capacity also in Section V. Finally, Section VI concludes the work. II. COMMON CLUSTERS IN MEASURED CHANNELS For the development of multi-link GSCMs, it is essential to understand the physical phenomena that increase correlation between different links. One of these phenomena is scatterers, or clusters, that are common for two or more links. Hence, it is vital to investigate how frequently the common clusters occur in real multi-link propagation scenarios. To this end, we investigate CCs based on dual-link channel measurements done in an office corridor environment. First, the methodology to extract CCs from measurement data is presented after which experimental results on will be provided. A. Extraction of Common Clusters From Measurement Data 1) Data Analysis: Physical scattering objects can be identified from the measurement data by combining the measured radio propagation path parameter estimates with the geometry information of a measurement environment. In this work, the parameter estimates have been obtained by the extended Kalman filter (EKF) [11]. Each MPC of the EKF parameter estimates includes the DoD, DoA, delay, and polarimetric path weights. Furthermore, each propagation path obtained by the EKF has a lifetime over a certain number of consecutive measurement samples, i.e., snapshots. In order to identify the physical scatterers for each MPC, the EKF estimates of the DoD, DoA and delay are used as inputs

Fig. 1. Extraction of common cluster from measurement data. The distance between the scattering points of different links and the angular separation of the scattering points seen from the MS determine if the cluster is considered as common.

for a measurement-based ray tracer [12]. This ray tracer implements an algorithm that plots rays on top of a floor plan of the environment according to the measured parameter estimates. It enables the MPCs to be explicitly mapped to physical scatterers in the environment. The identification of the scattering objects can be performed simultaneously for multiple links, making it possible to study if the same physical scatterer is common for the different links, and thus forms a CC. 2) Definition of a Common Cluster: In situations where the scatterer has a relatively large physical size, it is not always meaningful to consider the whole scatterer as common for different links. In such cases, even if the scattering source is the same physical object (e.g., a wall), the scattering points for different links might be separated by a large distance, and thereby an MS or BS equipped with antenna arrays may be able to resolve the scattering points in the angular domain. On the other hand, scattering points for the different links can be resolvable even if the distance between them is small in a case where the scattering object is very close to the antenna. Therefore, it is necessary to establish conditions defining CCs based on 1) the distance between the scatterers of different links , and 2) the angular separation of the scatterers seen from the MS , as shown in Fig. 1. It should be noted that multiple MPCs might be originating from the same physical scatterer at the same time instant thus forming a cluster. In such cases, the distance between the scatterers of the different links is calculated based on the cluster center; the coordinates of the cluster center are calculated as the power-weighted mean over the coordinates of the scattering points of the individual MPCs belonging to the same cluster. In Fig. 1, the small black dots correspond to the scattering points of individual MPCs and the blue and red dots are the cluster centers in different links. In this work, threshold values for the and are selected to be 5 meters and 45 degrees, respectively. The significance of common clusters quantifies the amount of power that propagates through the CC. The

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is determined from the measurement data in the following way. In a dual-link case, the significance of the th CC is denoted as a function of a measurement time instant by (1) where is the significance of the th common scatterer with respect to the total power of the th link as

(2) where . If the total number of scatterers that are common for the different links is denoted by , the total can be expressed by the sum of the significances of the individual CCs by

(3)

B. Significance of Common Clusters in an Office Corridor Scenario 1) Measurement Setup: The analyzed measurement was carried out in the corridor of the Department of Radio Science and Engineering in Aalto University by using a dual-link channel sounding system consisting of two channel sounders from Aalto University School of Science and Technology (Aalto) and Lund University (LU) operating at the frequency of 5.3 GHz [13]. The system is capable of simultaneously measuring two links having the MIMO matrix sizes of 30 30 and 30 32. A sample of a full MIMO matrix, i.e., snapshot, is measured every 39.32 ms, enabling measurements in dynamic environments. The measurements involved dual-polarization, but in the present analysis the polarizations have not been treated separately but they are summed up. In the measurement, the TX (from LU) was moved along a continuous route acting as a MS, such as a smart phone, whereas the two RXs (from LU and Aalto) were located at fixed positions to emulate WLAN BSs of neighboring cells. The floor plan of the measurement venue is shown in Fig. 2. 2) Results: The main propagation mechanism in the considered scenario is the waveguiding along the corridors in both links. In addition, DoDs pointing towards walls B and C are commonly seen on the MS side in both links. Interestingly, a noticeable share of energy propagates directly through wall B and the coffee room in the MS-BS1 link; this is possible since wall B and the right wall in the coffee room are outdoor walls having many windows meaning that the signal can penetrate the building through windows or window frames. In order to investigate in this scenario, the first scattering point seen from the MS on wall A was calculated and used to check the conditions for the CC. In addition, the points on wall B where the signal either propagates through the wall (MS-BS1 link) or reflects from it (MS-BS2 link) can be identified. In this scenario, other scatterers did not fulfill the criteria of the CC. Even if waves reflected from wall C are also seen

Fig. 2. The floor plan of the measurement environment in the considered scenario.

in parts of the measurement route, this propagation mechanism was not active in both links simultaneously, and thus was not identified as a common scatterer. The angular separation of the scattering points on wall A and B are plotted in Fig. 3(a). In the case of wall A, the angular separation is around 10 degrees in the beginning of the route, but after snapshot 200 it starts to increase; at this location the MS passes the corner of wall C and the scattering points in the MS-BS2 link start to move further south. The threshold value is exceeded approximately at snapshot 220. In the case of wall B, the angular separation of the scattering points varies more rapidly than in the case of wall A. Furthermore, wall B is an active common scatterer only in parts of the route. The distance between the scattering points on both walls A and B (Fig. 3(b)) follow the same trends as the angular separation. Also in this case, the threshold value is exceeded in the end of the measurement route. Fig. 3(c) shows separately for scatterers A (blue curve) and B (red curve) and the total (black curve). It is seen that the waveguiding along the corridor (A) is a significant propagation mechanism in both links, hence constituting a significant CC. Also wall B forms a CC in parts of the route. The total varies between 40% and 95%, but goes rapidly to zero around snapshot 220 due to the fact that the threshold values for the conditions of CC are exceeded. III. MULTI-LINK GEOMETRY-BASED CHANNEL MODELING When extending the current GSCMs to cover multi-link scenarios there are two main aspects to consider: 1) The singe-link behavior should remain the same, while at the same time 2) the correlation between links, i.e., interlink correlation, should be represented in a realistic way. In this section, a concept for extending the current GSCMs to support multi-link simulations is presented. First, the concept of common clusters, the proposed methodology in which the correlation between links in GSCMs can be controlled, is explained. Then, the implementation of the multi-link GSCM used in this paper is detailed. Finally, relationships between the multi-link GSCM implemented in this paper and the other existing GSMCs is briefly discussed.

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Fig. 4. Example of a common cluster (CC) in a scenario with one MS and two BSs. The correlation between different links can be controlled by changing the amount of power that propagates through the CC.

controlled by the cluster distributions and remains unchanged. The approach is based on the observations made above and in [6], that CCs can carry significant parts of the energy in realistic multi-link environments. B. Multi-Link GSCM Development In the proposed multi-link GSCM, clusters are generated so that each link is assigned with a set of uncommon clusters (UCCs) and a certain number of CCs. The UCCs are generated separately for each link and they contribute only to the impulse response of the designated link, whereas CCs are shared by the different links and contribute to both impulse responses, see Fig. 4. In order to control the correlation between different links, the amount of power that propagates through the CC is set to a desired value by the following procedure. First, the propagation path parameters, including the direction of departure (DoD) and direction of arrival (DoA), delay, and complex amplitude, are calculated for each MPC according to the geometrical locations of the antennas and clusters. Then, the power carried by the UCCs is scaled with a factor of so that the condition (4) Fig. 3. (a) The angular separation of the scattering points belonging to the different links seen from the MS. (b) The distance between the scattering points of different links. (c) The significance of common clusters as a function of the measurement location in snapshots.

A. Common Clusters in Geometry-Based Models A common cluster is a cluster that contributes to the channel between different links at the same time, as shown in Fig. 4. Since the amount of power carried by the CCs can be set to a desired value, it is possible to control the inter-link correlation between different links; the larger is the amount of power that is propagating via the CCs, the stronger is the correlation between the different links. The intra-link correlation, i.e., the correlation between antenna elements in a MIMO link, is as before

is satisfied. In (4), i.e., the significance of common cluster, defines the ratio between powers carried by the CCs and UCCs; and are the sum of powers carried by all the CCs and UCCs, respectively. Once the propagation path parameters with the desired have been obtained, the MIMO channel matrices are calculated for each link in the same way as for a conventional GSCM as

(5) where is the number of MPCs, is the amplitude of the th MPC, is the used radio frequency, is the propagation

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delay of the th MPC, and denotes the matrix transpose operation. Furthermore, and are the array response vectors calculated at the transmitter (TX) or receiver (RX) as

(6) where is the wave number, is the unit directional vector consisting of the DoD and DoA of the th MPC, and is the position vector of the th antenna element in the array. The term represents the inner product between vectors and . Finally, a random phase is added to each MPC in order to increase the number of independent realizations of the channel matrices [14]. C. Relationship With Other GSCMs The model developed in this work is based on clusters that emulate physical scattering objects of real environments, in the same way as in conventional GSCMs, and the MIMO channel matrices are constructed as usual based on the propagation path parameters by using (5). Regarding the single-link properties, the implemented GSCM includes some simplifications with respect to the more comprehensive GSMCs, such as [1]–[3]; in particular, only single-bounce clusters are considered, and the concept of visibility regions is not included in the model meaning that the activity of clusters as a function of location is not regarded. Furthermore, the full model parameterization (including parameters such as angular and delay spreads, cluster shadow fading, etc.) based on measurement data has not yet been considered. The novelty of the GSCM of this work is that a part of the clusters are shared by different links, which makes it possible to control the inter-link correlation. Despite the above-mentioned simplifications, the developed GSCM can be used to investigate the capability of the proposed modeling approach to reflect the essential features of multi-link scenarios, especially the ability to control the inter-link correlation. Furthermore, the idea of CCs can be applied in any other GSCMs as well, and, in fact, the modeling approach developed in this work has also been applied in the multi-link extension of the COST 2100 channel model [15]. For a detailed description of the implementation principles of the multi-link extension of the COST 2100 channel model, the reader is directed to [15].

Fig. 5. Flow chart of the method to investigate the effect on common clusters on system performance based on simulations and measurement.

desired , as shown in (4). The channel matrices for the different links can then be calculated with the MPC parameters obtained from the geometry of the environment and with the desired by (5). Finally, the channel matrices can be applied to the following equations in order to study the inter-link correlation and sum rate capacity. In Fig. 5, the corresponding procedure for the measurement data is also shown; CMC and SRC are studied based on measurement data and compared with the simulation results in Section V.

A. Definitions 1) Inter-Link Correlation: The inter-link correlation was evaluated by calculating the correlation matrix collinearity (CMC, or “collinearity”) as [15]

(7) where

is the correlation matrix of the th link calculated as

IV. EFFECT OF COMMON CLUSTERS ON SYSTEM PERFORMANCE In this section, the effect of the common clusters, or more precisely , on system characteristics is studied in terms of 1) the inter-link correlation and 2) the sum rate dual-link MIMO capacity by using the multi-link GSCM described in Section III. Fig. 5 shows a flow chart of the procedure of how the effect of common clusters on CMC and SRC is evaluated. At first, the propagation parameters, i.e., the DoD, DoA, complex amplitude, and delay, are calculated based on the geometrical locations of the clusters, BSs, and MSs. After that, the power carried by the uncommon clusters is scaled in order to obtain the

(8) is the complex transpose of a matrix; In (7) and (8), is the number of independent channel realizations; is the number of transmit antennas; and denotes the Frobenius norm. The CMC describes how similar the subspaces of the correlation matrices of the different links are, ranging between zero (matrices are orthogonal to each other) and one (matrices are similar).

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2) Sum Rate Dual-Link Capacity: The capacity values were calculated in the following way. First, the received power for the th link was calculated as

sum rate dual-link capacity and the sum rate single-link capacity

:

(15) (9) is the number of independent channel realizations; where is the number of receive antennas; is the number of transmit antennas; is the channel matrix of the th link; and denotes the Frobenius norm. In order to calculate the capacity, the channel matrices were normalized as

In (15), sub-indices “1” and “2” stand for links 1 and 2, meaning that first link 1 was considered as the desired link and link 2 as the interfering link, and then vice versa. In the description below, SRC and “capacity” as well as CMC and “collinearity” will be used interchangeably to improve readability. B. Simulation Studies

(10) In the dual-link case, the received signal can be written as [17] (11) where and are the normalized channel matrices of the desired and interfering link, and and are the transmitted signal vectors, respectively, and is an uncorrelated complex Gaussian noise vector. Since the channel matrices and the noise variance are normalized, and represent the signal-to-noise ratio (SNR) and interference-to-noise ratio (INR). The capacity values were calculated as the ergodic capacity for different channel realizations as [17]

(12) where, again, sub-indices “des” and “int” stand for the “desired” and “interfering” links. In our case, we assume that there is no channel state information at the transmitter (i.e., the transmit signal covariance becomes an identity matrix) and a full knowledge of the channel at the receiver. Next, we study the capacity in two different cases, i.e., in the single-link case (i.e., without interference) and in the dual-link case (i.e., with interference). When calculating the capacity in the single-link case, i.e., , the covariance matrix in (12) was set to (13) and when calculating the capacity in the dual-link case, i.e., , the covariance matrix was set to

(14) In the following, we analyze the relative sum rate capacity (SRC, or “capacity”), which is denoted by the ratio between the

The effect of the CCs on inter-link correlation and sum rate dual-link capacity was investigated by computer simulations in three different scenarios. In the first scenario, the locations of the clusters were changed in a controlled manner in order to study the relationships between , CMC and SRC and the influence of the environment through a simple example. In the simulations of these controlled channels the environment consisted of one UCC (per link) and one CC (shared by the different links). Next, the simulation studies were continued by placing the clusters in random locations. First, the random channels consisted of one UCC and one CC, and, after that, of five UCCs and one CC, all being randomly positioned. In each of the three scenarios, one MS and two BSs were located at fixed positions. The clusters consisted of five MPCs placed randomly within a diameter of one meter around the center point of the cluster. Furthermore, a 4-element x-oriented uniform linear antenna array (ULA) was used at the MS and BSs in each case. The and were both fixed to 10 dB in all the simulations. In the following, the presented CMC and SRC values are the average values over 100 independent channel realizations. Table I summarizes the three different simulation scenarios. As a general conclusion of the simulation studies, it can be said that has a significant effect on both the inter-link correlation and MIMO channel capacity; as increases, the CMC increases and SRC decreases. This indicates the ability of the multi-link GSCM based on CCs to manipulate the correlation between different links. It also shows that it is important not to neglect the effect of common clusters. Next, the findings from the simulation studies are discussed in detail separately for the controlled and random scenarios. 1) Controlled Channels: In the controlled scenario, clusters were located so that the CC and the UCC for the link MS-BS2 (UCC2) were at fixed positions whereas the UCC for the link MS-BS1 (UCC1) was moved on a circle with 45 degree steps around the MS, as shown in Fig. 6(a). The simulations with the different locations of UCC1 are marked with numbers 0–7 in Fig. 6(a). At each location of the UCC1, the CMC and SRC were simulated with ranging between 0% and 100%. Figs. 6(b) and (c) show the collinearity and capacity as a function of for the different locations of the UCC1. It is seen that the capacity is very high at low values of in most of the locations of the UCC1, and gradually decreases to approximately 10% of its original value as approaches

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TABLE I SIMULATION SCENARIOS

THE

100%. The collinearity behaves in the opposite way, i.e., whenever the capacity is high, the collinearity is low, and vice versa. However, at UCC1 locations 3 and 5 the capacity is low, and the collinearity almost one, with all values of . At UCC1 location 5, both UCCs are located exactly at the same position, meaning that the situation is equivalent to the case where all the clusters are common among the different links. At UCC1 location 3, there is a high correlation between the different links since the MS cannot distinguish the waves coming from locations 3 and 5 due to its antenna array orientation. 2) Random Channels: As shown above, the locations of the clusters may have a significant impact on the correlation and capacity values observed at different values of . In particular, it can be observed that with some combinations of the cluster locations collinearity is high and capacity is low even without the CC. In order to investigate the relationships between , collinearity, capacity, and cluster locations in a statistical manner, the simulation studies were continued by placing the clusters in random locations. The CDFs of the collinearity and capacity are shown for the first random scenario (one UCC, one CC) for the values of 0, 1, 10, 50, 90, 99, and 100% in Fig. 7(a) and (b). For each value of , the CDF curve includes the values of the collinearity and capacity from 1000 random channels. With the values of 0, 1, and 10%, the matrix collinearity behaves quite similarly and is less than 0.2 in approximately 60% of the cases. Even if for the most of the time the collinearity is low and capacity high with low values of , also highly correlated channels are observed: the collinearity is at least 0.8 in about 15% of the cases even without the CC. With the values of 0, 1, and 10%, the capacity gets high values for the most of time, as could be expected. It was also found that capacity is more sensitive than the collinearity to the change of in the range of 0 to 10%: for instance, at the CDF level of 0.5, the capacity decreased by approximately 25%-units when increased from 0 to 10%. This is an important observation in the sense that even if only a small amount of the power propagates through the common cluster, the impact on the system performance is significant compared to the case where common cluster is not considered at all. When is 50%, both the collinearity and capacity are almost uniformly distributed between the minimum and maximum values. With the values of 90, 99, and 100%,

we can see that the collinearity is very close to 1 the whole time. However, variations between the respective capacity curves are more clearly seen. The CDFs of the collinearity and capacity are shown for the second random scenario (5 UCCs, 1 CC) for the values of 0, 1, 10, 50, 90, 99, and 100% in Fig. 7(c) and (d). Again, the CDF curves include the values of the collinearity and capacity from 1000 random channels for each value of . In comparison with the first random scenario (1 UCC, 1 CC), the following observations can be made. First, with low values of (0, 1, and 10%), the collinearity is generally higher and therefore capacity lower; the same trends hold when is 50%. This can be explained by the fact that as the number of clusters increases, it is harder for the antenna array at the MS to separate them, and hence, the correlation between links is likely to increase. Obviously, with larger antenna arrays, this effect would be less significant due to better capability of spatial filtering. With high values of (90, 99, and 100%), the curves are very similar to the first random scenario, as could be expected, since anyway almost all the power propagates through the common cluster. V. COMPARISON BETWEEN MEASUREMENTS SIMULATIONS

AND

A. Capacity and Correlation in Measured Channels Fig. 8(a) shows the collinearity and capacity along the measurement route. The collinearity and capacity were calculated by applying the measured propagation path parameters obtained by the EKF to (5)–(15) and by using the same 4-element linear array as in the simulations of Section IV (see Fig. 5 for the flow chart of the procedure). Again, the collinearity and capacity were calculated as the mean over 100 independent realizations of the measured channels at each snapshot. Fig. 8(a) shows that the collinearity gets very high values in the beginning of the route but falls down to approximately 0.3 in the end of the route. The capacity behaves the opposite way, as was the case also in the simulation studies in Section IV. By comparing Figs. 8(a) and 3(c), we can clearly see that also in the measured channels, the inter-link correlation and sum rate capacity are strongly related to the significance of common clusters.

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Fig. 7. Effect of common cluster on collinearity and capacity simulated in the random scenarios. CDFs of the (a) collinearity and (b) capacity in the first random scenario (one UCC, one CC). (c) Collinearity and (d) capacity in the second random scenario (five UCCs, one CC). The CDFs include data from . 1000 random combinations of cluster locations with each value of the

Fig. 6. Effect of common cluster simulated in controlled channels. (a) Simulation environment. (b) The correlation matrix collinearity (CMC), and (c) the relative sum rate capacity (SRC) as a function of the significance of common cluster. The legends show the position of UCC1.

Fig. 8. (a) Collinearity (black curve) and capacity (red curve) as a function of the measurement location in snapshots. (b) Capacity in measurements and simulations. The CDFs of the capacity at snapshots 120 and 270 and of three independent simulation runs with corresponding significance of common cluster are shown. In the simulations, 2 UCCs (per link) and 2 CCs were generated in random locations.

B. Simulated vs. Measured Sum Rate Capacity Finally, in order to investigate the validity of the multi-link GSCM approach proposed in this paper, the simulations were compared with the measurements in terms of capacity. Two measurement locations were selected for the comparison. The first location was at snapshot 120, where the was as high as 85%, and the second at snapshot 270, where CCs did not exist anymore. In the simulation, two UCCs (per link)

and two CCs were randomly located around the simulation environment, whereas the BSs and the MS were at fixed positions. Fig. 8(b) shows the CDFs of the capacity over 100 channel realizations for the measurement (solid lines) and for three independent simulation runs (dashed and dotted lines). It is seen that the simulation can always predict the dual-link channel behavior very accurately in terms of the capacity when

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is 85%. When is 0%, the model predicts the behavior well for the most of the time; however, occasionally, due to random cluster locations, the correlation between links happens to be high in the simulation which results in underestimation of the capacity. VI. CONCLUSION In this paper, an approach to extend geometry-based stochastic channel models (GSCMs) to support multi-link simulations has been presented. The proposed approach is based on the concept of common clusters (CCs): the correlation between different MIMO links, i.e., the inter-link correlation, is controlled by adjusting the amount of power that simultaneously propagates via the same clusters in the different links. A multi-link GSCM was implemented, and the effects that the CCs have on inter-link correlation and on sum rate capacity were investigated based on simulations. The existence of CCs in real-world channels was confirmed by dual-link channel measurements in an office corridor scenario. The measurement results revealed that the significance of CCs can be as high as 95%. In both simulations and measurements, clear relations were found between the CC power, the inter-link correlation, and the sum rate dual-link capacity. Generally, as the amount of power carried by the CCs increases, the inter-link correlation increases and at the same time the sum rate capacity decreases. In addition, comparison between simulations and measurements in terms of the sum rate dual-link capacity revealed good agreement, indicating the validity of the proposed multi-link GSCM. The results of the paper indicate that the developed CC-based multi-link GSCM provides a suitable means for controlling the correlation between different MIMO links in a realistic manner. Furthermore, it is evidently vital to include CCs in GSCMs since neglecting them would lead to too optimistic performance results in system simulations. ACKNOWLEDGMENT The authors would like to thank Dr. P. Almers, Dr. T. Abrudan, Dr. A. Richter, and J. Koivunen for their help in measurements and data processing. Dr. J. Salmi is acknowledged for providing the codes for calculating the parameter estimates; Prof. A. Molisch for fruitful discussions on the modeling approach, and A. Palacios for his help in developing the channel model implementation.

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[5] J. Poutanen, K. Haneda, J. Salmi, V.-M. Kolmonen, and P. Vainikainen, “Analysis of correlated shadow fading in dual-link indoor radio wave propagation,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 1190–1193, 2009. [6] J. Poutanen, K. Haneda, J. Salmi, V.-M. Kolmonen, T. Hult, F. Tufvesson, and P. Vainikainen, “Significance of common scatterers in multi-link radio wave propagation,” in Proc. 4th Eur. Conf. on Antennas Propag. (EuCAP 2010), Barcelona, Spain, Apr. 2010, p. 1849081. [7] V.-M. Kolmonen, K. Haneda, T. Hult, J. Poutanen, F. Tufvesson, and P. Vainikainen, “Measurement-based evaluation of interlink correlation for indoor multi-user MIMO channels,” IEEE Antennas Wireless Propag. Lett., vol. 9, pp. 311–314, 2010. [8] V.-M. Kolmonen, K. Haneda, F. Tufvesson, J. Poutanen, and P. Vainikainen, “A dual-link capacity analysis of measured time-variant indoor channel,” Electron. Lett., 2010, Accepted for publication in. [9] N. Czink, B. Bandemer, G. Vazquez-Vilar, L. Jalloul, C. Oestges, and A. Paulraj, “Spatial separation of multi-user MIMO channels,” in Proc. IEEE 20th Int. Symp. on Personal, Indoor Mobile Radio Commun. (PIMRC 2009), Tokyo, Japan, Sep. 2009, pp. 1059–1063. [10] T. Hult, F. Tufvesson, V.-M. Kolmonen, J. Poutanen, and K. Haneda, “Analytical dual-link MIMO channel model using correlated correlation matrices,” presented at the 4th Eur. Conf. on Antennas Propag. (EuCAP 2010), Barcelona, Spain, Apr. 2010. [11] J. Salmi, A. Richter, and V. Koivunen, “Detection and tracking of MIMO propagation path parameters using state-space approach,” IEEE Trans. Signal Processing, vol. 57, no. 4, pp. 1538–1550, Apr. 2009. [12] J. Poutanen, K. Haneda, J. Salmi, V.-M. Kolmonen, A. Richter, P. Almers, and P. Vainikainen, “Development of measurement-based ray tracer for multi-link double directional propagation parameters,” in Proc. 3rd Eur. Conf. on Antennas Propag. (EuCAP 2009), Berlin, Germany, Mar. 2009, pp. 2622–2626. [13] V.-M. Kolmonen, P. Almers, J. Salmi, J. Koivunen, K. Haneda, A. Richter, F. Tufvesson, A. F. Molisch, and P. Vainikainen, “A dynamic dual-link wideband MIMO measurement system for 5.3 GHz,” IEEE Trans. Instrum. Meas., vol. 59, no. 4, pp. 873–883, Mar. 2010. [14] A. Molisch, M. Steinbauer, M. Toeltsch, E. Bonek, and R. Thoma, “Capacity of MIMO systems based on measured wireless channels,” IEEE J. Sele. Areas Commun., vol. 20, no. 3, pp. 561–569, Apr. 2002. [15] L. Liu, J. Poutanen, K. Haneda, P. Vainikainen, F. Tufvesson, and C. Oestges, “A multi-link extension of the COST 2100 MIMO channel model,” presented at the COST2100 11th Management Committee Meeting, Aalborg, Denmark, Jun. 2–4, 2010, TD(11)11012. [16] G. Golub and C. van Loan, Matrix Computations, 3rd ed. Baltimore, MD: The Johns Hopkins Univ. Press, 1996. [17] R. Blum, “MIMO capacity with interference,” IEEE J. Sel. Areas Commun., vol. 21, no. 5, pp. 793–801, 2003. Juho Poutanen was born in Helsinki, Finland, in 1983. He received the degree of Master of Science in technology and Licentiate of Science in technology from Aalto University School of Science and Technology, Helsinki, Finland, in 2007 and 2010, respectively, where he is currently working towards the Ph.D. degree. Since 2005, he has worked as a Research Assistant and Researcher in the Department of Radio Science and Engineering, Aalto University School of Science and Technology. His current research interests include radio channel characterization and modeling.

REFERENCES [1] A. F. Molisch, H. Asplund, R. Heddergott, M. Steinbauer, and T. Zwick, “The COST 259 directional channel model—Part I: Overview and methodology,” IEEE Trans. Wireless Commun., vol. 5, no. 12, Dec. 2006. [2] , L. M. Correia, Ed., Mobile Broadband Multimedia Networks—Techniques, Models Tools for 4G. Oxford, U.K.: Elsevier, 2006, p. 569. [3] WINNER II deliverable D1.1.2 V1.1, Online, WINNER Channel Models [Online]. Available: http://www.ist-winner.org/deliverables.html [4] F. Kaltenberger, D. Gesbert, R. Knopp, and M. Kontouris, “Correlation and capacity of measured multi-user MIMO channels,” in Proc. IEEE 19th Int. Symp. on Personal, Indoor Mobile Radio Commun. (PIMRC 2008), France, Sep. 2008, pp. 1–5, Cannes.

Fredrik Tufvesson (SM’10) was born in Lund, Sweden in 1970. He received the M.S. degree in electrical engineering in 1994, the Licentiate degree in 1998, and the Ph.D. degree in 2000, all from Lund University, Lund, Sweden. After almost two years at a startup company, Fiberless Society, he is now an Associate Professor of electrical and information technology. His main research interests are channel measurements and modeling for wireless communication, including channels for both MIMO and UWB systems. In addition, he also works with his company ResQU on wireless search and rescue equipment as well as research projects on OFDM and UWB system design.

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Katsuyuki Haneda (S’03–M’07) received the Doctor of Engineering degree from the Tokyo Institute of Technology, Tokyo, Japan, in 2007. He has been a Postdoctoral Researcher at the SMARAD Centre of Excellence, Aalto University (former Helsinki University of Technology), Espoo, Finland, since 2007. His current interests are radio wave propagation measurements and modeling, ultrawideband radio, and multiple-input multiple-output systems. Dr. Haneda is a member of the Institute of Electronic, Information and Communication Engineers (IEICE), Japan. He was the recipient of the Student Paper Award presented at the 7th International Symposium on Wireless Personal Multimedia Communications (WPMC’04).

Veli-Matti Kolmonen received the M.Sc. degree in technology from Helsinki University of Technology, Espoo, Finland, in 2004 and the D.Sc. degree in technology from Aalto University School of Science and Technology, Espoo, in 2010. Since 2003, he has been with the Department of Radio Science and Engineering, Aalto University School of Science and Technology, as a Research Assistant, Researcher, and currently as a Postdoctoral Researcher. His current research interests include radio channel measurements and modeling.

Pertti Vainikainen received the degree of Master of Science in technology, Licentiate of Science in technology and Doctor of Science in technology from Helsinki University of Technology (TKK), Espoo, Finland, in 1982, 1989 and 1991, respectively. From 1992 to 1993, he was Acting Professor of Radio Engineering, since 1993 Associate Professor of Radio Engineering and since 1998 Professor in Radio Engineering, all in the Radio Laboratory (since 2008 Department of Radio Science and Engineering) of TKK (since 2010 Aalto University). In 1993–97 he was the Director of the Institute of Radio Communications (IRC) of TKK, and a Visiting Professor in 2000 at Aalborg University, Denmark, and in 2006 at University of Nice in France. His main fields of interest are antennas and propagation in radio communications and industrial measurement applications of radio waves. He is the author or coauthor of six books or book chapters and about 350 refereed international journal or conference publications and the holder of 11 patents.

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Land Mobile Satellite Dual Polarized MIMO Channel Along Roadside Trees: Modeling and Performance Evaluation Michael Cheffena, Fernando Pérez Fontán, Frédéric Lacoste, Erwan Corbel, Henri-Jose Mametsa, and Guillaume Carrie

Abstract—We present a novel physical–statistical, generative model for the land mobile satellite (LMS), dual polarized, multiple-input-multiple-output (MIMO) channel along tree-sided roads. Said model is parameterized by means of a physical model based on the multiple scattering theory (MST) which accounts for the signal attenuation and scattering by trees. Moreover, finite-difference time-domain (FDTD) electromagnetic computations were performed to characterize the scattering pattern of an isolated tree, and to calculate the MIMO shadowing correlation matrix required by the model, and not provided by MST. This modeling framework also encompasses the single-input-multiple-output (SIMO)/space diversity case. To illustrate the capabilities of the developed model, time series were generated and used in system performance calculations. The obtained results give an insight into the advantages of dual polarized MIMO and SIMO/space diversity techniques in these very frequent scenarios and may help service providers in evaluating the technical feasibility of such systems. Index Terms—Diversity, LMS MIMO, signal fading, vegetation.

I. INTRODUCTION

T

HE true broadcast nature of satellite-based mobile communication systems offers great advantages for delivering multicast and broadcast services to both populated and isolated areas. However, due to the high path loss, limited satellite power, and other impairments, current land mobile satellite (LMS) systems show lower capacities and availabilities than those of terrestrial systems [1]. Their performance can be increased using multiple-input-multiple-output (MIMO) techniques. To design such systems, a good understanding of the propagation channel is required.

Manuscript received November 08, 2010; revised February 09, 2011; accepted July 02, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. This work is supported by the French Space Agency (CNES), French Aerospace Lab (ONERA) and Thales Alenia Space-France. M. Cheffena is with Gjøvik University College, N-2815 Gjøvik, Norway (e-mail: [email protected]). F. Pérez Fontán is with the University of Vigo, E-36200 Vigo, Spain (e-mail: [email protected]). F. Lacoste is with CNES, F-31401 Toulouse, France (e-mail: [email protected]). E. Corbel is with Thales Alenia Space—France, F-31037 Toulouse, France (e-mail: [email protected]). H.-J. Mametsa and G. Carrie are with ONERA, F-31055 Toulouse, France (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173447

Signal propagation in the LMS channel is affected by different propagation impairments, among which are signal attenuation and fading caused by vegetation. The signal attenuation due to vegetation depends on a range of factors such as tree type, whether the trees are in-leaf or out-of-leaf, whether the trees are dry or wet, the frequency band, the path length through foliage, etc. [2]. A single-input-single-output (SISO), roadside tree LMS channel model which takes into account the signal fading caused by position-dependent tree scattered fields and by swaying tree components due to wind was reported in [3] and [4]. Fade mitigation techniques (FMTs) such as MIMO might be used to counteract the signal fading caused by vegetation. Availability of realistic channel time series and detailed knowledge of their correlation properties are needed for performing accurate simulations [5]. Several studies on terrestrial MIMO systems can be found in the literature, while studies on LMS MIMO are rather limited, among them are [1] and [6]–[9]. In this paper, we present a novel physical–statistical, generative channel model for the roadside tree, LMS, dual-polarized MIMO channel, which includes as a special case the singleinput-multiple-output (SIMO) case. Fig. 1 shows the considered propagation scenario where a mobile terminal receives partially correlated co- and cross-polar, right- and left-hand circular polarized (R/LHCP) tree scattered fields from both sides of the road. The wanted model requires parameterization; this is achieved by means of a physical model based on the multiple scattering theory (MST) [10]–[12]. This technique is used to estimate the signal attenuation and scattering by a single tree. MST assumes a uniform distribution of scatterers in both azimuth [0, ) [3], [4], [13]. This assumption makes ) and elevation (0, it impossible to quantify spatial effects such as the cross-correlation of the shadowing affecting the direct signal reaching the receive antennas. To overcome this, finite-difference timedomain (FDTD) electromagnetic computations were performed to accurately calculate the MIMO shadowing correlation matrix. In addition, calculated tree scattering patterns are also shown, which coincide with results obtained using MST. To show the potential of the proposed physical–statistical, generative model, examples of performance evaluation for SISO, SIMO, and MIMO configurations were carried out using synthesized time series. The results give an insight into the advantages of polarization MIMO and SIMO/space diversity techniques and may be used in assessing the technical feasibility of LMS systems in roadside tree scenarios.

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Fig. 1. Propagation scenario for the LMS dual-polarized MIMO: a mobile terminal receives correlated co- and cross-polar (R/LHCP) tree attenuated and scattered fields from both sides of the road.

The paper begins in Section II by presenting the FDTD electromagnetic computation results. Section III discusses the basis of the proposed physical–statistical model which, in general, is oriented toward a MIMO configuration but also encompasses both the SISO and SIMO configurations. In this section, the MST-based SISO channel model used for parameterizing direct signal attenuation and multipath is briefly discussed. Then, we discuss the SIMO case. Finally, we go on to present the dual-polarized, physical–statistical, generative MIMO channel model. In Section IV, we present examples performance calculations using the synthetic time series. Such calculations include capacity and diversity studies. Finally, the conclusions are given in Section V. II. FDTD COMPUTATION FDTD is a numerical technique for solving electromagnetic problems where the computation space is divided into small cubic cells in which the time-domain fields are solved using an explicit finite-difference update scheme. Using FDTD, accurate solutions of the electromagnetic interaction with arbitrary-shaped objects can be obtained [14]. In this section, the attenuation and scattering characteristics of a tree are computed using an FDTD tool. The attenuation time series are further used to extract the correlation matrix of the shadowing effects in the LMS dual-polarized MIMO channel of interest. The input to FDTD is a three-dimensional cubically meshed tree model having a dielectric constant of 28 [13] and conductivity of 0.02 S/m [15]. The dimensions of the tree in the , and directions are 2.74, 2.64, and 3.17 m, respectively. The FDTD computation space and the tree model used are shown in Fig. 2. The computational volume is divided into a scattering field region and a total field region (which also includes the incident wave) by a virtual plane on which a plane wave is incident into the total field region. The whole region is surrounded by a perfectly matched layer (PML) implementing the absorbing boundary conditions needed to prevent false echoes from being produced at the boundaries of the computational volume. A cell size of 1 cm was utilized, which resulted in a highest usable frequency of 3 GHz. The number of cells in the , and directions were 373, 363, and 417, respectively, which resulted in a total of 56 461 383 cells.

Fig. 2. FDTD computation zones and boundary conditions. Cell size of 1 cm and total cells of 56 461 383 are used.

Two scenarios were investigated: the far-field scattering pattern and the total field in a straight line along the axis behind the tree (see the dashed line in Fig. 2). Two runs of the FDTD tool were performed, one with a vertical and the other with a horizontal polarized incident wave. These were then combined to yield circularly polarized signals. A Gaussian pulse was used as the source field. A near-to-far-field transformation was performed to calculate the far-field scattering pattern. Figs. 3 and 4 show the normalized far-field scattering pattern of the co- and cross-polar components of the RHCP and LHCP signals at 2 GHz, respectively. The results are obtained by rotating the observation point 360 around the tree as shown in Fig. 2, where 0 represents the line-of-sight (LOS) path between the satellite and the mobile terminal (through the tree). We can observe that the scattering patterns of the co-polar components have a forward lobe with an isotropic background, the same as with MST, as reported in [3] and [4], or the radiative energy transfer (RET), as reported in [16]. Fig. 5 shows the total received field along a straight line parallel to the axis behind the tree for the co- and cross-polar components of the RHCP and LHCP signals. The points at the start (before 0 m) and at the end of the straight line (after 2.64 m) are not blocked (LOS conditions) toward the source while the rest are shadowed by the tree (the tree is located between 0 to 2.64 m along axis). The fields along the straight line are passed through a running average filter (with ten point window size) for calculating the large-scale fading (shadowing) effects caused by the tree (see Fig. 6). As we move along the positive axis direction, we can observe from Fig. 6 the change of state due to tree shadowing, i.e., LOS-shadowing-LOS. Table I shows the MIMO shadowing (large scale fading) correlation matrix , calculated using the mentioned filtered FDTD series at 2 GHz. In Table I, R/R refers

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Fig. 3. Scattering patterns of the co- and cross-polar components of the RHCP signal at 2 GHz.

Fig. 5. Time series of the co- and cross-polar components of the RHCP and LHCP signal at 2 GHz.

Fig. 4. Scattering patterns of the co- and cross-polar components of the LHCP signal at 2 GHz.

Fig. 6. Shadowing time series of the co- and cross-polar components of the RHCP and LHCP signal at 2 GHz.

to the co-polar signal from an RHCP transmit antenna to an RHCP receive antenna, R/L refers to the cross-polar signal from an RHCP transmit antenna to an LHCP receive antenna, and so on. Note that the FDTD results presented in this section are only applicable when the tree is in leaf. There exist many very different tree configurations, and the shadowing cross-correlation may vary dramatically from tree to tree. This is an issue that requires further investigation, to be carried out at a later time, the main aim of this paper being the description of the physical–statistical model discussed next and how such a model can be parameterized. III. PHYSICAL–STATISTICAL, GENERATIVE ROADSIDE TREE LMS DUAL-POLARIZED MIMO CHANNEL MODEL Here, a family of physical–statistical, generative models for LMS roadside tree environments is presented, starting with the

TABLE I MIMO SHADOWING CORRELATION COEFFICIENTS OBTAINED FROM FDTD SIMULATIONS

SISO model and going on to present the SIMO and, finally, the MIMO models. Physical–statistical models are deemed more accurate than purely statistical ones as they take into account the geometry of the link(s), while they rely on physical (electromagnetic-based) methods for calculating the needed model parameters. The underlying assumption made in this family of models is that the received signal is composed of the direct component, which

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Fig. 7. Tree model for the LMS channel with randomly distributed and oriented leaves and branches. , , and are the orthonormal vectors of rectangular coordinate system.

may be subjected to shadowing and accompanied by so-called coherent component fluctuations, and the multipath component due to diffuse scattering, i.e., a Ricean channel. Thus, we implement a statistical random number generator fitting a Rice distribution whose parameters are changing as the terminal travels through a propagation environment described in terms of simple, canonical volumetric forms representing trees. Time variations are also taken into account, as mentioned earlier, especially for stationary terminals. The two Rice distribution parameters (direct signal amplitude and multipath power) are calculated using MST: the direct signal is affected by the specific attenuation of the tree canopy provided by MST once the geometrical path through the canopy is worked out for the different terminal route positions. The second component, the multipath power, is also parameterized by means of MST, which provides the average coherent and incoherent scattered powers; these are mapped to the relevant Rice distribution parameter, also taking into account the possible paths through and off the tree canopies on both sides of the street. At least two alternatives are possible for generating locally Ricean time series: one is using a point-scatterer approach (used in the current SISO and SIMO implementations), and the other is by filtering a complex random Gaussian series. The latter option has been selected for implementing the MIMO channel. A. LMS SISO Channel Model A SISO model/simulator was reported by the authors in [3] and [4]. The model uses MST as described in [10]–[13] with modifications to account for slant paths and circular polarization. In the model, the tree canopy is modeled as a vertically oriented cylindrical volume in a rectangular coordinate system defined by the orthonormal vectors , , and . The canopy volume contains randomly distributed and oriented leaves and branches. Leaves are modeled as thin lossy dielectric disks, branches as finite lossy dielectric cylinders, and the trunk as a finite lossy dielectric cylinder (see Fig. 7).

The SISO model generates the position-dependent signal fading by calculating the total coherent (the sum of coherently scattered and free-space field) and incoherent tree scattered fields. The phase variations in the scattered signal are accounted for using a point-scatterer approach, where the contribution from each tree is assumed to originate from a point in the center of the canopy from which the distance-dependent phase variations for the various route sampling points are calculated. In addition, the signal fading due to wind swaying is accounted for by modeling the tree components as masses attached to springs. The position-dependent fading and the signal fading due to tree swaying are then combined to give the overall signal fading caused by vegetation. The model is applicable for different polarizations and elevation angles and was validated in terms of first- and second-order statistics using measurements at 2 GHz (see [3] and [4] for more details). B. SIMO Receiver Space Diversity The previously described SISO channel model can easily be extended to the SIMO/space diversity case. The model is again based on the physical–statistical tree model (see Fig. 7) reported in [3] and [4] and MST. The considered propagation scenario is shown in Fig. 8: two antennas with the same polarization separated by a given distance are receiving tree attenuated and scattered co-polar signals from each side of the road. The fades at are generated by taking into aceach antenna element count the tree scattered fields from each side of the road as well as the LOS field, given by

(1) (2) (3) and are the number of trees on each side of the where road, is the total number of scatterers in a single tree, and is the wavenumber. Note here how the overall scattered signal from one single tree has now been split into components, provided that the link budget of the scattered power and the MST constraints are preserved. This shows a possible way toward a wideband model. Parameters and are the amplitudes of the incoherent scattered components from side one (satellite side) and side two (opposite side) of the road, respectively. Parameters and are the amplitudes of the coherent scattered field (side one) and the LOS field, respectively. The coherent and incoherent scattered fields can be estimated from the physical–statistical tree model reported in [3] and [4]. Parameters and are the initial phase and path length of each signal component, respectively. The coherent and incoherent scattered fields as well as the LOS field are received from one side of the road (see (1)), while only the incoherent scattered

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Fig. 8. Roadside tree LMS, SIMO/space diversity propagation scenario: two antennas with the same polarization separated by a given distance are receiving the tree attenuated and scattered co-polar signal from both sides of the road.

fields are received from the other side of the road (see (2)). These are combined to produce the signal received at each antenna position (see (3) and Fig. 8). The resulting simulated correlation coefficient versus antenna separation distance for the small scale fading (absolute values) is shown in Fig. 9 (for two co-polar RHCP antennas). As expected, we can observe that the correlation coefficient decreases with increasing antenna separation distance. The resulting simulated correlation coefficient was also fitted to the square of the zero-order Bessel function of the first kind, , where is the relative separation distance, and is the wavelength (see the dashed line in Fig. 9). It can be seen that the fit between the two curves is quite good. Thus, a model based on the zeroth-order Bessel function of the first kind could be used to model the correlation coefficient of the small scale fading in the roadside tree LMS SIMO/space diversity channel. Fig. 10 shows examples of the simulated received signal time series on the two antennas (RHCP co-polar antennas) for a separation distance of one wavelength. It can be seen that the time series have similar large-scale fading characteristics but relatively decorrelated small-scale fading due to the separation distance between the two antennas.

Fig. 9. Small-scale fading (absolute values) correlation coefficient versus antenna separation distance (for two co-polar RHCP antennas) for the simulated roadside tree LMS SIMO/space diversity (solid line) channel. Also shown is the theoretical curve of the square of the zeroth-order Bessel function of the first kind (dashed line).

Fig. 10. LMS SIMO receiver space diversity links at antenna separation distance of one wavelength (for two co-polar RHCP antennas).

C. LMS Dual-Polarized MIMO Channel Model The SISO channel model discussed in Section III-A can be extended to the MIMO case by taking into account the correlation between the co- and cross-polar channels. Table I gives the MIMO correlation matrix for the large scale fading obtained using FDTD. The correlation matrix for the small scale fading (multipath) can be found by assuming independent multipath fading on the MIMO channels as reported in [1] and [17]. As previously indicated, the underlying assumption is a set of locally Ricean processes whose parameters are slowly variant along the traveled route. The slow-gading correlation properties are then imposed on the direct signal component of the Rice process, and the fast variation correlation properties are imposed on the multipath component. The proposed model for the roadside tree LMS dual-polarized MIMO channel is presented in Fig. 11. In the model, the

correlated processes that are the inputs to the shadowing filter, see Fig. 11, are given by (4) where

are partially correlated processes. are independent real-valued white Gaussian processes with zero-mean and unit variance. is the Cholesky decomposition of . The complex white Gaussian processes (for ) are filtered (according to [18]) for Doppler spectrum shaping ( is the Doppler filter) (see Fig. 11). The resulting time series are then multiplied by the standard deviation of the noncoherent component of each channel (estimated by means of MST [3] and [4]) to produce the small

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Fig. 11. LMS dual-polarized MIMO channel simulator for roadside trees. and (for ) are independent complex and real-valued white is the Doppler filter. is the Cholesky factorization of . are partially correlated Gaussian processes with zero mean and unit variance, respectively. and are the standard deviation of the incoherent and the mean total coherent (which is the sum of coherently scattered and free-space field) processes. is the standard deviation of the total coherent component. and are the small and large scale fading, respectively. component, respectively. is the fading due to swaying vegetation. is the signal phase corresponding to the traveled distance. is the Doppler shift of the direct signal component. is a correlated complex signal envelope of the LMS dual-polarized MIMO channel.

scale fading. Similarly, the partially correlated processes, , are low-pass filtered by a shadowing filter with transfer function given by [19] (5) with (6) is the sampling distance and is the correlawhere tion distance. Note that shadowing is only applied to the coherent part [19]. can slightly differ between the co- and cross-polar shadowing channels [1]. Thus, the filtering step can modify the correlation coefficient between two channels. To deal with this effect, can be weighted by a correction coefficient prior to taking its Cholesky factorization [17]. The correction coefficient is given by [17] (7) and are the filter coefficients for the co- and where cross-polar channels as defined in (6). The outputs of the shadowing filter are first weighted by the total coherent component

parameter and then added to the attenuated direct signal (which are estimated using MST [3] and [4]). The time series are then converted to linear scale (i.e., to lognormal distributed time series) to obtain the large-scale fading. The smalland large-scale fading processes of each channel are summed and weighted by (estimated from the physical–statistical tree model reported in [3] and [4]) to account for the signal fading caused by wind swaying. Finally, the Doppler shift of the direct signal component is accounted for by multiplying each channel by , where is the phase corresponding to the traveled distance. The outputs of the simulator are partially correlated complex signal envelopes of the dual-polarized 2 2 MIMO channel, which incorporate the total fading caused by vegetation. Note that the model is also applicable in the nomadic case by assuming that wind swaying is the main cause of signal fading. Fig. 12 shows examples of simulated partially correlated roadside tree LMS dual-polarized MIMO channel time series. The system parameters used in the simulations are given in Table II. Sizes, densities, and dielectric constants of tree components reported in [13, Table I] were used. The periodic fading in the time series of the co-polar components indicate the presence of trees along the road. As expected, the simulated cross-polar levels are lower than the co-polar components.

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Fig. 12. Simulated partially correlated 2 2 dual-polarized MIMO channel time series. Simulation parameters are given in Table II.

TABLE II SYSTEM SIMULATION PARAMETERS

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Fig. 13. CDFs of the LMS channel capacities along the roadside tree scenario simulated both for SISO and dual polarized MIMO cases. The system simulation parameters are given in Table II. A signal-to-noise ratio of 20 dB is used.

channel matrix, , and denotes the matrix determinant. For the SISO case, the capacity is given by [20]

b/s/Hz

(10)

where is the normalized complex channel gain relative to the LOS. Fig. 13 presents the cumulative distribution functions (CDFs) of the LMS channel capacities for the dual-polarized MIMO and SISO cases calculated using (9) and (10), respectively. The channel time series are generated using the simulator shown in Fig. 11 using the parameters listed in Table II. As expected, we can observe the increase in capacity achieved with MIMO compared to the SISO case. B. Link Diversity IV. PERFORMANCE EVALUATION

Diversity improves link availability. The amount of diversity gain/improvement obtained depends on the degree of correlation between the various parallel links which, in turn, depends on the propagation environment. For the dual-polarized MIMO case, the instantaneous signal-to-noise ratio at the output of the maximum-ratio-combiner (MRC) is given by [21]–[23]

A. Channel Capacity For a narrowband MIMO system with transmit and receiver antennas, the receive signal is expressed as (8) where

is the transmitted signal, is the noise, and is the channel matrix, with being the channel response between the th transmit antenna and the th receive antenna. The capacity is given by [20] b/s/Hz

(9)

where is the identity matrix of size is the average signal-to-noise ratio, is the complex transpose of the MIMO

(11) where for

is the largest eigenvalue of ). For SIMO case

for

(or

(12) where and are the complex envelopes of the SIMO channel. Fig. 14 presents the CDFs of the received signal for the LMS roadside tree scenario for SISO, SIMO/space diversity (for two

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Fig. 14. CDFs of the LMS received signal along roadside tree areas for SISO, SIMO receiver space diversity (for two co-polar RHCP antennas, one wavelength apart) and dual-polarized MIMO diversity links. The system simulation parameters are given in Table II.

co-polar RHCP antennas, one wavelength apart), and dual-polarized MIMO diversity with MRC. We can observe the significant diversity gain achieved with dual-polarized MIMO and SIMO/space diversity compared to the SISO case. It can also be seen that the best performance is achieved with dual-polarized MIMO diversity. This is because, first, the cross-polar components are not lost and contribute to increase the sum of signal-to-noise ratios at the output of the MRC. Second, we can observe from Fig. 12 that the cross-polar components are especially useful when the link is shadowed by the roadside trees. At these positions, the levels of the co- and cross-polar components are comparable (see Fig. 12), which results in significant diversity gains. V. CONCLUSION In this paper, we studied the LMS dual-polarized MIMO channel along roadside tree areas. A novel physical–statistical, generative tree model based on multiple scattering theory was proposed for calculating the attenuation and scattering effects. FDTD electromagnetic computations were performed to characterize the tree scattering pattern and to calculate the shadowing cross-correlation matrix of the dual-polarized MIMO channel. Generally, the use of FDTD has advantages in obtaining an accurate solution of electromagnetic interaction with arbitrary objects; however, it also has limitations in terms of the size of the computation volume relative to the wavelength, which is directly related to the required simulation time. This means that performing FDTD simulations over large computation areas/volumes may not be feasible, even using parallel computing. In addition, a channel model/simulator for the SIMO receiver space diversity was also presented using the physical–statistical tree model, thus extending the SISO model in [3] and [4]. The physical–statistical approaches discussed are more effective for simulating large scenarios compared to complex phys-

ical models, and more accurate than merely empirical or statistical models. In addition, performance analyses of the LMS SISO, dualpolarized MIMO and SIMO/space diversity configurations were carried out. Compared to the SISO case, significant increases in performance were observed for the dual-polarized MIMO and SIMO/space diversity cases. The results obtained can be used to evaluate the technical feasibility of LMS systems in roadside tree scenarios. They also give an insight into the kinds of system performance analyses that could be carried out using the models developed in this paper. In general, the proposed channel models can be used to carry out different system-level analyses such as capacity, bit-error-rate, etc. Future work includes validating the developed LMS dual-polarized MIMO and SIMO/space diversity channel models using measurements, as well as carrying out further comparisons between MST and FDTD results. ACKNOWLEDGMENT The authors would like to thank the French Space Agency (CNES), French Aerospace Lab (ONERA) and Thales Alenia Space—France for supporting this work. The authors would also like to thank X. Ferrieres and E. Bachelier of ONERA for helping with the FDTD computations. In addition, the authors would like to thank L. Castanet of ONERA for his useful comments. REFERENCES [1] P. R. King and S. Stavrou, “Low elevation wideband land mobile satellite MIMO channel characteristics,” IEEE Trans. Wireless Commun., vol. 6, no. 7, pp. 2712–2720, Jul. 2007. [2] M. O. Al-Nuaimi and A. M. Hammoudeh, “Measurements and predictions of attenuation and scatter of microwave signals by trees,” Proc. Inst. Electr. Eng. Microw. Ant. Prop., vol. 141, no. 2, pp. 70–76, Apr. 1994. [3] M. Cheffena and F. P. Fontan, “Land mobile satellite channel simulator along roadside trees,” IEEE Antennas Wireless Propag. Lett., vol. 9, pp. 748–751, 2010. [4] M. Cheffena and F. P. Fontan, “Channel simulator for land mobile satellite channel along roadside trees,” IEEE Trans. Antennas Propag., vol. 59, no. 5, pp. 1699–1706, May 2011. [5] G. J. Byers and F. Takawira, “Spatially and temporally correlated MIMO channels: Modeling and capacity analysis,” IEEE Trans. Veh. Technol., vol. 53, no. 3, pp. 634–643, May 2004. [6] C. Oestges, “A stochastic geometrical vector model of macro- and megacellular communication channels,” IEEE Trans. Veh. Technol., vol. 51, no. 6, pp. 1352–1360, Nov. 2002. [7] M. Sellathurai, P. Guinand, and J. Lodge, “Space-time coding in mobile satellite communications using dual-polarized channels,” IEEE Trans. Veh. Technol., vol. 55, no. 2, pp. 188–199, Jan. 2006. [8] G. Alfano and A. D. Maio, “A theoretical framework for LMS MIMO communication systems performance analysis,” in Proc. 3rd Int. Waveform Diversity Design Conf., Jun. 4–8, 2007, pp. 18–22. [9] K. P. Liolis, J. Gomez-Vilardebo, E. Casini, and A. Perez-Neira, “On the statistical modelling of MIMO land mobile satellite channels: A consolidated approach,” presented at the 27th AIAA Int. Commun. Satellite Syst. Conf. (ICSSC), Edinburgh, U.K., Jun. 2009. [10] L. L. Foldy, “The multiple scattering of waves,” Phys. Rev., vol. 67, no. 3, pp. 107–119, 1945. [11] M. X. Lax, “Multiple scattering of waves,” Rev. Mod. Phys., vol. 23, no. 4, pp. 287–310, 1951. [12] S. A. Torrico, H. L. Bertoni, and R. H. Lang, “Modeling tree effects on path loss in a residential environment,” IEEE Trans. Antennas Propag., vol. 46, no. 6, pp. 872–880, Jun. 1998. [13] Y. L. C. de Jong and M. H. A. J. Herben, “A tree-scattering model for improved propagation prediction in urban microcells,” IEEE Trans. Veh. Technol., vol. 53, no. 2, pp. 503–513, Mar. 2004.

CHEFFENA et al.: LAND MOBILE SATELLITE DUAL POLARIZED MIMO CHANNEL ALONG ROADSIDE TREES

[14] K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwells equations in isotropic media,” IEEE Trans. Antennas Propag., vol. AP-14, no. 3, pp. 302–307, May 1966. [15] A. A. Chukhlantsev, A. M. Shutko, and S. P. Golovachev, “Conductivity of leaves and branches and its relation to the spectral dependence of attenuation by forests in meter and decimeter band,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., Jul. 21–25, 2003, pp. 1103–1105. [16] N. C. Rogers, A. Seville, J. Richter, D. Ndzi, N. Savage, R. Caldeirinha, A. K. Shukla, M. Al-Nuaimi, K. Craig, E. Vilar, and J. Austin, “A generic model of 1–60 GHz radio propagation through vegetation—Final report,” in Radio Agency, U.K., May 2002 [Online]. Available: http://www.ofcom.org.uk/static/archive/ra/topics/research/ topics/propagation/vegetation/vegetation-finalreportv1_0.pdf [17] G. Carrie, J. Lemorton, and F. Perez-Fontan, “State-of-the-art review of LMS MIMO channel models at s and c band upgrade of the validity domain of the available channel models,” ONERA, Toulouse, France, Tech. Rep., Apr. 2010. [18] T. Aulin, “A modified model for the fading signal at a mobile radio channel,” IEEE Trans. Veh. Technol., vol. 28, no. 3, pp. 182–203, Aug. 1979. [19] F. Perez-Fontan and P. M. Espineira, Modelling the Wireless Propagation Channel: A Simulation Approach With MATLAB. Chichester, U.K.: Wiley, 2008, ISBN: 978-0-470-72785-0. [20] J. G. Foschini and J. M. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Pres. Commun., vol. 6, no. 3, pp. 311–335, 1998. [21] T. K. Y. Lo, “Maximum ratio transmission,” IEEE Trans. Commun., vol. 47, no. 10, pp. 1458–1461, 1999. [22] C. H. Tse, K. W. Yip, and T. S. Ng, “Performance tradeoffs between maximum ratio transmission and switched-transmit diversity,” in Proc. 11th IEEE Int. Symp. Personal, Indoor, Mobile Radio Commun., 2000, pp. 1485–1489. [23] M. Kang and M. S. Alouini, “Largest egenvalue of complex Wishart matrices and performance analysis of MIMO MRC systems,” IEEE J. Sel. Commun., vol. 21, no. 3, pp. 418–431, Apr. 2003.

Michael Cheffena received the M.Sc. degree in electronics and computer technology from the University of Oslo, Norway, in 2005 and the Ph.D. degree from the Norwegian University of Science and Technology (NTNU), Trondheim, Norway, in 2008. For one year, he was a visiting researcher at the Communications Research Centre (CRC), Canada. From 2009 to 2010, he made a postdoctoral study at the University Graduate Center (UNIK), Kjeller, Norway. From 2010 to 2011, he was a Postdoctoral Fellow at the French Space Agency (CNES), Toulouse, France. Currently, he is an Associate Professor at Gjøvik University College, Norway. His research interests include modelling and prediction of radio channels for both terrestrial and satellite links.

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Fernando Pérez Fontán was born in Villagarc´ıa de Arosa, Spain. He received the Diploma degree in telecommunications engineering and the Ph.D. degree from the Technical University of Madrid, Spain, in 1982 and 1992, respectively. He is a Full Professor with the Telecommunications Engineering School, University of Vigo, Vigo, Spain. He is the author of a number of international magazine and conference papers. His main research interest is in the field of mobile fixed radio communication propagation channel modeling.

Frédéric Lacoste received the Engineer degree from Ecole Nationale Supérieur d’Ingénieurs en Construction Aéronautique et Spatiale (ENSICA), France, in 2002 and the Ph.D. degree in EM waves propagation from Ecole Nationale Supérieure de l’Aéronautique et de l’Espace (SUPAERO), France, in 2005. In 2005, he joined the French Space Agency (CNES), Toulouse, France, where he is currently working on propagation channel modeling and measurements for fixed and mobile Earth–Space communication systems. He was involved in various European and worldwide working groups dealing with Earth–Space propagation modeling, such as SatNEx I and II, COST 280, and currently COST IC0802, NoE-EWP, and ITU-R study group 3.

Henri-Jose Mametsa received the Diploma degree in telecommunication engineering and the Ph.D. degree in electronics from the Ecole Nationale des Telecommunications de Bretagne, France, in 1984 and 1986, respectively. He co-directed Ph.D. students and received a postdoctoral degree (required to advise doctoral students or to oversee research) from the Université Paul Sabatier, Toulouse, France. He worked as an Engineer in the Antennas Design Department of Thomson-CGR before joining the Electromagnetism and Radar Department of the Office National d’Etudes et de Recherches Aerospatiales (ONERA), Toulouse, France, where he has been working in different studies on electromagnetic scattering problems. His current research interests include modeling electromagnetic scattering from man-made targets and natural media.

Guillaume Carrie was born on June 20, 1979. He received the Engineer Diploma degree in aeronautics and the D.E.A. degree in signal processing from ENSICA, Toulouse, France, in 2003 and the Ph.D. degree in array processing for GNSS receivers from SUPAERO, Toulouse, France, in 2006. From November 2006 to year-end 2007, he was working in SILICOM as a Research Engineer on the development of experimental receivers and on simulations, both for Galileo systems. Since January 2008, he has been working in the Radio Communication and Propagation Research Unit of the Electromagnetism and Radar Department of ONERA, Toulouse, France. His current research interests are mainly focused on propagation channel modeling both for fixed and mobile satellite systems and on channel adaptive GNSS receivers.

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Empirical-Stochastic LMS-MIMO Channel Model Implementation and Validation Peter R. King, Tim W. C. Brown, Member, IEEE, Argyrios Kyrgiazos, and Barry G. Evans, Senior Member, IEEE

Abstract—Land Mobile Satellite (LMS) networks, forming a key component of future mobile Internet and broadcasting, can benefit from Multiple-Input Multiple-Output (MIMO) techniques to improve spectral efficiency and outage. LMS-MIMO networks can be obtained using multiple satellites with single polarization antennas with spatial multiplex channel coding, or by a single satellite with dual polarization antennas providing polarization multiplex channel coding. In this paper, a guide is presented showing the steps required to implement a simple empirical-stochastic dual circular polarized LMS-MIMO narrowband channel model with validation both with and without a line of sight. The model is based on an S-band tree-lined road measurement campaign using dual circular polarizations at low elevations. Application of the model is aimed at LMS-MIMO physical layer researchers and system designers, who need an easy to implement and reliable model, representative of typical LMS-MIMO channel conditions. Index Terms—Channel model, Land Mobile Satellite (LMS), multiple-input multiple-output (MIMO), propagation, stochastic.

I. INTRODUCTION

T

HE benefit of applying multiple-input multiple-output (MIMO) techniques to the Land Mobile Satellite (LMS) channel, in terms of capacity gain and diversity gain, was shown in [1] and [2] respectively. In recent years, the use of MIMO in terrestrial wireless systems including the next generation wireless networks, IEEE 802.11n [3] as well as wide area networks, IEEE 802.16m [4] and long term evolution of third generation mobile (3GPP LTE) [5] has become widespread. More recently the use of MIMO for LMS has gained interest with regards to satellite based digital video broadcasting standards DVB-SH and DVB-NGH [6]. However, before LMS-MIMO systems are in widespread use, suitable and simple to implement channel models that give a general model of the radio environment are required. This paper defines an empirical-stochastic channel model for such use. As is typical for LMS channel models, as well as the model presented in this paper, large scale fading comprises Markov Chains to represent the “on/off” nature of the channel and filtered log-normal simulation to represent the shadowing effects, and Ricean simulation to represent the small scale fading effects [7]. However, this model extends the capabilities to the

Manuscript received November 29, 2010; revised September 23, 2011; accepted October 10, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. This work was supported in part by the EU FP6 project SatNex (Satellite Communications Network of Excellence). The authors are with the Centre for Communication Systems Research, University of Surrey, Surrey GU2 7XH, U.K. (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TAP.2011.2173448

Fig. 1. Diagram of satellite MIMO channel structure.

MIMO case, where its stochastic properties are derived from an S-band tree-lined road measurement campaign using dual circular polarizations at low elevations. Furthermore, this model in particular compared to existing models to date [8], [9] considers the interdependence between the small scale fading. The authors have found the most appropriate means to accommodate this interdependence is to use a Ricean fading model, where the co-polar and cross-polar components are suitably correlated. Section two of this paper describes the typical factors unique to a dual circular polarization LMS-MIMO channel modeling, including the need for a four-state Markov chain to form simultaneous dual polar shadowing models as well as small-scale fading models. This is followed by sections detailing the measurement campaign carried out to show the Markov chain behavior in the LMS-MIMO channel. A step by step guide is then provided in generating the proposed empirical-stochastic model informed by measurement data. The reader can use the information presented to implement the necessary code for such a model. Finally validation tests are shown to clarify the model’s application in both line of sight and non line of sight regions. II. LMS-MIMO CHANNEL MODEL CONSTRUCTION The structure of an LMS-MIMO channel model is a 2 2 MIMO system whereby the two antennas at each end are dual circular polarized with right hand and left hand circular polarizations (RHCP and LHCP) as illustrated in Fig. 1. The model presented in this paper is considered to be suitable for the L-band and S-band frequency ranges such that the ionospheric and tropospheric effects are considered negligible. The largest impact would be Faraday rotation in the ionosphere [7], which would be overcome using circular polarization. Ignoring any ionospheric and tropospheric effects, the main item of interest for satellite MIMO is the multipath caused by local scatterers near to the mobile. The scattering caused in this region will create some depolarization from RHCP to LHCP and from LHCP to RHCP, which are represented in a 2 2 MIMO

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channel matrix, , where there are two co-polar (RHCP to RHCP and LCHP to LHCP) and two cross-polar circularly polarized channels (RHCP to LHCP and LCHP to RHCP). These four channels are conveniently represented as follows with subscripts R and L (1) where the channel matrix is used as the multiplicative component within the channel so that the output signal vector received relates to the input signal vector by the at the mobile, following equation: (2) is a vector to represent additive white Gaussian noise where at the receiver. It is therefore of interest to model the channel state at time , . The simplest means to model the LMSMIMO channel is to use a stochastic random process, which will define the distribution of channel states (or first order statistics), but it is also necessary to define how the channel evolves, by considering what is known as the second order statistics. For satellite MIMO, it is best to break the channel into three components: 1) Free space path loss—This is defined theoretically by the well known Friis’ formula [7] though for convenience of being able to analyze the channel, it is normalized in this case, since it is merely an offset value. 2) Shadowing or large scale fading—When the mobile is on the ground, it may either have a direct line of sight link to the satellite, or there may be a building, tree or other large scattering object blocking the direct path. Thus the mobile is within the shadow of the scatterer and will be subject to extra path loss. In the case of satellite communications, the mobile is constantly moving in and out of the shadow regions as illustrated in Fig. 2. Here the mobile is a vehicle moving along the road, it will enter regions between scatterers on its left hand side where it will have a line of sight link with the satellite. Therefore there is a need to statistically model scenarios where there is both high and low shadowing. Therefore it is necessary to model when the mobile is switching between high and low shadowing, which is best achieved by using a Markov chain [10]. 3) Small scale fading—In the local area around the mobile there will be several scattering objects, which will produce reflected, refracted and diffracted signals. As the mobile moves, these reflections, refractions and diffractions are constantly changing and thus the received signal is constantly changing. In some instances, the reflected signals will add up constructively in phase, while in other cases they will add up destructively out of phase and the received signal will go into a deep fade. It is therefore necessary to separately model the small scale and large scale fading characteristics of the channel as it changes over time with mobile movement. For LMS-MIMO, there are a number of modeling challenges not addressed in other LMS channel models that must be considered and which have led to the construction of a simple to

Fig. 2. Diagram illustrating an example of high and low shadowing regions.

implement stochastic model provided in this paper. The factors that require consideration include the following: • The MIMO branches are in the circular polarization domain, rather than the spatial domain. Therefore, channel multiplexing occurs in this domain, which will give different characteristics in the eigen decomposition of the channel, as will be seen from measurement data later in this paper. Therefore different eigen characteristics [11] from conventional MIMO channel models need to be modeled. • The large scale fading changes constantly when switching from high to low shadowing. This produces different characteristics for the co-polar and cross-polar channel branches and likewise should be modeled to be consistent with simultaneous measurements of these channels. Furthermore the shadowing characteristics should be compared for both polarizations so that their interdependence is maintained. • The small scale fading channels for each of the four MIMO paths are not necessarily independent, especially when there is a line of sight link. Therefore in such circumstances, the interdependence must be appropriately modeled so that both the model and real measured data have comparable eigen decomposition. Before developing models, the Markov chain, polarization and interdependence characteristics need to be identified from real measurement data, which the next section of this paper addresses. After describing the measurements, this paper describes the stages involved in creating the large scale fading characteristics, Markov chain and small scale fading. III. MEASUREMENT SETUP Extensive measurements were carried out on the edge of the town of Guildford, UK, representative of a suburban/rural area that would be applicable to LMS-MIMO during the summer time (with trees in full foliage). An artificial terrestrially based platform (acting as a satellite) was placed on top of a hill overlooking a road, as illustrated in Fig. 3 containing directional RHCP and LHCP antennas, spaced just under one wavelength apart. Each antenna had a gain of 12 dBi and a 3 dB beamwidth of 30 . A mobile van contained the receiver and its roof was fitted with an omnidirectional RHCP and LHCP antenna spaced four wavelengths apart. These two antennas had a beamwidth of 70 in elevation. The satellite elevation angles ranged from 7 to 18 as the mobile moved along the tree-lined road. Although many operational satellite elevations exceed these, some geostationary and low Earth orbiting mobile satellite services are required to work at low elevations. The present experiment therefore represents these as worst case system scenarios, where

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Fig. 3. Diagram of measurement setup of artificial platform.

such elevations enable the highest degrees of multipath. Varying levels of Rice factor, as defined by the Ricean distribution, as well as channel correlations provide a usefully wide range of empirical results. An Elektrobit Propsound wideband MIMO channel sounder was configured for a carrier frequency of 2.45 GHz and a bandwidth of 200 MHz. Each MIMO channel was obtained sequentially by using fast switching at a rate of 152.7 Hz, which is over twice the maximum Doppler shift of 73 Hz for the vehicle speed, thus meeting Nyquist criteria. This is assumed to be the case on the tree-lined road where there were few vehicles in motion. Within the data, suitable results were found whereby the channel could be captured within the channel sounder’s sensitivity giving a signal to noise ratio that enabled the multipath to be measured without error due to receiver noise. There were many cases of interference from local wireless area networks that had to be filtered out from the measurement data and replaced with interpolated data. Data sampling being more than the required Nyquist criteria meant it was possible to achieve this. An example of the measurement data obtained to illustrate the Markov chain behavior of the high and low shadowing is shown in Fig. 4 for all four MIMO branches. For clarity, the free space loss (FSL) is normalized out of the channel. Clearly it can be seen that there are different small scale fading characteristics in high and low shadowing regions, as well as Markov chain characteristics that are related for co-polar and cross-polar channels though they are required to be generated separately. The next section will explain in detail how the large scale fading, Markov chain and small scale fading are generated in three separate steps and then integrated in order to form a working channel matrix.

Fig. 4. Sample measurement showing the Markov chain characteristics of the LMS-MIMO channel.

In order for these two sets of four shadowing models to have interdependence, a 4 4 correlation matrix for large scale fading, , is then applied [7] to both high and low shadowing as analysis of measurement data has shown both shadowing cases to follow the necessary Gaussian distribution. This will accommodate the interdependence between the four MIMO branches so that correlated shadowing and is formed as follows:

(3) where the 1/2 denotes the Cholesky factorization. An appropriate set of values for are taken from the measurement data representing a typical tree lined road in a suburban environment. To assist with understanding the matrix formation, the matrix has notations for each element where as an example, the correlation, gives the correlation of the shadowing between the right to right hand branch and the left to left hand branch. Therefore all sixteen possible permutations of this notation are shown in the matrix as follows, from which values from the measured data are then given

IV. MODEL GENERATION A. Step 1—Generate Large Scale Fading for High and Low Shadowing For 2 2 MIMO, four simultaneous models of high shadowing that will vary over distance (i.e. in non line of sight region) are required to produce vector and four simultaneous models of low shadowing (i.e. in line of sight region) are required to produce vector , in dB by using zero mean, unity standard deviation Gaussian random noise signals.

(4)

The correlation values are high, as expected due to the close proximity of the two transmit and two receive antennas and other measurements have shown that high correlation is maintained in different channel scenarios. Using these correlations, eight time-synchronized simulations are created that are defined

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TABLE I SHADOWING MODEL MEAN AND STANDARD DEVIATIONS

by the following process in order to form the second order statistics [12], [13]:

(5) where the time variation is determined by a coherence distance, for a given mobile speed, with sample time and and are the correlated Gaussian distributed random variables with zero mean and unity standard deviation. Measurements used in this paper have shown to be 25 m on average for a tree-lined road environment. The range of values recorded spanned from 23 m through to 29 m. It is assumed in this case that each sample, , is taken for every meter. The shadowing then requires normalization where a set of standard deviations to the shadowing represented by vectors and and mean values, represented by vectors and , all in dB, are applied, where denotes elementwise multiplication and the normalized, filtered and correlated shadowing, and are therefore:

(6) Empirical values of standard deviations and and mean values, and for co-polar and cross-polar channels in the tree-lined road environment in dB are shown in Table I, which are derived generically from all measurement data taken as the highest and lowest values. Finally the data must be reshaped to create two separate 2 2 channel matrices and . B. Step 2—Generate Markov Chain Having generated data for high and low shadowing sequences, a Markov Chain [10] is used to select between the regions of high and low shadowing for both co-polar and cross-polar channels. This allows the sharp transitions that occur as a mobile moves past buildings as illustrated in Fig. 2 to be suitably modeled. Therefore if two polarizations are considered, there are four possible Markov states as illustrated in Fig. 5. It is assumed that the behavior is the same whichever of RHCP or LHCP is being transmitted. Once the polarization is defined at the transmit end, these four possible states therefore consider whether the co-polar or cross-polar channels at the receive end are both in a high or low state or in opposite states, as can happen in certain instances. Given that there are

Fig. 5. Illustration of the four Markov states for the LMS-MIMO channel.

four possible states, there are therefore sixteen possible state transitions as shown by the arrows. The Markov chain statistics are extracted from the measurement data (once a threshold is selected for high and low shadowing in the measurement data) and the results are shown in Table II, which are derived from analyzing the Markov chain of all measurement samples. The Markov chain derived from the measurement data using the chosen threshold was analysed to ensure that where state transitions did occur, they were true cases of a real transitions. There can be cases with extreme low probability where a high state shadowing falls below the threshold while also a low state threshold rises above the threshold. Inspection of the Markov chain removed any of these remotely possible occurrences. The columns of the state transitions represent the probability of one state moving to another listed in the right hand column, while each row represents the probability of moving to the state shown on the right hand column from a previous state shown on the bottom row. Thus the top right hand state transition of 0.1037 is the probability of moving from state “CP High, XP High” to “CP Low, XP Low”, where CP is a co-polar channel and XP is a cross-polar channel. In the majority of cases for this measurement, both CP and XP are in a high shadowing state, which reflects the measurement scenario being a road lined with houses and trees with foliage thus providing dense multipath and the satellite at a low elevation. From applying the Markov chain analysis, sampled every meter, to the large scale shadowing, a 2 2 channel matrix, can finally be created. After producing the Markov chain, the data must be up-sampled to match the resolution of the small scale fading that is generated next. Up-sampling is required because the rate of change of fading for the large scale fading is considerably low compared to that of the small scale fading and therefore does not require such a large scale of sampling (based upon the size of ) in the first instance. However, for the large scale fading to be integrated with the small scale fading at a later stage, it is necessary that the large scale fading matches the necessary sampling rate for the small scale fading.

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TABLE II MARKOV STATE AND STATE TRANSITION TABLE

to allow the well known Kronecker model to be applied [15] to model the correlated small scale fading, as follows: (8) where vec is the vectorize function. Values for the small scale fading correlation matrix are also taken from measurements, where the values are derived as an average of correlation values evaluated over the whole sampled measurement data. The format of matrix follows the same pattern as that used for in (4):

TABLE III COMPARISON OF MEAN AND STANDARD DEVIATION VALUES OF COMPLEX CORRELATION MAGNITUDE AGAINST RICE FACTOR

(9)

C. Step 3—Generate Small Scale Fast Fading The small scale fading is modeled in this case by a Ricean distribution, where the low shadowing region will have a higher Rice factor than that of the high shadowing region, which will be subject to denser multipath. The usage of values of Rice factors based on measurements are discussed later in Table III. Using the Rice factors, Ricean fading with appropriate second order statistics can be generated for each MIMO branch by using a ring scatterer model [14] (though other well known methods to generate small scale fading such as Doppler filtering and autocorrelation matrices [7] are equally acceptable). For each sample , the small scale fading elements, denoted by subscripts of are derived in this case as:

(7) where is the sampling factor equal to the sampling frequency divided by the maximum Doppler shift, due to mobile movement. The Rayleigh (or scattered) part of the small scale fading is normalized by so that its mean is unity. The components of the Rayleigh part will arrive at angle and have a random phase . The four elements are arranged into the 2 2 matrix . In the high shadowing regions, there is in general a non line of sight (NLOS) condition and the Rice factor is low. In the case of the LMS, the scattering rich environment local to the mobile terminal provides low correlation between the antenna branches, while at the satellite there are directional antennas with highly orthogonal circular polarizations, thus their correlation is also low. At each end therefore, the correlation is controlled independently and also remains low in a non line of sight scenario, which therefore justifies that the channel is separable in order

In the case where there is low shadowing and a line of sight (LOS), the channel cannot be considered separable and thus the Kronecker assumption does not hold. Thus the Kronecker model has been extended here such that it is suited to a 2 2 satellite MIMO system in a LOS environment with dual circular polarization, which enables polarization multiplexing. Firstly a co-polar correlation matrix, (within which a complex correlation [7], of and is used) is defined as the following 2 2 matrix: (10) The phase information in the matrix may be used, though as the validation section later on will clarify, it is not essential to include when generating a model. Secondly a cross polar correlation matrix, is also defined in a similar way. The correlation component, is derived by taking an average of the complex correlation of and and the correlation of and . Again the phase information is not essential and it is assumed the two antennas at the transmit end have similar characteristics in terms of gain patterns and polarization purity. The same must also be true at the receive end, though the transmit antennas do not have to be the same as the receive antennas. The 2 2 correlation matrix for the cross-polar is defined as follows: (11) The two matrices in (10) and (11) will influence the orthogonality of the right hand and left hand polarizations, which will be key to a MIMO channel. A 1 2 channel vector of the co-polar components, , is then generated using Rice factors determined from measurement using (7) and then the two co-polarizations are correlated to gain as follows: (12)

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TABLE IV COMPARISON OF MAXIMUM AND MINIMUM XPD AGAINST RICE FACTOR

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TABLE V CORRELATION, XPD AND RICE FACTOR VALUES USED IN THE NLOS AND LOS CASES FOR VALIDATION

Likewise the same can be done for the cross polar components, which have a very different correlation and Rice factor compared to the co-polar case: (13) The four elements once generated can easily be inserted into . After a 2 2 matrix to generate the small scale fading, applying the correlation, it is necessary to re-normalize the mean values of all four MIMO branches. For the cross polar components, and , the mean values must also be divided by the square root of the cross polar ratio, . The XPD is defined as the ratio of the mean co-polar power to the mean cross-polar power. It is assumed XPD is the same whether the co-polar component is left hand or right hand circularly polarized. Measurements provided data showing Rice factors ranging from 0 to 10 for co-polar data. The cross polar Rice factors were also found to be wide ranging, though as a rule they are always less than the co-polar Rice factor for a set of samples, thus any Rice factors can be selected for a model that adhere to the rule, though corresponding XPD and correlations have to be used alongside given Rice factors. Table III and Table IV present suitable corresponding values of correlation and XPD respectively taken from analyzing measurement data available. In the case of a high Rice factor, the co-polar correlation will be inherently high, while for a low Rice factor the correlation is lower and has a greater variance. XPD can be as high as 15 dB for a high Rice factor, though on average it is closer to 10 dB. For lower Rice factors, where the scattering causes significant de-polarization the average XPD is closer to 0 dB.

Fig. 6. Cumulative distribution plot of the modeled and measured channel for high shadowing (NLOS).

D. Step 4—Integrate Steps 1, 2 and 3 Now that the large and small scale fading channels are created, they can simply be multiplied together to form the final channel model such that: (14) where denotes an elementwise multiplication of the two matrices. It should be noted that the resultant large scale fading is already normalized to the bulk mean free space path loss and any other losses in the ionosphere or troposphere. However, the resultant small scale fading must be normalized to unity mean power. V. LMS-MIMO CHANNEL MODEL VALIDATION OF SMALL SCALE FADING An important validation for MIMO channel models is to ensure that the eigenvalue cumulative distributions produced by

Fig. 7. Cumulative distribution plot of the modeled and measured channel for low shadowing (LOS).

the model are in good agreement with measured data. This will not only ensure that the first and second order statistics of the physical channel are suitably modeled but also that the interdependence between them is suitably accounted for in order to demonstrate the diversity and multiplexing capabilities of the model. To demonstrate the validation of the model, two LOS and NLOS cases were chosen, which had values of Rice factor, XPD and correlation shown in Table V. The values for Rice factor are in linear form. The following three subsections compare the first order, second order and eigen analysis as a validation of the model proposed using appropriate sections of the measurement data. The narrowband measurement data used for validation has a

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Fig. 8. Comparison of the right to right hand and left to left hand polarized Doppler spread in NLOS and LOS. Fig. 10. Comparison of the model and measurement eigenvalues for the high shadowing (NLOS) region.

Fig. 9. Validation of the second order statistics based on level crossing rate and average fade duration.

sampling rate of more than twice the maximum Doppler shift so as to meet Nyquist criteria. A. First Order Statistics Fig. 6 and Fig. 7 illustrate the cumulative distribution of the small scale fading for all four branches of the NLOS and LOS regions. In both cases there is good agreement between the measurement data and model, where in the LOS scenario, a wider gap can be identified between co-polar and cross-polar branches. It is interesting to note that the mean value of the cross-polar component for LHCP transmission is shifted by over 6 dB when compared to RHCP, where the multipath was found to better combine constructively within the sampled time window. The model, however, has not accommodated this difference, since the negligible contribution of the cross-polar element to the MIMO channel has no real effect on the capacity or eigen analysis. B. Second Order Statistics Fig. 8 shows the Doppler spread in both left hand to left hand and right hand to right hand polarized cases, where polarization makes little difference in LOS or NLOS. The

Fig. 11. Comparison of the model and measurement eigenvalues for the low shadowing (LOS) region.

Doppler spread shown verifies the suitability of the Ricean distribution for small scale modeling based on a Classical bath tub model with the addition of a delta function for the Rice component [7]. A high Rice component is identified in Fig. 8 for the LOS case while still a small Rice component is identified in the NLOS case due to non uniform angle of arrival. A further validation of the second order statistics is presented in Fig. 9, which shows a good agreement between level crossing rate and average fade duration when comparing the measured narrowband data and the modeled narrowband data. Free space loss and the maximum Doppler frequency are labeled FSL and respectively. C. Eigen-Analysis Fig. 10 presents results of the eigen analysis of the model and measurement data as well as the modeled data for the NLOS case. Clearly there is a good consistency, which verifies the Kronecker model approach is sufficient for this scenario. In this graph, the notation is denoted as an eigenvalue where is 1 or 2 for a 2 2 MIMO system.

KING et al.: EMPIRICAL-STOCHASTIC LMS-MIMO CHANNEL MODEL IMPLEMENTATION AND VALIDATION

Fig. 11 on the other hand compares measured and modeled eigenvalues in the LOS case using the new model approach. Compared to the NLOS case, the LOS channel is clearly rich in polarization multiplexing, as opposed to diversity because the eigenvalue distributions are closer. This is expected due to fewer scatterers. Results are in agreement, though it should be noted that in this validation, the phase information was applied in the correlation matrices. Were the phase information not applied, the second eigenvalue would marginally change its gradient, moving away from the measured data by less than 2 dB. Given the negligible impact this would have on modeled channel capacity, use of the phase information is therefore not important. A similar scenario occurs when modeling other LOS regions. VI. CONCLUSION The procedure for implementing a simple empirical-stochastic based model for the dual circular polar 2 2 LMS-MIMO channel has been presented along with results to validate the model at low elevation, which is based on switching between high and low shadowing regions with different multipath conditions. The validation of the model at such elevations will also be suited to higher elevation angles where the multipath is reduced and the opportunity to implement polarization multiplexing is increased. The well known Kronecker model is suitable for the non line of sight case, while a new model has been presented to be applied to a polarization multiplexing rich scenario in the line of sight case. Comparisons show good accuracy in both cases. Given the simplicity of generating a Markov chain and correlated small scale and large scale fading, it is highly appropriate for conformance testing for satellite MIMO applications with the simplicity of controlling the channel through altering Rice factors, correlation and XPD values according to guidelines presented. ACKNOWLEDGMENT The help of U. Ekpe at the University of Surrey is acknowledged for extracting the relevant narrowband measurement data. REFERENCES [1] P. R. King and S. Stavrou, “Capacity improvement for a land mobile single satellite MIMO system,” IEEE Antennas Wireless Propag. Lett., vol. 5, no. 1, pp. 98–100, Dec. 2006. [2] P. R. King, P. Horváth, F. Pérez-Fontán, I. Frigyes, and S. Stavrou, “Satellite channel impairment mitigation by diversity techniques,” presented at the IST Mobile Summit, Jun. 2005. [3] IEEE 802.11n Standard for Information Technology—Telecommunications and Information Exchange Between Systems—Local and Metropolitan Area Networks—Specific Requirements, IEEE 802.11n, 2009 [Online]. Available: http://standards.ieee.org [4] IEEE 802.16 Standard for Local Metropolitan Area Networks, IEEE 802.16, 2009 [Online]. Available: http://standards.ieee.org [5] Third Generation Partnership Project [Online]. Available: http://www. 3gpp.org [6] Digital Video Broadcasting Standards [Online]. Available: http://www. dvb.org [7] S. R. Saunders and A. A. Aragón- Zavala, Antennas and Propagation for Wireless Communications, 2nd ed. London, U.K.: Wiley, 2007. [8] M. Sellathurai, P. Guinand, and J. Lodge, “Space-time coding in mobile satellite communications using dual-polarized channels,” IEEE Trans. Veh. Tech., vol. 55, no. 2, Jan. 2006.

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[9] K. P. Liolis, J. Gomez-Vilardebo, E. Casini, and A. Perez-Neira, “On the statistical modelling of MIMO land mobile satellite channels: A consolidated approach,” in Proc. IET and AIAA Int. Communications Satellite Systems Conf., Edinburgh, U.K., 2009, p. 422. [10] F. P. Fontan and P. M. Espiñeira, Modelling the Wireless Propagation Channel: A Simulation Approach With MATLAB. London, U.K.: Wiley,, 2008. [11] R. G. Vaughan and J. B. Andersen, Channels, Propagation and Antennas for Mobile Communications. London, U.K.: IEE Press, 2002. [12] M. Gudmundson, “Correlation model for shadow fading in mobile radio systems,” IEE Electron. Lett., vol. 27, no. 23, pp. 2145–2146, 1991. [13] M. J. Marsan, G. C. Hess, and S. S. Gilbert, “Shadowing variability in an urban land mobile environment at 900 MHz,” IEE Electron. Lett., vol. 26, no. 10, pp. 646–648, 1990. [14] M. Pätzold, Mobile Fading Channels. London, U.K.: Wiley, 2002. [15] J. P. Kermoal, L. Schumacher, K. I. Pedersen, P. E. Mogensen, and F. Frederiksen, “A stochastic MIMO radio channel model with experimental validation,” IEEE J. Sel. Areas Commun., vol. 20, no. 6, pp. 1211–1226, Aug. 2002.

Peter R. King received the B.Sc. degree in electronic engineering (telecommunications) from the University of Essex, U.K., in 1989, and the M.Sc. degree in mobile & satellite communications and the Ph.D. degree in mobile satellite radio propagation from the University of Surrey, U.K., in 2002 and 2007 respectively. He has worked in radio frequency and radio propagation research & development since 1990 for many leading organizations such as Lucent Technologies, Nortel, Roke Manor Research, Samsung, TTP Communications, Airspan, Thales, ITT Defence and AceAxis. He now runs a small RF consultancy business, providing solutions for mobile, satellite, aircraft and wireless radio communication systems, circuits and products. In addition to his consultancy work, he continues to research and teach at the University of Surrey where he is a visiting academic. His research interests include terrestrial and satellite radio propagation, and high-performance radio: power amplifiers, receivers, transmitters, frequency synthesis and power amplifier linearization.

Tim W. C. Brown (S’00–M’04) received the B.Eng. degree in electronic engineering and the Ph.D. degree in antenna diversity for mobile terminals from the University of Surrey, U.K., in 1999 and 2004, respectively. Since completing his doctoral research, he has continued his research interests in antennas, propagation and radio frequency (RF) engineering. This has included postdoctoral research from 2004–2006 at Aalborg University, Denmark and his present post as a Lecturer in RF, antennas and propagation at the Centre for Communication Systems Research (CCSR), University of Surrey. His current research interests include mobile terminal antennas, satellite communications, multiple input multiple output (MIMO), ultrawideband (UWB), radar, radio frequency identification (RFID), near field communications (NFC) and vehicular technologies.

Argyrios Kyrgiazos received the Dipl.-Eng degree in electrical and computer engineering from the National Technical University of Athens (NTUA), Greece and the M.Sc. degree in mobile and satellite communications from the University of Surrey, U.K., in 2008 and 2010, respectively, where he is currently working towards the Ph.D. degree. In 2008, he joined the Greek army for his mandatory duty. His research interests include wireless terrestrial and satellite communications with emphasis on physical layer and link layer issues, and satellite radio propagation.

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Mr. Kyrgiazos is a member of the Institution of Engineering and Technology (IET) and a member of the Technical Chamber of Greece (TEE).

Barry G. Evans (M’86–SM’98) until 2009 was Pro Vice Chancellor for Research and Enterprise at the University of Surrey and Director of the Centre for Communication Systems Research which is a 150 strong postgraduate research centre. He has a personal research background in satellite and mobile communications, researching in speech coding, radio propagation, advanced physical layers and cognitive radio with over 500 research publications and three text books to his name. He now runs a number of research projects in satellite communications with

ESA and industry and leads the Surrey part of the UK-India network of excellence in next generation networks. He also leads the communications platform in Surrey’s Knowledge Transfer Network. He is Editor of the International Journal of Satellite Communications, an OFCOM spectrum advisory board member, Chair of the steering committee of SatNEx, an EU/ESA network of excellence, a member of the steering council of the Integral Satellite Initiative and Director of a spin off company Mulsys Ltd. Prof. Evans is a Fellow of the Royal Academy of Engineering.

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Effectiveness of Relay MIMO Transmission by Measured Outdoor Channel State Information Kentaro Nishimori, Naoki Honma, Tomoki Murakami, and Takefumi Hiraguri

Abstract—This paper investigates the effectiveness of the multiple input multiple output (MIMO) transmission with the aid of relay nodes by using measured outdoor channel state information (CSI) for the source, relay, and destination which are used in cooperative transmission. Single/multi-user MIMO (SU/MU-MIMO) systems have attracted much attention as the technology enhances the channel capacity with a limited frequency band. In this paper, cooperative transmission using the relay station is applied to SU/MU-MIMO systems: Relay MIMO transmission. Although the performance of relay MIMO transmission is affected by the actual propagation environment, the performance has not yet been investigated using measured propagation channel data in outdoor scenarios. In this paper, we demonstrate that the channel capacity with the relay MIMO transmission can be improved compared to the conventional MIMO transmission without the relay nodes, especially in multi-user scenarios. Moreover, orthogonal polarization is introduced and its effectiveness is shown in further improving the channel capacity of relay MIMO transmission. Index Terms—Cooperative transmission, heterogeneous pathloss condition, orthogonal polarization, relay station, single/multi-user MIMO (SU/MU-MIMO).

I. INTRODUCTION

D

UE to the recent popularity of mobile phones and broadband wireless local area network (W-LAN), the multiple-input multiple-output (MIMO) technique is incorporated into these broadband wireless systems using OFDM to achieve higher transmission speeds without expanding the frequency band [1], [2]. Moreover, multiuser MIMO (MU-MIMO) systems have recently attracted much attention as the technology enhances the total system capacity by generating a virtual large MIMO channel between a base station and multiple terminal stations [3]. From the viewpoint of decreasing the transmission power and expanding the service area, cooperative transmission using relay stations was investigated [4]–[7]. In cooperative transmission, the source (S), destination (D), and relay (R) share their resources in order to forward data, achieving a spatial diversity gain against fading. In this paper, we incorporate MIMO or MU-MIMO techniques into cooperative transmission. In other words, MIMO transmission using the relay station, Relay MIMO transmission is effective from the viewpoint of frequency utilization and spatial diversity. Manuscript received June 01, 2010; revised March 20, 2011; accepted May 11, 2011. Date of publication December 06, 2011; date of current version February 03, 2012. This work was supported in part by KAKENHI, Grant-in-Aid for Young Scientists (B) 22760272. The authors are with Niigata University, Niigata 950-2181, Japan (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173434

Since cooperative transmission is a recently developed technique, detailed propagation characteristics have not yet been thoroughly investigated in conventional studies, especially on outdoor scenarios. For example, the path loss conditions are assumed to be the same in the S-D, S-R, and R-D links in [6]. Moreover, R is assumed to be located between S and D. However, the conditions regarding antenna deployment for S, D, and R are different in actual scenarios. The relay stations must be deployed at high locations in order to ensure line of sight (LOS) environment. The base stations should be basically located on the rooftops of buildings. On the other hand, the antenna heights of the terminal stations are usually low compared to that of the surrounding buildings. Hence, the performance of relay MIMO transmission is greatly affected by the actual propagation environment due to the different conditions for S, R, and D. Although there are a lot of measurement results regarding MIMO/MU-MIMO transmission in outdoor environment (for example, [8]–[11]), the performance of relay MIMO transmission has not been thoroughly studied using measured propagation channel data in outdoor scenarios. In this paper, we evaluate the channel capacity of MIMO transmission with a relay station considering actual measured channel state information (CSI) for the S-D, S-R, and R-D links. First, the channel capacity is derived using relay MIMO transmission, and the influence of the relay MIMO transmission on the channel capacity is clarified when heterogeneous path loss conditions are given for the S-D, S-R, and R-D links. Then, we compare the channel capacities between conventional and relay MIMO transmissions using the measured CSI. Since MIMO transmission with orthogonal polarization can reduce the spatial correlation [9], [11], particularly between the relay and base stations, the effectiveness using orthogonal polarization is clarified. The remainder of this paper is organized as follows. In Section II, we derive the channel capacity when employing the relay MIMO transmission and discuss the influence from the heterogeneous path loss conditions. Section III describes the employed measurement environment. In Section IV, the effectiveness of the relay MIMO transmission in an actual outdoor scenario is demonstrated. Moreover, the effect of orthogonal polarization, which reduces the spatial correlation, is investigated in Section IV. II. CHANNEL CAPACITY IN THE RELAY MIMO TRANSMISSION A. Derivation of Channel Capacity Fig. 1 shows the transmission scheme for the relay MIMO. We extend the scheme in [4] to MIMO transmission. In this paper, R is assumed to decode and forward the signals transdenote the index mitted by S using two time slots. Let

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Fig. 2. Analysis model for Model A.

transmission rate in time slots 1 and 2, respectively, the sum rate, , must satisfy the condition below. (5) (6) denotes the noise power. In order for D to decode the where signal without bit error, the achievable transmission rate in time slot , must satisfy

Fig. 1. Transmission scheme in the relay MIMO. (a) Slot 1, (b) Slot 2.

number of the time slot. As shown in Fig. 1, S transmits signals to R and D in time slot 1. , and denote the number of antennas at S, R, and D, respectively, as shown in Fig. 1. When the signal transmitted by S in time slot 1 is represented by , the received signals at D and R, and , respectively, in time slot 1 are given by (1) and (2) denotes the average signal energy, when A where and B denote the transmitter and receiver, respectively. represents the channel matrix, where the average power is equal to one. denotes the Gaussian noise at receiver A. Next, in time slot 2, both S and R transmit signals to D. Similar to time slot 1, the signal received by D in time slot 2, is given by (3) where we assume that the number of antennas at S and R staand are same. When using (1)–(3), the received tions, signals at D in time slots 1 and 2, is expressed as

(4) denotes the transmit signals by S in where time slots 1 and 2. In the following, the channel capacity for the relay MIMO is derived. The idea in [4] can be extended when considering MIMO transmission. When and denote the achievable

(7) (8) Moreover, in order for R to decode the signal without bit error, the achievable transmission rate in time slot 1, , must satisfy (9) Since the sum rate, , must satisfy the capacity for the reception at R and D, the sum rate is constrained by (10) (more details are given in [4]). Uplink transmission is considered in this paper. For the multiuser transmission, we assume that all the user terminals are regarded as S. The total number of antennas for the multiple source stations are set to be in Fig. 1. Similarly, when considering the multiple relay stations, the total number of antennas at all the relays are set to be in Fig. 1. B. Basic Characteristics Considering Heterogeneous Pathloss Conditions In this subsection, the channel capacity for the relay MIMO derived in Section II.A is evaluated by computer simulation. Fig. 2 and 3 show the models (Model A and B) used in the evaluation. The main parameters in Model A and B are shown in Table I. Condition is assumed in Fig. 2 and this condition is the same with that in [4]. R is located at the center between S and D in Model A. The path loss coefficient : Path loss, : Distance between the transmitter and receiver) is the same and is set to 3.5 for the S-D, S-R, and R-D links in Model A. is a typical value for mobile communications. It is clear that the channel capacity is maximized for condition if the path loss conditions are the same for S-R and

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Fig. 3. Analysis model for Model B.

TABLE I CONDITIONS FOR MODEL A AND B

TABLE II PATH LOSS MODEL WITH HETEROGENEOUS PATH LOSS CONDITIONS

Fig. 4. Channel capacity using the relay MIMO versus CNR. (a) Model A, (b) Model B.

R-D when considering 2-hop transmission without S-D transmission. However, R cannot be located at the center between S and D when actual installation space regarding the antennas is considered. Moreover, since the antenna heights are different among S, R and D, heterogeneous path loss conditions [12], [13] between the S-D, S-R, and R-D links must be considered in actual scenarios. In order to evaluate the difference with the conventional model such Model A, Model B is regarded as a realistic model in a micro/macrocell environment as shown in Table I. The path loss coefficient for S-D, in Model B is also set to 3.5. In order to express the path loss coefficient for R-D, , Ichitsubo model is adopted [12], [13]. Table II presents parameters of Ichitsubo’s model. and [dB] are functions of the antenna heights of the transmitter and receiver as shown in Table II. This model was obtained considering many measurements, which were carried out with 2 GHz band in urban areas in Japan. Moreover, the path losses obtained by the measurements and the equation in Table II agree well with each other, when the transmissions of Tx 32 [m]—Rx 32 [m], Tx 32 [m]—Rx 15 [m], and Tx 32 [m]—Rx 2 [m] are considered [12], [13]. Here, Tx A [m]—Rx B [m] represent the antenna heights of the transmitter and receiver at A and B [m], respectively. becomes 3.0 when the antenna heights in Table I are used. is changed due Since the path loss coefficient for S-R, to path visibility which discriminates whether an environment is LOS or Non-LOS (NLoS) [14], we assume that ranges from two to six in Model B. For the sake of simplicity, the channel responses for S-D, S-R, and R-D are assumed to be

i.i.d., i.e., Rayleigh fading. are set to four, respectively. Fig. 4 shows the channel capacity versus the Carrier to Noise power Ratio (CNR) at S-D link. The number of trials is 10 000 and the channel capacity in Fig. 4 is calculated by averaging all the data. The channel capacity of single input single output (SISO) is plotted for reference. Coop and S-D in Fig. 4 represent the channel capacity for the relay MIMO and transmission at S-D link without the aid of relay station, respectively. Fig. 4 shows that the channel capacity for the relay MIMO using Model B is higher than that using Model A. The improvements in the channel capacity when using the relay MIMO transmission (Coop in Fig. 4) compared to that for the conventional MIMO transmission without the relay station (S-D in in Fig. 4) in Models A and B are 3.7 and 6.0 bits/s/Hz, respectively, when ranges from 2 to 4: the effectiveness of the relay MIMO is observed when considering actual propagation parameters. This is because the path loss at R-D link in Model B is less than that in Model A. On the other hand, the channel capacity using the relay MIMO transmission is severely degraded when is greater than or equal to five. Since the channel capacity using the relay MIMO transmission is denoted by (10), the total channel capacity is affected by the channel capacity at S-R link, , when is small. Fig. 5 shows the channel capacity versus the path loss coefficient at S-R link, . The figure shows that the channel capacity is suddenly degraded when becomes greater than 4.3 in Coop of Model B. Moreover, the channel capacity for the relay MIMO (Coop) is lower than that for conventional MIMO (S-D) when is greater than 4.9. Here, equals 4.1, if the

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Fig. 5. Channel capacity versus pathloss coefficient stations.

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between S and R

Ichitsubo model is used at S-R link: could be assumed to be less than 4. Hence, we indicate the effectiveness using the relay MIMO transmission if the pathloss co-efficient at S-R link is the typical value in a realistic propagation environment. However, how the pathloss conditions change depends on the propagation environment. We show the results regarding CSI measurement and clarify the effectiveness of the relay MIMO transmission in an actual outdoor environment hereafter. III. MEASUREMENT ENVIRONMENT Fig. 6 shows the measurement environment. The measurements were carried out at the central area of Yokkaichi city in Japan, where is assumed to be a typical urban area. As shown in Fig. 6, relay stations are located at six points (R1 to R6 in Fig. 6. We assume uplink MIMO transmission using R1 to R6. The transmitters and receivers are equipped at R, because R must transmit the signal to D and receive the signal from S. The antenna height on the R station is changed from 3 to 9 m. The transmitters are equipped at S shown in Fig. 6. The antenna height on the vehicle is 2.2 m. The receivers at D are equipped at the site on the steel tower. The antenna height on the steel tower is 50 m. Table III shows the distance of S-D and R-D links. represents the index number for R and S in Fig. 6. As shown in Fig. 6, S moved near R at the speed of 30 to 50 km/h. Hence, we assumed that S , R and D are a pair for the evaluation when considering relay MIMO transmission. S (Max.)/S (Min.) denotes the maximum/minimum distance of S-D link, respectively, as shown in Table III. The parameters for the measurement to obtain the CSI are given in Table VI. The pathloss co-efficient in Section II.B is not used for the measurement. The transmit power by S and R is constant and its value is 2 [W]. Hence, not only the small fading effect but also influence due to the path loss are included in the measurement results. We measured the MIMO channel matrix for the S-D, S-R, and R-D links. Data were obtained at the interval of 50 ms in each measurement course. The location of R is selected so that the propagation environment of R-D link is LoS. For S-D links, the propagation environment is regarded as NLoS except for the neighborhood around D because there are 15 to 40 m high buildings around the measurement course. The CSI is obtained by transmitting the OFDM signals. Short and long preamble signals are used for the timing synchronization and CSI estimation, respectively. The channel capacity for the relay MIMO is obtained using the CSI and equations derived in Section II.

Fig. 6. Measurement environment.

TABLE III DISTANCE OF S-D AND R-D LINKS [M]

The antenna configurations for S, R and D are represented in Fig. 7. As shown in Fig. 7, the number of antennas at S, R and D, , and , are set to 4, 4, and 8, respectively. The array element spacing at S is 0.5 wavelengths. The array element spacing at R and D is 1.0 wavelength. A circular array is used for S, in order to reduce the dependency on the angle from S. Linear arrays are used at R and D. Omni-directional antennas are used at S and R. The geometry of the dual polarized subarray at D is shown in Fig. 8 [11]. Eight vertical and horizontal dipoles are arranged vertically. Each polarization array has an individual RF feeder. A reflector is placed at the backside of the element for suppressing the backlobe. The actual gain of the subarray is 14.5 dBi for both polarizations. The 3 dB beamwidth of this antenna is 90 degrees for both polarizations. The cross-polarization discrimination (XPD) between vertically and horizontally polarized antennas is 24.5 dB in the broadside direction. In Sections IV.A and IV.B, we use sleeve antennas as vertically polarized antennas. We compared the channel capacity due to the difference in polarization in Section IV.C, i.e., vertical, horizontal, and vertical/horizontal polarizations. A slot antenna is used as a horizontally polarized antenna. Table IV shows the combination of antennas which are used for S and R in Fig. 7. The numbers of antennas which are used at D in Fig. 7 are shown in Table V. Fig. 9 shows the cumulative density function (CDF) of the CNR when S-D, S-R and R-D transmissions are considered. We created a no-signaling period with the interval of 320 sec to

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Fig. 7. Antenna configurations for S, R, and D.

Fig. 9. CNR characteristics. Fig. 8. Geometry of antenna at D.

IV. EFFECTIVENESS OF THE RELAY MIMO TRANSMISSION USING MEASURED CSI

TABLE IV COMBINATION OF ANTENNAS FOR S AND R IN FIG. 7

TABLE V NUMBERS OF ANTENNAS USED AT D IN FIG. 7

measure the noise power. We used same receivers at R and D. dBm/Hz ( The measured noise power was [dBm] at 20 MHz). The CNR is calculated as follows: (11) where [dBm] is the received power. The vertical polarization is used and all the measured data are considered in Fig. 9. Fig. 9 shows that the CNRs for the R-D and S-R links are much higher than that for the S-D link because there is basically a LOS for the R-D and S-R links. Hence, we expect that the channel capacity to be improved by using the relay MIMO transmission.

A. Single-User Case In this section, the effectiveness of MIMO transmission employing the relay station is demonstrated using measured CSIs when considering a single user MIMO (SU-MIMO) scenario. Fig. 10 denotes the channel capacity due to the difference in antenna height of R. The values for , and are all four. For comparison, the channel capacity of the conventional MIMO transmission without the aid of relay station (S-D in Fig. 10) is plotted in the figure. Fig. 10 shows that there is a 4.5 bits/s/Hz channel capacity improvement by using the relay MIMO transmission (Coop in Fig. 10) compared to that when using the conventional MIMO transmission (S-D). When we focus on the difference due to the difference in the antenna height of R, the channel capacity when m is slightly degraded compared to that when or 9 m, because the or 9 LOS environment is guaranteed at R-D link when m. Hence, the antenna height of R, is fixed at 9 m hereafter. The channel capacity versus the transmit power is plotted in Figs. 11 and 12. Since the transmit power at the terminal station (S) is generally set to be lower than that at the base station (D), it is very important to evaluate the effect of using R denotes the power when changing the transmit power. ratio between S and R in Figs. 11 and 12. Although the actual transmit power by R is identical with that by S in the measureis changed when the post processing is employed. ment, Figs. 11 and 12 take into account all the measured courses and

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Fig. 10. Channel capacity due to difference in antenna height of R station (SU). MIMO, Fig. 13. Measurement scenario for multi-user case (3-user case).

the number of transmit antennas is equal to that of the receiver antennas. B. Multi-User Case

Fig. 11. Channel capacity versus transmit power (SU-MIMO, ).

Fig. 12. Channel capacity versus transmit power (SU-MIMO, ).

10% and 50% of the CDF are shown in these figures. In Fig. 10, , and are 4, 4, and 4, and in Fig. 9 they are 2, 2, and 8, respectively. Figs. 11 and 12 show that a higher channel capacity is obtained using the relay MIMO transmission compared to that for using the conventional MIMO transmission, regardless of the transmission power. When ( , we observe a 4 bits/s/Hz and 1 bit/s/Hz improvement in the channel capacity. Similarly, when ( , we observe a 1 bit/s/Hz and 0.8 bits/s/Hz improvement in the channel capacity. Hence, we find that the relay MIMO is the most effective when the transmit powers between the R and S stations are almost the same. Moreover, regarding the number of antennas, the effect of the relay MIMO is maximized when

Next, we focus on a multiuser scenario. Fig. 13 shows the measurement scenario for multi-user case. 3-user case is described in Fig. 13 as an example. For the evaluation on the multiuser scenario, , and are set to 2, 2, and 8, respectively. In other words, a four-user evaluation is possible if the total number of transmit antennas at S or R is equal to the number of antennas at D. The number of source stations (users) is assumed to be equal to the number of relay stations. As shown in Fig. 6, S moves near R , and S and R are a pair in MU-MIMO relay transmission. Here, when the number of users is , the source and relay stations with is picked up from S (R in Fig. 6. 3 users (sources) and relays are selected in Fig. 13. We assume multiple S access multiple R (multiple Coop), and multiple S accesses D (multiple S-D) at the same time in Fig. 6. We consider all possible combinations of multiple S (R ) and D for the number of users. Hence, there are 15, 20 and 15 combinations when is set to be two, three and four, respectively. The total number of antennas on S and R for the channel capacity evaluation are and , respectively. The different path loss condition is considered for each user and CNRs for each user are different, because the transmit power is constant (2W). Fig. 14 shows the CDF for multi-access channel (MAC) capacity. All the measured data were included in this figure. Fig. 14 shows that the improvement in the channel capacity when using the relay MIMO (Coop in Fig. 14) is higher compared to that when using the conventional MIMO (S-D in Fig. 14) when the number of users is increased. In particular, an improvement of 8 bits/s/Hz in the channel capacity when using the relay MIMO is obtained when , compared to that when using the conventional MIMO. Fig. 15 shows the MAC channel capacity versus the number of users. The 10% and 50% values of the CDF are plotted in this figure. Fig. 15 shows that the channel capacity using relay stations (Coop in Fig. 15) can be improved compared to when using the conventional MIMO transmission, when the number of users is increased. Although the diversity effect exists for the single user case in the conventional MIMO transmission (S-D

NISHIMORI et al.: EFFECTIVENESS OF RELAY MIMO TRANSMISSION BY MEASURED OUTDOOR CHANNEL STATE INFORMATION

Fig. 14. Channel capacity considering MU-MIMO transmission.

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Fig. 16. CNR characteristics between V-Pol. and H-Pol.

TABLE VI MEASUREMENT CONDITIONS

Fig. 15. Channel capacity versus the number of users.

in Fig. 15), the degree of improvement in the channel capacity is abated when the number of users increases. On the other hand, the relay MIMO improves the channel capacity in proportion to the number of users. As a result, we find that there is a 1.5 fold improvement in the channel capacity when considering a 4-user case. C. Effectiveness Using Orthogonal Polarization In this subsection, we demonstrate the effectiveness when using orthogonal polarization. S2(R2), S5(R5), and S6(R6) in Fig. 6 are used as the locations for S and R when considering a comparison among vertical, horizontal, and orthogonal (vertical and horizontal) polarizations. Fig. 16 shows the CDF of the CNR when considering S2(R2), S5(R5), and S6(R6). The CNRs when employing vertical and horizontal polarization are plotted in Fig. 16. The figures show that the CNR for vertical polarization is slightly higher than that for horizontal polarization for the S-D, S-R and R-D links. Tables VII–IX show a channel capacity comparison among vertical polarization (V.-Pol.), horizontal polarization (H.-Pol.) and orthogonal polarization (V. and H.-Pols.) when considering SU-MIMO transmission. The results for CDF=10% are given in these tables. The numbers of antennas for S, R and D are given in each table. Tables VII–IX show that the channel capacity using V.-Pol is slightly higher than those using H.-Pol and V.H.-Pol., when the conventional MIMO transmission (S-D in Tables VII–IX) is considered, because the received CNR with V.-Pol. is slightly higher than that with H.-Pol. Next, we focus on the channel capacity for the S-R and R-D links in Tables VII–IX. Tables VII–IX show that the channel

TABLE VII CHANNEL CAPACITY COMPARISON ( [BIT/S/HZ])

, CDF=10%

TABLE VIII CHANNEL CAPACITY COMPARISON ( [BIT/S/HZ])

, CDF=10%

TABLE IX CHANNEL CAPACITY COMPARISON ( [BIT/S/HZ])

, CDF=10%

capacity using V.H.-Pol is higher than those using V.-Pol. and H.-Pol., when considering the S-R and R-D links. In order to examine the reason, we present spatial correlation comparisons among V.-Pol., H.-Pol., and V.H.-Pol. for the S-D, S-R, and R-D links, respectively in Fig. 17. The figure shows the spatial correlation is high when using V-Pol. and H-Pol. Particularly, the spatial correlation for the R-D link when using V-Pol. and H-Pol. exceeds 0.95 with a very high probability. On the other hand, the

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Fig. 18. MAC channel capacity comparison among V., H. and V.H.-Pols (S-D, CDF=10%).

Fig. 17. Spatial correlation comparison.

spatial correlation is reduced by using V.H.-Pol. Hence, orthogonal polarization is effective in environments where the spatial correlation is very high when using a single polarization. Finally, we focus on the channel capacity for relay MIMO (Coop in Tables VII–IX). Tables VII–IX show that the channel capacity of Coop is higher than that for the S-D link. Hence, the relay MIMO transmission is effective regardless of the antenna polarization. On the other hand, the channel capacity is almost the same between V-Pol. and V.H.-Pol. Fig. 18–20 shows the relationship between users and the MAC channel capacity due to the difference of the polarization. The conditions for evaluation are same with those in IV.C. The results for % are shown in the figure. The figure shows that the improvement in the channel capacity is higher when using the relay MIMO (Coop in Fig. 19) compared to that when using conventional MIMO (S-D in Fig. 18), when the number of users is increased. In particular, a 4 to 6 bits/s/Hz improvement in the channel capacity when using the relay MIMO is obtained when , compared to that when using conventional MIMO. When considering conventional MIMO transmission (S-D), the V-Pol. can obtain the highest channel capacity in a multiuser scenario. On the other hand, the channel capacity with the V.H.-Pol. is higher than that with the V-Pol., when considering the relay MIMO transmission (Coop). Fig. 20 shows that the V.H.-Pol. can obtain the highest channel capacity for the S-R and R-D links. Hence, we confirmed that vertical and horizontal polarization can contribute to further improving the channel capacity in the relay MIMO transmission. V. CONCLUSION In this paper, we investigated the effectiveness of the relay MIMO transmission when considering actual measured CSI for

Fig. 19. MAC channel capacity comparison among V., H. and V.H.-Pols (Coop, CDF=10%).

Fig. 20. MAC channel capacity comparison among V., H. and V.H.-Pols (S-R, R-D, CDF=10%).

the S-D, S-R, and R-D links. First, we clarified that the difference in path loss conditions among the S-D, S-R, and R-D links is very important in evaluating relay MIMO transmission. Then, we evaluated the channel capacity in a single-user case using the measured CSI. The effect on the relay MIMO is shown to be maximized when the number of transmitting antennas is equal to that for the receiving antennas. Moreover, the effectiveness of the relay MIMO in a multiuser scenario is shown. We found a 1.5 fold improvement in the channel capacity when using the relay MIMO compared to that for conventional MIMO without the aid of relay stations, when considering a 4-user case. Finally, it is clarified that the use of orthogonal polarization contributes to further improving the channel capacity in a multiuser scenario compared to when using single polarization, because the spatial correlation is reduced by the relay MIMO transmission with orthogonal polarization, especially between R-D links.

NISHIMORI et al.: EFFECTIVENESS OF RELAY MIMO TRANSMISSION BY MEASURED OUTDOOR CHANNEL STATE INFORMATION

ACKNOWLEDGMENT The authors thank Y. Makise, M. Ida, and Dr. M. Yoshikawa of NTT Advanced Technology Corporation for their help in conducting the outdoor field measurements.

REFERENCES [1] G. L. Stuber, J. R. Barry, S. W. Mclaughlin, Y. Li, M. A. Ingram, and T. G. Pratt, “Broadband MIMO-OFDM wireless communications,” Proc. IEEE, vol. 92, pp. 271–294, Feb. 2004. [2] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Personal Commun., vol. 6, pp. 311–335, 1998. [3] Q. H. Spencer, C. B. Peel, A. L. Swindlehurst, and M. Haardt, “An introduction to the multi-user MIMO downlink,” IEEE Commun. Mag., vol. 42, pp. 60–67, Oct. 2004. [4] R. U. Nabar, H. Bolcskei, and F. W. Kneubuhler, “Fading relay channels: Performance limits and space-time signal design,” IEEE J-SAC, vol. 22, no. 6, pp. 1099–1109, 2004. [5] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Info. Theory, vol. 50, no. 12, pp. 3062–3080, Dec. 2004. [6] K. Yamamoto, H. Maruyama, T. Shimizu, H. Murata, and S. Yoshida, “Spectral efficiency of fundamental cooperative relaying in interference-limited environments,” IEICE Trans. Commun., vol. E91-B, no. 8, pp. 2674–2682, 2008. [7] K. Hayashi, K. Shirai, T. Himsoon, W. P. Siriwongpairat, A. K. Sadek, K. J. R. Liu, and H. Sakai, “Optimum relay position for differential amplify-and-forward cooperative communications,” in Proc. Wireless Personal Multimedia Communications (WPMC 2006), Sep. 2006, pp. 766–770. [8] V. Erceg, P. Soma, D. S. Baum, and S. Catreux, “Multiple-input multiple-output fixed wireless radio channel measurements and modeling using dual-polarized antennas at 2.5 GHz,” IEEE Trans. Wireless Commun., vol. 3, no. 6, pp. 2288–2298, Nov. 2004. [9] K. Nishimori, Y. Makise, M. Ida, R. Kudo, and K. Tsunekawa, “Channel capacity measurement of 8 2 MIMO transmission by antenna configurations in an actual cellular environment,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3285–3291, Nov. 2006. [10] H. Taoka, K. Dai, K. Higuchi, and M. Sawahashi, “Field experiments on ultimate frequency efficiency exceeding 30 Bit/Second/Hz using MLD signal detection in MIMO-OFDM broadband packet radio access,” in Proc. IEEE VTC2007-Spring, Apr. 2007, pp. 2129–2134. [11] N. Honma, R. Kudo, K. Nishimori, Y. Takatori, A. Ohta, and S. Kubota, “Antenna selection method for terminal antennas employing orthogonal polarizations and patterns in outdoor multiuser MIMO system,” IEICE Trans. Commun., vol. E91-B, no. 6, pp. 1752–1759, Jun. 2008. [12] K. Nishimori, R. D. Taranto, H. Yomo, P. Popovski, Y. Takatori, R. Prasad, and S. Kubota, “Spatial opportunity for cognitive radio systems with heterogeneous path loss conditions,” in Proc. IEEE 65th Vehicular Technology Conf. (VTC2007-Spring), Apr. 2007, pp. 2631–2635. [13] S. Ichitsubo, T. Furuno, T. Nagato, T. Taga, and R. Kawasaki, “2 GHz-band propagation loss prediction in urban areas; antenna heights ranging from ground to building roof,” IEICE Tech. Rep., A., pp. 96–15, May 1996. [14] Y. Ito, , Y. Hosoya, Ed., “Radiowave propagation handbook,” in The Distribution of Height and Width Of Buildings. Japan: Realize Inc., 1999, pp. 342–349.

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Kentaro Nishimori received the B.E., M.E., and Ph.D. degrees in electrical and computer engineering form Nagoya Institute of Technology, Nagoya, Japan, in 1994, 1996 and 2003, respectively. In 1996, he joined the NTT Wireless Systems Laboratories, Nippon Telegraph and Telephone Corporation (NTT), Japan. He was a Senior Research Engineer at NTT Network Innovation Laboratories. He is now an Associate Professor in Niigata University. He was a Visiting Researcher at the Center for Teleinfrastructure (CTIF), Aalborg University, Aalborg, Denmark, from Feb. 2006 to Jan. 2007. His main research interests are spatial signal processing including MIMO systems and interference management techniques in heterogeneous networks. Prof. Nishimori is a senior member of IEICE. He received the Young Engineers Award from the IEICE of Japan in 2001, Young Engineer Award from IEEE AP-S Japan Chapter in 2001, Best Paper Award of Software Radio Society in 2007 Distinguished Service Award from the IEICE Communications Society in 2005, 2008 and 2010, and the Best Paper Award of IEICE in 2011. He was an Associate Editor for the Transactions on Communications for the IEICE Communications Society from May 2007 to May 2010 and Assistant Secretary of Technical Committee on Antennas and Propagation of IEICE from June 2008 to May 2010.

Naoki Honma received the B.E., M.E., and Ph.D. degrees in electrical engineering from Tohoku University, Sendai, Japan in 1996, 1998, and 2005, respectively. In 1998, he joined the NTT Radio Communication Systems Laboratories, Nippon Telegraph and Telephone Corporation (NTT), Japan. He is now an Associate Professor in Iwate University. His current research interest is planar antennas for high-speed wireless communication systems. Prof. Honma s a member of IEICE. He received the Young Engineers Award from the IEICE of Japan in 2003, the APMC Best Paper Award in 2003, and the Best Paper Award of IEICE Communication Society in 2006, respectively.

Tomoki Murakami received the B.S. degree in electrical, electronics and computer engineering and the M.E. degree in electrical engineering and bioscience from Waseda University, Tokyo, Japan, in 2006 and 2008, respectively. In 2008, he joined NTT Network innovation Laboratories, Nippon Telegraph and Telephone Corporation (NTT), Yokosuka, Japan. His current research interests include multiuser MIMO systems and resource allocation.

Takefumi Hiraguri received the M.E. and Ph.D. degrees from the University of Tsukuba, Ibaraki, Japan, in 1999 and 2008, respectively. In 1999, he joined the NTT Access Network Service Systems Laboratories, Nippon Telegraph and Telephone (NTT) Corporation. He is now an Associate Professor in Nippon Institute of Technology. He has been engaged in research and development of high speed and high communication quality wireless LANs systems. Prof. Hiraguri is a member of IEICE.

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Single and Multi-User Cooperative MIMO in a Measured Urban Macrocellular Environment Buon Kiong Lau, Senior Member, IEEE, Michael A. Jensen, Fellow, IEEE, Jonas Medbo, and Johan Furuskog

Abstract—We study the potential benefits of cooperative multiple-input multiple-output signaling from multiple coherent base stations with one or more mobile stations in an urban macrocellular environment at 2.66 GHz. The analysis uses fully-coherent measurements of the channel from three base stations to a single mobile station equipped with four antennas. The observed channels are used to explore the gains in capacity enabled by cooperative base station signaling for point-to-point and multi-user communications. The analysis shows that for point-to-point links, the average capacity for cooperative signaling is 53% higher than that achieved for a single base station. For downlink and uplink communication with three mobile users, cooperative signaling yields average sum rate increases of 91% and 63%, respectively. Index Terms—Cooperative systems, multiple-input tiple-output (MIMO) systems, multiuser channels.

mul-

I. INTRODUCTION

W

HILE multiple-input multiple-output (MIMO) technology has demonstrated the potential for offering significant improvements in spectral efficiency for wireless communication, realization of these gains depends on the communication environment. For example, in cellular systems, compact device sizes at the mobile station (MS) limit the number of antennas that can observe independent fading [1]–[3]. At the base station (BS), the elevated position and sectorized nature of the antennas lead to limited observed angular spread, again limiting the benefit of multiple antennas for reasonable inter-element spacing. While work has been accomplished to limit coupling and improve performance for compact element spacing at the MS [2], less work has addressed the issue of limited angle spread at the BS. One potential solution to this problem, however, involves using multiple BS sites working cooperatively, a solution that also potentially enables significant benefit in terms of interference control in multi-user signaling [4]–[6]. At its simplest Manuscript received June 16, 2010; revised September 09, 2011; accepted October 12, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. This work was supported in part by Telefonaktiebolaget LM Ericssons Stiftelse för Främjande av Elektroteknisk Forskning, VINNOVA under Grant 2008-00970 and in part by the U. S. Army Research Office under the Multi-University Research Initiative (MURI) Grant # W911NF-07-1-0318. B. K. Lau is with the Department of Electrical and Information Technology, Lund University, Box 118, SE-221 00 Lund, Sweden (e-mail: [email protected]). M. A. Jensen is with the Electrical and Computer Engineering Department, Brigham Young University, Provo, UT 84602 USA (e-mail: [email protected]). J. Medbo and J. Furuskog are with Ericsson Research, Ericsson AB, SE-164 80 Stockholm, Sweden (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173443

level, such coordination involves scheduling based on awareness of interference created by multiple BS sites [7], although more sophisticated cooperation is also possible. For example, the benefit of cooperative BS communication has been studied in the context of determining the channel and shadowing correlation properties for multiple BS sites and a single MS [8], [9], although [9] did not achieve coherence across the multiple BSs and the equipment in [8] led to phase uncertainties in the measurements. The pioneering work in [10], while using incoherent measurements from multiple BSs, uses a statistical analysis based on the low correlation between the channels from the different BSs [11] to allow exploration of the point-to-point and multi-user capacity assuming BS coherence in a campus environment at 5.2 GHz. Also, recent time-synchronized multi-BS and multi-MS measurements demonstrate the associated interference characteristics and are used to discuss some implications of cooperative MIMO signaling for multiple users in a limited fashion [12], although here the results are for a microcellular environment. More recent work has focused on coherent channel measurements either from multiple BS sectors or from multiple BSs [13]. For example, the work in [14] develops cooperative communication for MIMO downlink communication and demonstrates its performance using coherent measured channels from two sectors at the same BS site. Some experimental data from multiple BSs in a cooperative environment are also reported in [15], although the focus of this work is on comparing the behaviors of channel eigenvalues predicted using ray tracing with those observed in the channel measurements. Since the initial submission of the present paper, new results have appeared in the literature showing the impact of BS cooperation in several scenarios based on coherent multi-cell measurements [16], [17]. This paper reports on the analysis of fully-coherent measurements from three BS sites to a single MS in a macrocellular environment, measurements that complement those that have been recently reported. The observed channels are first used to explore the gains achieved with cooperative MIMO signaling to a single user. This analysis shows that channel gain imbalance plays a dominant role in determining the measured multi-BS capacity, consistent with conventional understanding, and that BS cooperation leads to an increase in average capacity of 53% over that achieved using a single BS. In places where all base stations contribute nearly equal signal power to the MS, this increase in average capacity can exceed 100%. We then turn our attention to the performance of cooperative MIMO for multi-user communications involving two and three MSs for both the downlink or broadcast channel (BC) and the uplink or multiple access channel (MAC) [5] based on different signaling strategies over the observed channels. This analysis shows that cooperative

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LAU et al.: SINGLE AND MULTI-USER COOPERATIVE MIMO IN A MEASURED URBAN MACROCELLULAR ENVIRONMENT

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TABLE I SPECIFICATIONS FOR THE ERICSSON CHANNEL SOUNDER

Fig. 1. Birds eye view of measurement environment.

MIMO signaling can provide an average multi-user throughput that is up to 91% higher than that achievable using more traditional multiple-access strategies under favorable channel conditions. One important area within this field of cooperative BS communication is the development of models that can predict the achievable performance. Some of the findings in this work demonstrate that traditional channel models can explain the key behaviors observed in cooperative BS channels provided that the models include key properties of the link gains, which is a useful observation for future channel model development. However, a key challenge is knowing the typical distribution of these link gains in practical implementation scenarios and validating any developed models against measured observations. The measurements reported here therefore provide critical understanding that will assist in the development of models appropriate for cooperative BS communication. II. MEASUREMENT SETUP The considered urban macrocell environment is the built up area within Kista (also called “Mobile Valley”), Stockholm, Sweden, depicted in Fig. 1. Three BS sites were selected that emulate a realistic cellular deployment topology. At each BS, a single antenna mounted a few meters above the average rooftop level of approximately 25 m transmits a linearly-polarized (45 from vertical) signal. The main lobe of each antenna pattern is pointed downwards between 6 and 8 from horizontal and approximately towards the centroid of the triangle formed by the three BS sites. The MS consists of two dipole and two loop antennas mounted on the top of a measurement van as a square array with an inter-element spacing of approximately 30 cm, which is 2.6 wavelengths at the excitation frequency. Measurement of the channel between all three BS and four MS antennas is accomplished using the Ericsson channel sounder that is based on a prototype for LTE [18] but with a custom frame structure and rate. A single transmit unit generates orthogonal frequency-division multiplexing (OFDM) channel sounding symbols that are distributed to the antennas at the three BS sites using RF-over-fiber equipment. To avoid problems with non-orthogonality of the OFDM symbols due

Fig. 2. Location of BSs and routes 1 and 2 – traveled by the MS. Distances in meters from the starting points are indicated by circles and diamonds for routes 1 and 2, respectively.

to the MS mobility, the transmissions from these three BS antennas are time multiplexed at the symbol level. The MS uses four parallel receiver chains to simultaneously down-convert the signals from the four receive antennas. Disciplined rubidium clocks (Stanford Research Systems, PRS10) at the transmitter and receiver provide a highly accurate synchronization (Allan standard deviation less than ) between the BS and the MS. Based on this timing reference, error in the measured propagation distance over all routes is less than 1 m. The resulting system generates a full 4 3 MIMO channel matrix at a rate of 1500 observations per second (based on 0.667 ms probing frames), but because of bandwidth limitations between the system and the storage medium, the observations are stored at a rate of 190 channels per second, providing high spatial resolution given the maximum van speed of 30 km/hr. All of the parameters used in the measurements are provided in Table I. The measurements consist of data from two different routes, each requiring approximately 9 minutes of measurement time. The routes include regions of line-of-sight (LOS), obstructed line-of-sight (OLOS), and non-line-of-sight (NLOS) propagation. The position data for each channel sample is logged using a GPS receiver. Fig. 2 shows the two routes along with markers indicating the distance traveled along each route and the positions of the base stations. The observed signal-to-noise ratio (SNR) computed by extracting the signal and noise powers from

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the channel impulse response is 28 dB on average, with the SNR for the strongest BS-to-MS link always above 22 dB and rarely below 25 dB. We emphasize that the unique feature of this data is the coherence between the measurements from the different BSs, a feature that allows us to determine the impact of BS cooperation. Throughout this discussion, several reference cases will be presented where the network must match a BS to one or more MSs, a pairing that requires some level of cooperation among the BSs. However, when the term cooperative BS is used, it explicitly refers to the case where the BSs jointly and coherently participate in the communication to the MS. III. POINT-TO-POINT SIGNALING (MACRODIVERSITY) We first study the communication between cooperative BSs and a single MS with antennas. Let represent the measured multi-BS (MIMO) channel matrix at the th frequency with th column representing the single-input multiple-output (SIMO) link from the th BS. Each channel matrix is normalized so that the average of the channel power gains for the strongest BS-to-MS link is unity, or where

Fig. 3. Average capacity for the best BS-to-MS link and for cooperative capacity using all BS links for the MS on route 1.

(1) represents the number of frequencies, and indicates a Frobenius norm. If represents the total power transmitted and if the additive noise is modeled as a zero-mean, unit-variance complex Gaussian random process, then with this normalization can be considered the average single-input single-output (SISO) SNR observed on the strongest BS-to-MS link [19]. The point-to-point capacity at each location averaged over the frequencies and assuming that the base stations do not possess channel state information (CSI) is then given by (2) indicates a conjugate where is the identity matrix and transpose. We perform capacity analysis assuming a reference SNR of 10 dB, which is at least 10 dB below the SNR observed in the measurements. Fig. 3 plots the point-to-point capacity performance of the best single BS-to-MS link and the cooperative communication using all BS-to-MS links for route 1 shown in Fig. 2. To achieve improved visual clarity in this plot, the results are smoothed in the displacement variable with a moving average filter over a window of 10 wavelengths and down-sampled. These results demonstrate that BS cooperation provides significant potential capacity performance gain, particularly in regions where the MS lacks a clear view to a single (and therefore dominant) BS, such as for positions between 300 and 700 m or 900 and 1200 m. As a reference, the average capacity achieved when the channel coefficients are modeled as independent identically distributed (i.i.d.) zero-mean complex Gaussian random variables with 10 dB SISO SNR is indicated by the black triangle on the plot,

Fig. 4. Average channel gains for the three BSs and the dominant three for the MS on route 1. eigenvalues of

revealing that the capacity falls short of what is achievable under ideal propagation conditions. Fig. 4 shows the average channel gains for the three BSs as well as averages of the largest three eigenvalues of as a function of position along route 1. Comparison of these results with the capacity in Fig. 3 shows that the dominant three eigenvalues and the capacity are largest when the channel gains are nearly equal since all three BSs can effectively participate in the communication. A similar yet less dramatic capacity increase occurs when two BSs enjoy a strong link to the MS, such as for MS positions between 1700 and 1800 m. The point that cooperative communication provides gains when the MS lacks a dominant link to a single BS can be more emphatically demonstrated using a simple analysis involving two quantities. The first is the ratio of the average cooperative capacity to the average capacity of the best BS-to-MS link. The second is the 3GPP geometry factor, which is defined as the ratio of the power received on the best BS-to-MS link to the sum of the noise and the powers received on the other links [20], [21]. However, we are interested in using this metric to quantify the relative channel gains from each BS to the MS, and

LAU et al.: SINGLE AND MULTI-USER COOPERATIVE MIMO IN A MEASURED URBAN MACROCELLULAR ENVIRONMENT

Fig. 5. Two dimensional pdf of the 3GPP geometry factor and increase in the average cooperative capacity relative to the average capacity of the best BS-to-MS link for all channels in routes 1 and 2.

Fig. 6. CDF of the capacity for the channels on routes 1 and 2 with and without BS cooperation. The CDF for i.i.d. Gaussian random matrices scaled by the average channel gains for each BS and MS are also shown for comparison.

therefore we exclude the noise in our analysis. Mathematically, if (see (1)), then (3) Fig. 5 plots the joint probability density function (pdf) of these two quantities for the combined data from the two routes. This result clearly shows that when the geometry factor is near 0 dB indicating that all three BSs have similar gains to the MS, the cooperative communication provides significant gain. However, when the geometry factor is large indicating a dominant BS-to-MS link, cooperative communication provides little capacity benefit. Fig. 6 plots the cumulative distribution function (CDF) of the average capacities achieved for both the best BS-to-MS link and for cooperative communication using the combined data for both routes, a result that shows significant benefit of BS cooperation. In fact, for this combined data the average capacity resulting from BS cooperation is 53% higher than that achieved using the best BS-to-MS link.

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To investigate the observation made in the analysis of Fig. 5 that gain imbalance in the three BS links plays a critical role in determining the capacity, we scale the elements of the i.i.d Gaussian channel matrix by the gains computed from the observed channels. Specifically, we 1) scale the columns of by the gain averaged over all receive antennas and frequencies for each BS antenna and 2) scale the rows of by the gain averaged over all transmit antennas and frequencies for each MS antenna. Mathematically, we have , where and are diagonal matrices whose diagonal elements represent the average channel power gain for each MS and BS antenna, respectively. Note that this is consistent with the well-known Kronecker model for the channel spatial covariance [22] where and are receive and transmit correlation matrices, respectively. However, choosing these as diagonal matrices enforces zero correlation among the channel transfer functions at the different antennas, a model previously used for antenna arrays with inter-element separation exceeding four wavelengths [23]. The CDF of the capacity resulting from these scaled i.i.d. matrices is compared to that of the measured channel in Fig. 6. As can be seen, scaling by the average gain per BS antenna (assuming ) leads to an excellent match to the measured capacity. Further comparison between the capacity achieved with the BS-scaled i.i.d. matrices and that obtained using the measured channels shows that they differ by less than 1% at each location. This highlights the dominant influence of channel gain imbalance on the capacity performance for cooperative BS signaling and indicates that the Kronecker correlation model with diagonal transmit and receive correlation matrices works well in this type of cooperative BS environment. In contrast, the scaling by the average MS gains (assuming ) results in a capacity that is close to the average capacity predicted by i.i.d. channels without scaling (indicated by the black triangle in Fig. 6). This is an indication that the average channel gains for different MS antennas are similar, despite the fact that the MS antennas include both vertical (V) and horizontal (H) polarizations. To investigate this further, for transmission from the th BS we compute the ratios , where we have dropped the frequency index notation for convenience. Table II presents the average of several values of , where we use the notation V/V (H/H) to indicate that and are the indices associated with the two vertically-polarized (horizontally-polarized) MS antennas and the notation V/H to indicate the average over the four combinations where and are associated respectively with vertically- and horizontally-polarized MS antennas. While clearly the gain for the vertical polarization is higher than that for the horizontal polarization, the imbalance is relatively small, confirming our postulation that the channel gains for the different MS antennas are similar. IV. MULTI-USER SIGNALING The point-to-point analysis detailed in Section III reveals a number of interesting aspects regarding the cooperative MIMO channel. However, practical cellular systems support multiple users, and it is therefore intriguing to explore the performance

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TABLE II AVERAGE CHANNEL POWER GAIN RATIOS FOR VANTENNAS ON THE MS

AND

beamformer represented by the unit-norm vector to the received signal. If the additive noise at each receiver is modeled as a zero-mean, unit-variance complex Gaussian random process, the sum rate experienced for this BC is [24], [25]

H-POLARIZED

(5) impacts associated with multiple cooperative BSs communicating with multiple MSs. We will first consider the downlink channel (BC) and then focus our attention on the uplink channel (MAC) [5]. Throughout this analysis, we focus on MSs on the measurement routes. Since the data was obtained for a single mobile node, this means that we use channels measured at different times to obtain the required channel data from the BSs to the spatially-displaced users. Naturally, the channel is not strictly static over the time interval between these two different measurements, and therefore the performance we obtain does not generally represent the instantaneous performance that would be obtained for simultaneous links. However, the focus of this analysis is to explore statistical trends over an ensemble of situations. Since the major scattering environment (buildings, parked vehicles, etc.) does not change over the measurement times, this study provides statistically representative multi-user performance behavior. We assume that each MS only receives or transmits a single data stream, and therefore uses multiple antennas only for diversity or beamforming. While it is possible to also allow each MS to receive or transmit multiple simultaneous streams (multiplexing), inclusion of this capability is of limited value in this study since 1) the cooperative BSs only have three antennas in total, so that even with only one MS can accommodate multiple streams, 2) all of the various configurations used in the comparative study can support a single stream (but not necessarily multiple streams), and therefore this allows for fair comparisons, and 3) inclusion of multi-stream communication adds complexity without providing detailed additional understanding regarding the trends enabled by the cooperative communication. The channel normalization is similar to that used for the single-user analysis. However, in this case of multiple users, we must preserve the differences in channel gain to each MS. If the channel matrix from the BSs to the th MS at the th frequency is with th column , we scale the matrices for all MSs as where (4) Note that in the following we drop the frequency index for notational simplicity, recognizing that all sum rate results represent averages over the frequencies. A. BC Topologies cooperative BSs apply a beamformer to For the BC, the the signal for the th MS represented by the vector , where the th element of the vector is the complex weight applied to the signal from the th BS. The th MS then applies a

where (6) We assume that the total transmit power among all BS antennas is constrained to be a constant such that [24] (7) With the normalization of (4) and given that we have assumed Gaussian noise with unit variance, this total power can once again be considered the SISO SNR to the strongest BS-to-MS link. Also, implicit in this assumption is that the BSs use power control and can change their power allocation up to a total of . While we could adopt a per-antenna power constraint so that all BSs transmit the same power [26]–[28], our observation matches that of other studies [27] that while this per-antenna constraint slightly reduces the capacity, the resulting trends match those obtained with the sum power constraint. As a result, we use the simpler sum power constraint of (7) in the analysis. 1) MISO Signaling: We first assume that each MS receives using only one of the vertically-polarized antennas in a multiple-input single-output (MISO) configuration. Assigning this antenna to be antenna #1, we have for each MS, where indicates a transpose. Maximum Power Pairing: As a reference case, each mobile user establishes a link with the BS for which the BS-to-MS gain is maximum, even if multiple MSs share the same BS. Therefore, each transmit beamformer has only a single non-zero entry of value . However, this simple reference case is at a strong disadvantage since it does not benefit from intelligent spatial processing capabilities and therefore can create significant interference at each MS. Motivated by this observation, for this case only we also compute the sum rate when the MSs equally divide the communication time (time division multiple access or TDMA). In this case, each beamformer has a single non-zero entry of value , the second term in the denominator of (6) is zero, and we scale (5) as . The final reference sum rate for this technique is given as the maximum of the rates computed with and without TDMA. Optimal Pairing: While pairing each MS to a BS based on the maximum channel gain is simple, it will certainly not maximize the network sum rate. We therefore explore a second reference scenario in which we compute the sum rate for each possible BS-MS pairing and select the pairing that achieves the largest sum rate. Once again, the transmit beamformer for each MS has only a single non-zero entry of value . However,

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this situation implies additional cooperation, since the network must know the CSI from all BSs to each MS to determine this optimal pairing. RCI: Finally, we consider a true cooperative MISO BC where the beamformer for each MS is selected to achieve an appropriate balance of high signal strength for the th MS and low interference for the other MSs. To construct the beamforming vectors, we use the iterative regularized channel inversion (RCI) method that, assuming the correct initial conditions, achieves the optimal sum rate under the constraint of linear processing [24], [25], [29]. For our work, we initiate the iteration using the transmit beamformers obtained for the optimal pairing. This is not guaranteed to converge to the absolute optimum, but does show the improvement possible using a practical beamforming algorithm. It should be noted that improved performance can be obtained by using non-linear processing known as dirty paper coding (DPC) [5], [30]. While DPC will achieve higher capacity, the capacity difference in most cases is relatively minor, and the trends with channel conditions for DPC and RCI beamforming are similar [24], [31]. To avoid the complex encoding and decoding process associated with DPC and to be consistent with the other linear processing assumed throughout this paper, we choose to use the simpler RCI for our comparative study. 2) MIMO Signaling: Because we have multiple antennas at each MS, we can also explore the BC when these antennas are used. In this case, we use the same scenarios as outlined above for the MISO case. However, we assume that the th MS knows (through training) the effective channel for and can therefore construct a minimum-mean-squared error (MMSE) beamformer from [29] (8) is chosen so that the vector has unit norm. For the iterwhere ative RCI algorithm, a new MMSE beamformer for the receiver is computed at each step of the iterative computation. Furthermore, to pair each MS with the BS for which the gain is highest, we select the BS associated with the column of that has the highest norm. B. MAC Topologies Optimal Pairing: The multiple access channel results when multiple MSs transmit simultaneously and uncooperatively to the cooperative BSs. As a reference case, we assume that each MS transmits from antenna #1 and that the BSs cannot coherently cooperate. For each possible pairing between the th MS and the th BS, we compute the sum rate from (5) with (9)

is the th element of and each MS transmits where a power of . The pairing that achieves the best sum rate is selected as the reference topology.

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Cooperative BS: To formulate the capacity when BS cooperation is considered, we let the vector represent the th column of . If we continue to assume that each MS transmits from antenna #1, we can construct the channel matrix whose th column is . Since the MSs cannot cooperate, the capacity for cooperative BSs is equivalent to the point-to-point capacity for an uninformed transmitter based on the composite channel matrix , or (10) Cooperative BS/Tx Diversity: Finally, to explore the benefit of exploiting the multiple antennas at each MS, we apply transmit selection diversity, where each MS selects the antenna that achieves the maximum signal strength at the BSs, in addition to the cooperative BS processing. To accomplish this, for each MS we select the value of that maximizes the norm of the vector . The vector is used in place when constructing the channel matrix for use in (10). of C. Results The computational results for these multi-user signaling strategies based on the measured data use or MSs and an average SISO SNR of 10 dB. The data exhibits a coherence bandwidth, defined here as the frequency separation at which the correlation coefficient of the data falls below 10%, of at least 1 MHz, and therefore to save computational burden the sum rate is computed at 1 MHz intervals over the full bandwidth and averaged in frequency. Given the large set of possible combinations of locations for the different MSs, we must select a multi-user scenario to use in the analysis. Referring to Fig. 2, the first MS, designated as , moves along the entirety of routes 1 and 2. The remaining MSs are either at point 1 or point 2 which are respectively 700 m or 900 m from the starting point along route 2, locations that allow these MSs to observe multiple BSs. Specifically, when , simulations are run for the second MS at both points, while when is at point 1 while is at point 2. 1) BC Topologies: Before studying composite sum rate statistics for the presented scenario, we investigate the sum rate as moves along route 1 between the displacements of 200 m and 1000 m with at point 1 to allow discussion of the impact of different propagation characteristics on the sum rate. The top plot in Fig. 7 shows the sum rate achieved assuming BC MISO signaling for the three topologies discussed in Section IV.A1, where the data has been smoothed as discussed in Section III. We first observe that the maximum power pairing works well compared to the optimal BS-MS pairing when is on the main roads (e.g., between displacements of 750 and 900 m) and enjoys nearly LOS (or strong urban canyon) propagation and therefore a dominant link with a single BS. However, when deviates into a small “inlet” (e.g., between displacements of 250 and 550 m), the maximum power pairing increases the multi-user interference, and therefore a different pairing that reduces interference is beneficial. We emphasize that in these interference-limited scenarios, the maximum power pairing would suffer significant additional degradation

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Fig. 7. Sum rates computed for different MISO BC and MAC signaling aptravels along a portion of route 1 and is at point 2. proaches when The SISO SNR is 10 dB.

were it not for the ability to switch to TDMA. But we also note that in a few cases (not shown), the TDMA capability allows the maximum power pairing to outperform the optimal pairing. Finally, since the link gain for two or more BSs to a single MS is similar in these regions, allowing the multiple BSs to collaborate to control interference and maximize link gains through application of the RCI beamforming weights provides significant additional sum rate capability. Fig. 8 plots the cumulative distribution function (CDF) of the data using both MISO BC and MIMO BC signaling (Sections IV.A1 and IV.A2) for MSs, with the statistics computed by concatenating the simulations for at points 1 and 2. It is intuitive that having multiple antennas at the receivers (MIMO BC) enables an increase in the average sum rate. However, these results also show that for MIMO BC signaling, the optimal pairing provides a sum rate approaching that achieved using the full RCI beamforming. This situation occurs because each MS uses knowledge of the transmit beamforming weights to construct its own MMSE receive beamforming weights and therefore is able to suppress the bulk of the interference. This is in contrast to the case of MISO BC signaling, where the receiver is unable to use array signal processing for interference suppression. As a result, the benefit of cooperative transmission is generally less significant for MIMO BC signaling with this optimal pairing, although it should be again emphasized that such optimal pairing requires significant network cooperation and that the multi-antenna reception requires additional complexity at each MS. In most networks, achieving this level of complexity is more feasible in the infrastructure (BS) rather than in the MSs. Therefore, these results reveal that BS cooperation is an effective technique for dramatically improving the performance. Fig. 9 shows the CDF obtained when MSs for MISO BC signaling. Because , communicating with three MSs uses all of the spatial resources available from the cooperative BSs. In this case, the average sum rate achieved with cooperative transmission (RCI) is 91% higher than that achieved with maximum power pairing. This compares with a relative increase

Fig. 8. CDF of the sum rate achieved for different MISO and MIMO BC sigtravels along the entirety of routes 1 and 2 and naling approaches when is either at point 1 or point 2. The SISO SNR is 10 dB.

Fig. 9. CDF of the sum rate achieved for different MISO BC signaling aptravels along the entirety of routes 1 and 2 and and proaches when are at two different points along route 2. The SISO SNR is 10 dB.

of 37% for the two-user scenario considered in Fig. 8. Furthermore, because of the increased interference created by simultaneous transmissions to three different MSs, using the optimal pairing provides some benefit over the maximum power pairing, although it still naturally falls far short of what is achievable using full BS cooperation. 2) MAC Topologies: The bottom plot in Fig. 7 provides the sum rate for the uplink (MAC) scenarios detailed in Section IV.B as moves along route 1 between the displacements of 200 m and 1000 m with at point 1. Once again, we observe significant performance benefit when the base stations can cooperate in the multi-user reception. Interestingly, when is between the displacements of 200 and 700 m, which is where cooperation tends to give the most benefit, using transmit selection diversity offers little additional benefit. This occurs because the signal processing achieved by the cooperative receivers (BSs) already leverages the diversity in the channels. However, over the region from 750 to 900 m, where cooperation is less beneficial because each MS has a

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each MS has a single antenna. For MAC signaling, the average improvements are 44% and 63% for two and three single-antenna MSs, respectively, with even more gains achievable using multiple antennas at each MS. Such dramatic capacity improvement motivates further study of coherent cooperative communications for macrocellular settings. REFERENCES

Fig. 10. CDF of the sum rate achieved for different MAC signaling approaches travels along the entirety of routes 1 and 2 and and (if when applicable) are at one of two different points along route 2. The SISO SNR is 10 dB.

dominant link to a different BS, the use of transmit diversity to overcome fast fading is highly effective. Finally, Fig. 10 shows the CDF of the sum rate achieved for the uplink scenarios for both and MSs. These results reveal increases in the average sum rate of 44% and 63% achieved for 2 and 3 MSs, respectively, assuming only a single antenna used at each MS (no transmit diversity). Perhaps the most striking observation is that the average rate achieved for MSs is only slightly higher than that achieved for MSs. This occurs because the impact of the increased total power transmitted is partially offset by the increased interference when , particularly when only one or two BSs experience a strong link to the MSs. The effect is particularly dominant when using optimal pairing since in this technique the BSs cannot cooperate to reduce the multi-user interference, and as a result the sum rate for MSs is generally lower than that for MSs. When all three BSs experience a strong link to the MSs and coherent cooperation is allowed, then the sum rate achieved for is much larger than that for , as evidenced by the differences in the two curves at the high sum-rate levels (upper portion of the curves). Unfortunately, such situations are rare, which is why they occur at relatively low probability. V. CONCLUSION This paper uses fully-coherent measurements from three BS sites to a single MS in a macrocellular environment to explore the potential gains achievable with cooperative BS communication for single-user and multi-user scenarios. Specifically, computations with the data for point-to-point links demonstrate that the average capacity increases by 53% as a result of cooperative BS communication. The analysis further shows that the capacity behavior follows that achieved with i.i.d. Gaussian random channel matrices whose columns are properly scaled to achieve the observed BS-to-MS gains. Evaluation of the data with practical BC signaling strategies shows that cooperation between the BSs can increase the average multi-user sum rate by 37% and 91% for two and three MSs, respectively, when

[1] J. W. Wallace and M. A. Jensen, “Mutual coupling in MIMO wireless systems: A rigorous network theory analysis,” IEEE Trans. Wireless Commun., vol. 3, pp. 1317–1325, July 2004. [2] B. K. Lau, “Multiple antenna terminals,” in MIMO: From Theory to Implementation, C. Oestges, A. Sibille, and A. Zanella, Eds. San Diego: Academic Press, 2011, pp. 267–298. [3] M. A. Jensen and J. W. Wallace, “A review of antennas and propagation for MIMO wireless communications,” IEEE Trans. Antennas Propag., vol. 52, pp. 2810–2824, Nov. 2004. [4] D. Gesbert, S. Hanly, H. Huang, S. S. Shitz, O. Simeone, and W. Yu, “Multi-cell MIMO cooperative networks: A new look at interference,” IEEE J. Selected Areas Commun., vol. 28, pp. 1380–1408, Dec. 2010. [5] A. Goldsmith, S. A. Jafar, N. Jindal, and S. Vishwanath, “Capacity limits of MIMO channels,” IEEE Trans. Inf. Theory, vol. 21, pp. 684–702, Jun. 2003. [6] S. Zhou, M. Zhao, X. Xu, J. Wang, and Y. Yao, “Distributed wireless communication system: A new architecture for future public wireless access,” IEEE Commun. Mag., vol. 41, pp. 108–113, Mar. 2003. [7] V. Jungnickel, M. Schellmann, L. Thiele, T. Wirth, T. Haustein, O. Koch, W. Zirwas, and E. Schulz, “Interference aware scheduling in the multiuser MIMO-OFDM downlink,” IEEE Commun. Mag., vol. 47, pp. 56–66, Jun. 2009. [8] N. Jaldén, P. Zetterberg, B. Ottersten, and L. Garcia, “Inter- and intrasite correlations of large-scale parameters from microcellular measurements at 1800 MHz,” EURASIP J. Wireless Commun. Netw., 2007. [9] M. Alatossava, A. Taparugssanagorn, and V. Holappa, “Measurement based capacity of distributed MIMO antenna system in urban microcellular environment at 5.25 GHz,” in Proc. IEEE Vehicular Technology Conf. Spring, Singapore, May 11–14, 2008, pp. 430–434. [10] V. Jungnickel, S. Jaeckel, L. Jiang, U. Krüger, A. Brylka, and C. von Helmolt, “Capacity measurements in a cooperative MIMO network,” IEEE Trans. Veh. Technol., vol. 58, no. 5, pp. 2392–2405, Jun. 2009. [11] S. Jaeckel, L. Thiele, A. Brylka, L. Jiang, V. Jungnickel, C. Jandura, and J. Heft, “Intercell interference measured in urban areas,” in Proc. 2009 IEEE Int. Conf. Commun., Dresden, Germany, Jun. 14–18, 2009, pp. 1–6. [12] T. W. C. Brown, P. C. F. Eggers, and K. Olesen, “Simultaneous 5 GHz co-channel multiple-input-multiple-output links at microcellular boundaries: Interference or cooperation?,” IET Proc. Microw. Antennas Propag., vol. 1, no. 6, pp. 1152–1159, Dec. 2007. [13] R. Irmer, H.-P. Mayer, A. Weber, V. Braun, M. Schmidt, M. Ohm, N. Ahr, A. Zoch, C. Jandura, P. Marsch, and G. Fettweis, “Multisite field trial for LTE and advanced concepts,” IEEE Commun. Mag., vol. 47, pp. 92–98, Feb. 2009. [14] V. Jungnickel, L. Thiele, T. Wirth, T. Haustein, S. Schiffermüller, A. Forck, S. Wahls, S. Jaeckel, S. Schubert, S. Gäbler, C. Juchems, F. Luhn, R. Zavrtak, H. Droste, G. Kadel, W. Kreher, J. Mueller, W. Stoermer, and G. Wannemacher, “Coordinated multipoint trials in the downlink,” in Proc. 5th IEEE Broadband Wireless Access Workshop (BWAWS)/IEEE GLOBECOM Workshops, Honolulu, HI, 30 Nov.–4 Dec. 2009, pp. 1–6. [15] R. Fritzsche, J. Voigt, C. Jandura, and G. P. Fettweis, “Verifying ray tracing based CoMP-MIMO predictions with channel sounding measurements,” in Proc. Int. ITG/IEEE Workshop on Smart Antennas (WSA’10), Bremen, Germany, Feb. 23–24, 2010, pp. 161–168. [16] R. Irmer, H. Droste, P. Marsch, M. Grieger, G. Fettweis, S. Brueck, H.-P. Mayer, L. Thiele, and V. Jungnickel, “Coordinated multipoint: Concepts, performance and field trial results,” IEEE Commun. Mag., vol. 49, pp. 102–111, Feb. 2011. [17] P. Marsch, M. Grieger, and G. Fettweis, “Field trial results on different uplink coordinated multi-point (CoMP) concepts in cellular systems,” in Proc. IEEE Global Telecomm. Conf., Miami, FL, Dec. 6–10, 2010, pp. 1–6. [18] Y. Selen and H. Asplund, “3G LTE simulations using measured MIMO channels,” in Proc. IEEE Global Telecomm. Conf., New Orleans, LA, 30 Nov.–4 dec. 2008, pp. 1–5.

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[19] J. W. Wallace, M. A. Jensen, A. L. Swindlehurst, and B. D. Jeffs, “Experimental characterization of the MIMO wireless channel: Data acquisition and analysis,” IEEE Trans. Wireless Commun., vol. 2, pp. 335–343, Mar. 2003. [20] S. Plass, X. G. Doukopoulos, and R. Legouable, “Investigations on link-level inter-cell interference in OFDMA systems,” in Proc. Symp. on Communications and Vehicular Technology, Liege, Belgium, Nov. 23, 2006, pp. 49–52. [21] “Analysis for Simulation Scenario Definition to Interference Mitigation Studies,” Tech. Rep. Document R4-060117, Feb. 2006, 3GPP TSG RAN WG4. [22] J. P. Kermoal, L. Schumacher, K. I. Pedersen, P. E. Mogensen, and F. Frederiksen, “A stochastic MIMO radio channel model with experimental validation,” IEEE J. Selected Areas Commun., vol. 20, pp. 1211–1226, Aug. 2002. [23] V. Pohl, V. Jungnickel, T. Haustein, and C. von Helmolt, “The effect of path loss variations on the capacity of MIMO systems,” in Proc. 5th Eur. Personal Mobile Communications Conf., Glasgow, U.K., Apr. 22–25, 2003, pp. 458–462. [24] M. Stojnic, H. Vikalo, and B. Hassibi, “Rate maximization in multiantenna broadcast channels with linear preprocessing,” IEEE Trans. Wireless Commun., vol. 5, pp. 2338–2342, Sep. 2006. [25] A. L. Anderson, J. R. Zeidler, and M. A. Jensen, “Reduced-feedback linear precoding with stable performance for the time-varying MIMO broadcast channel,” IEEE J. Sel. Areas Commun., vol. 26, pp. 1483–1493, 2008. [26] S. Shi, M. Schubert, N. Vucic, and H. Boche, “MMSE optimization with per-base-station power constraints for network MIMO systems,” in Proc. 2008 IEEE Int. Conf. Commun., Beijing, China, May 19–23, 2008, vol. 55, pp. 4106–4110. [27] F. Boccardi and H. Huang, “A near-optimum technique using linear precoding for the MIMO broadcast channel,” in Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing, Honolulu, HI, Apr. 15–20, 2007, vol. 3, pp. 17–20. [28] W. Yu and T. Lan, “Transmitter optimization for the multi-antenna downlink with per-antenna power constraints,” IEEE Trans. Signal Processing, vol. 55, pp. 2646–2660, Jun. 2007. [29] Q. H. Spencer, J. W. Wallace, C. B. Peel, T. Svantesson, A. L. Swindlehurst, and A. Gummalla, “Performance of multi-user spatial multiplexing with measured channel data,” in MIMO System Technology and Wireless Communications. Boca Raton, FL: CRC Press, 2006. [30] G. Caire and S. Shamai, “On the achievable throughput of a multiantenna Gaussian broadcast channel,” IEEE Trans. Inf. Theory, vol. 49, pp. 1691–1706, July 2003. [31] J. Lee and N. Jindal, “High SNR analysis for MIMO broadcast channels: Dirty paper coding versus linear precoding,” IEEE Trans. Inf. Theory, vol. 53, pp. 4787–4792, Dec. 2007. Buon Kiong Lau (S’00–M’03–SM’07) received the B.E. degree (with honors) from the University of Western Australia, Perth, Australia and the Ph.D. degree from Curtin University of Technology, Perth, in 1998 and 2003, respectively, both in electrical engineering. During 2000 to 2001, he worked as a Research Engineer with Ericsson Research, Kista, Sweden. From 2003 to 2004, he was a Guest Research Fellow at the Department of Signal Processing, Blekinge Institute of Technology, Sweden. Since 2004, he has been at the Department of Electrical and Information Technology, Lund University, where he is now an Associate Professor. He has been a Visiting Researcher at the Department of Applied Mathematics, Hong Kong Polytechnic University, China, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, and Takada Laboratory, Tokyo Institute of Technology, Japan. His primary research interests are in various aspects of multiple antenna

systems, particularly the interplay between antennas, propagation channels and signal processing. Dr. Lau is an Associate Editor for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION and a Guest Editor of the 2012 Special Issue on MIMO Technology for the same journal. From 2007 to 2010, he was a Co-Chair of Subworking Group 2.2 on “Compact Antenna Systems for Terminals” (CAST) within EU COST Action 2100. Since 2011, he has been a Swedish national delegate and the Chair of Subworking Group 1.1 on “Antenna System Aspects” within COST IC1004.

Michael A. Jensen (S’93–M’95–SM’01–F’08) received the B.S. and M.S. degrees from Brigham Young University (BYU), Provo, UT, in 1990 and 1991, respectively, and the Ph.D. degree from the University of California, Los Angeles, in 1994, all in electrical engineering. Since 1994, he has been at the Electrical and Computer Engineering Department, BYU, where he is currently a Professor and Department Chair. His research interests include antennas and propagation for communications, microwave circuit design, and multi-antenna signal processing. Dr. Jensen is currently the Editor-in-Chief of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. Previously, he was an Associate Editor for the same journal and for the IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS. He has been a member and Chair of the Joint Meetings Committee for the IEEE Antennas and Propagation Society, a member of the society AdCom, and Co-Chair or Technical Program Chair for six society-sponsored symposia. In 2002, he received the Harold A. Wheeler Applications Prize Paper Award in the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION in recognition of his research on multi-antenna communication.

Jonas Medbo received the Högskoleexamen på Fysikerlinjen degree (B.S.) in physics from Stockholm University, Sweden, in 1986 and the Ph.D. degree in particle physics from Uppsala University, Sweden, in 1997. From 1986 to 1989, he was with Ericsson Telecom AB developing software for protection and monitoring of telecommunication transmission lines. Since 1997, he has been with the Propagation Group at Ericsson Research. His main research interests are measurements and modeling of radio channel and propagation as well as positioning of user equipment in wireless communications. He has contributed to the Hiperlan/2, IEEE 802.11 TGn, COST 273 and 3GPP SCM channel models.

Johan Furuskog received the M.Sc. degree in engineering physics from Uppsala University, Uppsala, Sweden, in 2007. After graduating, he joined Ericsson Research, Kista, Sweden, as a researcher where much of his work has concerned testbed development and field trials with focus on MIMO channel characteristics and LTE multi-antenna performance. He is currently involved in testbed projects targeting design and deployment of future radio access technologies and works with concept development and evaluation of new components for the LTE standard.

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User Influence on MIMO Channel Capacity for Handsets in Data Mode Operation Jesper Ødum Nielsen, Boyan Yanakiev, Ivan B. Bonev, Morten Christensen, and Gert Frølund Pedersen

Abstract— The current paper concerns realistic evaluation of the capacity of the MIMO channel between a BS and handheld device, such as a PDA or smartphone, held in front of the user’s body (data mode). The work is based on measurements of the MIMO channel between two widely separated BSs in a micro-cellular setup, and six handsets located in an indoor environment. The measurements are done simultaneously in both the 773.5–778.5 MHz and 2250–2350 MHz bands, and from the two BSs. The handsets are realistic types and were measured both in free space and with twelve different users, using both one and two hands. The random capacities of the channels are evaluated in terms of outage capacity. For an SNR of 10 dB, median capacities in free space of about 4.4–4.7 bit/s/Hz for the low band and about 3.3–3.8 bit/s/Hz for the high band were found. The mean decrease in outage capacity due to the user was found to be up to about 2.2 bit/s/Hz, depending on the band and handset. More results are presented in the paper. Index Terms—Channel capacity, dual-band propagation, MIMO channels, optical link, propagation measurements, user-interaction.

I. INTRODUCTION

D

URING the last 10–15 years it has been known that the power transmitted and received from a mobile handset (or cellular phone) may vary significantly. The importance of this has often been reported with differences of several dB’s found between handsets [1], and in some cases variations of more than 10 dB were found for different users of the same handset [2]–[5]. The large variations stress the importance of including the user in the design and testing of future handsets, since this has an impact on network performance, battery lifetime, and general user experience. For a long time handsets have typically been used in talk mode, i.e., the situation where the handset is held by the user next to the head for voice usage. A current market evolution is from voice-centric devices into devices where data and applications are equally or more important, such as for smart mobile platforms or smartphones, collectively referred to as “handsets” Manuscript received September 17, 2010; revised June 02, 2011; accepted June 16, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. The work of J. Ø. Nielsen and B. Yanakiev was supported in part by the Danish National Advanced Technology Foundation via the Converged Advanced Mobile Media Platforms (CAMMP) project. The results and conclusions presented by the authors in this article are not necessarily supported by the other partners of the CAMMP project. J. Ø. Nielsen, I. B. Bonev, and G. F. Pedersen are with the Antennas, Propagation and Radio Networking Section, Department of Electronic Systems, Faculty of Engineering and Science, Aalborg University, DK-9220 Aalborg, Denmark. B. Yanakiev and M. Christensen are with Molex Antenna Business Unit, DK-9220 Aalborg, Denmark. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173435

in the following. With this trend, data mode operation becomes more important where the handset is in front of the user and held with one or two hands. The locations of the user’s hands and fingers on the handset may be different from those used in talk mode [6]. It is known that the user’s hand is the single most important issue when considering the variation in performance in terms of power obtained with different users [7]. Therefore large performance variations may also be expected in data mode operation, since the user’s fingers still may interact with the antennas. Along with the trend towards data mode operation comes a demand for higher data rates. Given the scarcity of radio spectrum, a promising way to achieve higher data rates is to employ multiple-input multiple-output (MIMO) techniques utilizing several antennas on both the transmitter (Tx) and receiver (Rx) side. For example the upcoming long-term evolution (LTE) standard has MIMO capabilities [8]. Today’s mobile handsets are densely packed with battery, electronics, and are often equipped with several antennas for different systems. Since small handsets are generally preferred by the users, adding more antennas for MIMO will be difficult and require compromises to be made between the performance and the design and location of the antennas on the handset. The influence of the user’s hand on the MIMO performance will be crucial. It is well known that the performance of a MIMO system is highly dependent on the properties of the radio channel between the Tx and Rx [9], and thus must be included in evaluation. Given that the user interacts with the handset antennas in the near-field, possibly in a dynamic way, it is difficult to include all aspects of both the mobile environment and the user influence without actually including both in a performance measurement. The work in [10] reports on some of the first results on MIMO performance for handheld devices based on propagation measurements with a handset and several live users. It may be possible to simplify the evaluation, e.g., by using radiation pattern measurements including users, similar to what has been done in the context of single-input single-output (SISO) handset performance evaluation, see [11], [12]. Evaluation of diversity systems, i.e., single-input multiple-output (SIMO), in handsets have also been carried out in this way including phantoms of the user head and hand for talk mode scenarios in [13] and data mode in [14]. Another approach to performance evaluation is presented in [15]. Here a combination of the radiation pattern measurements, including user phantoms, and models of the propagation channel is used, where the model describes all individual plane waves in the channel. Assuming far-field conditions, this method allows a practical separation of antenna measurements and propagation

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measurements. The work in [15] considers only talk mode. Data mode operation results are given in [16] and [17], where a significant user influence on the capacity was found. For data mode, the work in [18] studies the influence of the user’s hand on the capacity, based on simulations of the channel. Based on simulations of both the channel and the radiation patterns, [19] considers the influence of the user’s body when the device is carried in a pocket. In the latter two references a significant reduction of (ergodic) capacity was found due to the user. Other related work includes [20] where the capacity of handsets in data mode is studied with special focus on cross-polarization difference (XPR), based on anechoic room measurements, and [21] where methods for MIMO antenna evaluation are studied, utilizing channel measurements, but focusing on methods rather than practical devices. The early work in [22] studies the performance of different principal antenna types based on propagation measurements, but without user influence. From simulations and measurements in a setup with dipoles in a reverberation chamber, including a simple user phantom and assuming uncorrelated Rx branches, the work in [23] provides a parametric study of how the capacity is influenced by the reduced efficiency and signal blocking, that may be introduced from a nearby user. Much of the earlier work employs phantoms to mimic the influence of the user, but issues like dynamic behavior and variations in the MIMO performance among the users are difficult to include with phantoms. Furthermore, results on different types of handsets antennas used in data mode are scarce. The main topic of the current work is the performance evaluation, in terms of capacity, of different realistic MIMO handsets. Focus is on both achievable capacity as well as the influence of the users of the handsets. The investigations are based on an extensive radio channel measurement campaign in a micro-cellular setup. Simultaneous measurements were carried out from two base stations (BSs) in both 773.5–778.5 MHz and 2250–2350 MHz bands. Six realistic handsets of different types, all equipped with two antennas, are all measured in an indoor environment both in free space and with twelve users in data mode. The next section describes the measurements in more detail, including the developed handsets equipped with optical units ensuring correct data acquisition. Section III describes the processing of the raw measurement data, while Section IV concerns the obtained results on mean effective gain (MEG), capacity and the user influence. Section V concludes the paper. II. MEASUREMENT SETUP A. Scenario Successful use of spatial multiplexing modes in a MIMO system requires a rich scattering environment with a wide angular spread of scatterers both near the Tx and the Rx. This generally results in a high rank channel matrix with low correlation among the elements, which in turn results in a high channel capacity [24]. For a cellular network a BS should preferably be near rooftop level or below and not in a highly elevated location that might be preferred from a network coverage point of view. Clearly a successful network has to provide a compromise

Fig. 1. View from the antenna location of BS2.

Fig. 2. View towards BS1 from the measurement site.

TABLE I OVERVIEW OF THE TWO BASE STATIONS

of both high capacity and coverage. In an attempt to create a realistic scenario for the measurements used in the current work, a setup with two base stations (BSs) was used. BS1 was envisioned to result in high capacity channels, being located some 150 m away from the measurement building with partial line of sight (LOS) and the antennas near rooftop height of surrounding buildings. In contrast, BS2 was located about 500 m away on top of a tall building overlooking the surrounding buildings. An overview of the base stations is given in Table I and Figs. 1–2. Both indoor and outdoor measurements were made, where the current paper focuses on the indoor part. The measurements took place inside a 3rd floor room with windows towards BS1, where the LOS was partly blocked by buildings. In the room a 4 m by 4 m square was marked on the floor. During the first 5 s of a measurement the user walked from a corner forward along one side of the square to the next corner; the next 5 s the user walked backwards towards the first corner. This was then repeated resulting in a total measurement time of 20 s in which the user kept the same orientation. Four handsets (described below) were measured simultaneously, held by four test users each walking along one of the four sides of the square.

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TABLE II OVERVIEW OF HANDSETS USED

Two bands were measured simultaneously. An effective sounding bandwidth of about 5 MHz was used at the center frequency of 776 MHz. This band is subsequently referred to as the low band (LB). The high band (HB) was centered at 2300 MHz where an effective sounding bandwidth of about 100 MHz was used. The two bands were chosen to resemble the LTE bands in the 700–800 MHz and 2.3–2.6 GHz ranges, respectively [25]. In practice, both the center frequencies and the bandwidths are compromises given the available equipment and unused frequency spectrum, resulting in the unequal bandwidths. C. Handsets The six handsets used in this work are special mock-up handsets which are realistic with respect to the antennas, electromagnetic properties, shape and handling, and at the same time allows for connection to the channel sounding equipment. A straightforward approach would be to connect the antennas in the handsets to the sounder using conventional coaxial cables, but this is an undesirable solution. It is well known that the use of conducting cables on small devices changes the electromagnetic properties, because the cable becomes part of the antenna [26]–[28]. Coaxial cables for measurements need to be low-loss and phase-stable, and are typically of the order 1 cm in diameter, somewhat inflexible and heavy. Attaching such a cable to a small device often makes its handling difficult and hence unnatural, where it is noted that a stiff choke may be needed on the cable, in order minimize the cable influence. In addition, the cable may have to be lead out at an awkward location on the device with respect to easy handling. An attractive way to avoid the above mentioned problems is to use an optical fiber between the handset and the sounding equipment. By modulating a laser diode with the RF signals received by the antennas it is possible to transfer the signals to the sounder using a flexible plastic fiber. The main difficulty is in designing optical units that are small enough to fit into a typical handset. As described in detail in [29], this has been done for the current work. The six handsets used in this work all have integrated optical units and all have two antennas, single or dual-band. All the handsets were placed in a plastic casing from PC-ABS material made in a rapid prototyping printer. The material has , which is comparable to most plastics found in today’s phones. The reason for this is to mimic the user handling as closely as possible. The plastic covers provide natural feeling and prevents the user from directly touching the PCB and disturbing the currents and fields in an abnormal way. Finally, grip markings were embedded on the covers for better grip control. An overview of the six handsets is given in Table II. Note that ‘H6’ is missing from the list. This handset was part of the measurement campaign, but broke during the campaign and therefore the data was discarded. In all cases the handsets are designed for 50 MHz and 100 MHz bandwidth in the LB and HB, respectively. D. User Grips and Repetitions Two grips were used, one hand (OH) and two hand (TH). In each case the users placed their fingers in predefined markings

Fig. 3. Handset grips, one hand (OH) for H2 (left) and two hand (TH) for H1 (right).

on the handsets and held the handset in front of the body at an angle of about 45 . The two grips are shown in Fig. 3. As mentioned above, variation in performance is expected among the users and therefore more users are involved to allow averaging. Since no a priori information exist on the capacity distribution, measurements with twelve users were carried out based on the experience with measurements of MEG [30]. All combinations of the four square sides, two grips and twelve users were measured twice. Firstly with the handsets H1, H2, H3, H4, and secondly with the handsets H1, H5, H6, H7. In addition all handsets were measured in free space where the handsets were mounted at an angle of 45 using Styrofoam on top of a table with wheels. The table was then pushed by a person (bending down) to be measured in the same way as with the users. These measurements were made twice. E. Sounder Setup The measurements were carried out using a MIMO channel sounder [31], allowing truly simultaneous measurement of the channels from all seven (three LB and four HB) Tx antennas on the base stations, to the four dual-band Rx antennas. These four Rx antennas are located, one in each, in the four different handsets that are measured at the same time. As described above, each handset has two antennas which are connected via a multiplexing switch. Hence, eight dual-band Rx antennas are measured, so that in total a 7 16 MIMO (Tx Rx) wide band channel matrix was measured at a rate of 60 Hz to cope with

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channel changes due to the movements of the users and other changes in the channel. III. MEASUREMENT STATISTICS Given the measurements described in the previous section, different MIMO constellations can be studied, i.e., which frequency band and how many Tx and Rx antennas are used. The following are considered in this work, BS1,Lo

The two LB Tx antennas from BS1 are used to form a compact 2 2 MIMO setup for each handset.

BS1,Hi1-2

Similarly, two of the HB Tx antennas from BS1 are used to form a compact 2 2 MIMO setup.

BS1,Hi1-4

All four HB Tx antennas from BS1 are used, resulting in a compact 4 2 MIMO setup.

BS1 2,Lo

This is a 3 2 distributed MIMO setup where the two Tx antennas from BS1 are used in addition to the single Tx antenna on BS2. Via the normalization described below it is assumed that the Tx power is adjusted so that the average Rx power is the same from BS1 and BS2.

The MIMO channel is described by the matrix consisting of the elements where indices denote the -th square side, the -th Tx antenna, -th Rx antenna, and -th time index. The MIMO constellations and the choice of handset defines the channels used, and is indicated by the -index. The scalar is the complex gain of the narrow-band channel between the Tx and Rx antennas, obtained via discrete Fourier transforms of the measured impulse responses (IRs). To ensure a fair comparison the channels are normalized to the mean power of all handsets in free space. The mean is computed independently for every Tx antenna, mainly to remove path loss differences in the distributed MIMO case and between bands. The free space average power gain for the -th Tx antenna is computed as

where the signal to noise ratio (SNR) is is the -th eigenvalue of the matrix and . The number of Tx antennas for the constellation is given by . The channel capacity is random, and hence a statistical approach is needed. A useful measure is the outage capacity (OC) [32], which is the value such that the probability , where is the probability level in percent. Thus, the term OC is another name for capacity percentile. This work focus on , and , i.e., OC at the 10%, 50%, and 90% levels, respectively. The percentiles are found from the empirical cumulative distribution functions (CDFs) by combining all instantaneous capacities from all four square sides, i.e., for all values of and . The capacity results presented in this work are assuming an SNR ratio of 10 dB for the average handset, obtained via the normalization described above. This is equivalent to fixing the Tx power and is aimed at creating a fair comparison among the handsets. For example some handsets may have antennas with higher efficiency than the average and as a result effectively have a higher average SNR. The issue of normalization and hence SNR ratio is related to the update rate of the power control in the cellular system. The normalization chosen in the current work is based on the average over the complete route (four sides of the square path). Hence both slow and fast fading is preserved and the SNR will vary locally along the route, depending on the handset antennas and the channel. This ensures a fair comparison of the handsets, which would be difficult if, e.g., the slow fading was estimated and removed individually for the handsets, approximating fast power control. With the aim of understanding capacity results it is useful to study the SISO channels comprising the MIMO channels in terms of MEG. The MEG was originally defined as the ratio of the average power obtained with an antenna under test to the average power obtained with a reference antenna, where the averaging is over measurements carried out in the same realistic environment [33]. Denoting by a complex sample of the IR at time-index , delay-index , for the -th Tx antenna, -th Rx antenna, and measured in the -th side of the square in the room, the average total power gain is computed as

(1) (4) where is the number of sides of the square, is the number of Rx antennas of the handsets, and is the number of IR samples along each side. The averaging is done over handsets. The normalized channel matrix has the elements (2) Assuming no knowledge at the Tx about the channel state, the instantaneous channel capacity is given by [9]

(3)

where is the number of delay samples, is the number of Tx antennas for the considered band and base. The meaning of and are defined as for (1). The value of may be viewed as the MEG for the -th antenna of handset/ band , where the reference antenna is a hypothetical antenna collecting all the transmitted power in both polarizations. Note that is computed in (4) using the wideband data since the measurements are calibrated for equal Tx power in the LB and HB, having different bandwidths. The body loss (BL) for the -th Rx antenna is defined as the ratio of average total power gains with and without a user [5] (5)

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TABLE III PATH LOSS OBTAINED FROM FREE SPACE MEASUREMENTS. AVERAGE OVER ALL HANDSETS AND RX ANTENNAS

Fig. 4. The MEG in free space conditions. The -axis indicates the handsets. The different lines in the plot indicates combinations of base, band, and Rx antenna element. The measured points are connected by lines only to ease reading.

where is the average total power gain in free space conditions, and is the gain when a user is present. The body loss not only includes signal power absorbed in the user’s body, but also indirect changes in the received power due to the user, such as de-tuning of the antenna and load-pull of power amplifiers in case of uplink transmission. In the following all MEG statistics are based on the logarithms of the mean channel gain . The presence of a user is expected to result in lower OC compared to the free space case [17], [34]. With the purpose of studying this influence, the term capacity loss (CL) is introduced. In analogy with the BL, the CL is the difference in OC obtained with and without the user when handset is operated in the same environment. More precisely, the CL is defined as (6) where

is the OC at the % level, for the -th user, and is the similar OC obtained from the -th measurement in free space conditions. In order to also quantify the variation of the OC among the users, the capacity variation (CV) is defined as the sample standard deviation (7)

where

is the mean OC among the users. IV. RESULTS

A. Free Space MEG The MEG for the free space case is shown in Fig. 4, where the handsets are given on the -axis and all combinations of the two base stations, the two bands, and the two Rx antennas are shown using different lines. First of all it is evident that the gains for the channels originating in BS2 are much smaller than those from BS1. This is due to the longer distance and hence path-loss. Furthermore, for BS1 the HB channel has a higher loss than the corresponding LB channel. Table III lists the path loss averaged over the handsets and Rx antennas, and here the

Fig. 5. The mean of the body loss obtained with 12 different users. The -axis labels are in the form Hn/Grip, where “Hn” is the handset and “Grip” is either OH (one-hand) or TH (two-hand). The different lines in the plot indicates combinations of base, band, and Rx antenna element. The measured points are connected by lines only to ease reading.

LB to HB difference is found to be 10.4 dB. Using Friis’ power transmission equation and assuming, for a moment, free space propagation conditions and identical gains in both the Tx and Rx antennas, the change in frequency alone results in about 9.4 dB power difference. Although these assumptions are dubious it illustrates the importance of the frequency dependence of the channel gain. The MEG depends on the joint properties of the channel in terms of power distribution versus angle, and the properties of the handset in terms of radiation patterns, including polarization and efficiency. The performance may be analyzed using these terms, see e.g., [12], but here it is simply noted from Fig. 4 that there may be several dB’s of difference between the two Rx antennas of the same handsets, especially for H1, H2, and H7, as well as among the handsets. B. Body Loss The mean BLs of all combinations of handset, grip, base, band, and Rx antenna are shown in Fig. 5. From the plot both very high values of about 15 dB are found and also very low found, down to about dB. The negative BL of about dB for H2 is for the Rx2 antenna which is located at the top of the handset, and therefore may be affected only slightly by the users, as evidenced by the generally small BL values for this handset. Although a negative BL is possible theoretically, the observed negative BL may also be the result of a small BL and measurement inaccuracy (see later in Section IV.E). Also for H7, the negative BL is obtained for Rx2 which is located at the top of the handset. The very high 13–15 dB BL found for H7, LB, Rx1 has been identified to be

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Fig. 6. The outage capacity (OC) for the different handsets in free space conditions. The four plots represent different MIMO constellations. Top-left: BS1, low band. Top-Right: BS1 2, low band. Bottom-left: BS1, high band, Tx1-2. Bottom-Right: BS1, high band, Tx1-4. The measured points are connected by lines only to ease reading.

caused by severe de-tuning. This antenna is furthermore located at the bottom of the handset and hence likely to be affected by the users. 1) Top/Bottom Differences: Some of the handsets have both an antenna mounted at the top as well as the bottom of the handset, where the user is much more likely to influence the antenna performance. For these handsets the mean difference in BL for the bottom and the top mounted antenna is about 5.5 dB. For all these handsets the bottom antenna has a higher BL than the top antenna, but the difference is varying from about 0.4 dB for H1, BS1, HB to about 14 dB for H7, BS2, LB. 2) OH/TH Differences: When the TH grip is used the BL is about 1.5 dB larger on average compared to the BL when the OH grip is used. Again, the differences vary depending on the specific combination, but in all cases the TH grip results in the largest BL, ranging from about 0.1 dB for H2, BS2, LB, Rx2, to about 4 dB for H1, BS1, HB, Rx1. 3) Left/Right Differences: Regarding the handsets where both the antennas are top mounted, the two antennas may also have a difference in the BL. For H3 the right antenna has a BL 4–5 dB larger than the left antenna. For H4 the difference is smaller and less clear, and which antenna has the largest body loss depends on the grip. The BL for the left antenna of H5 is about 1.1 dB larger than for the right. Thus, there is no clear tendency and this probably depends on the particular design.

Finally, it is noted that the BL obtained with a given antenna is very similar for BS1 and BS2, as expected. C. Free Space Capacity Fig. 6 shows the OCs at the 10%-, 50%-, and 90%-level for free space conditions. The results are computed as described in Section III, using the four different MIMO constellations. It should be noted that H3 does not have LB antennas and H5 does not have HB antennas. The expression in (3) shows that in general the capacity depends on both the eigenvalues and the SNR. However, it is well known that capacity is strongly dependent on the SNR with a weaker dependence on the eigenvalues [35]. Therefore it is not surprising that the results of Fig. 6 agree well with the MEG shown in Fig. 4. H4 only has a single antenna in the LB which explains the generally lower capacity of this handset compared to, e.g., H1. Although H7 is a two antenna handset in both the LB and HB the performance in terms of power is rather poor (Fig. 4). In both bands it is essentially a single antenna Rx, resulting in a generally low capacity. With the above comments on power for the LB, 2 2 MIMO can be formed effectively for H1, H2, and H5. Comparing , these handsets, the OCs are found to be fairly similar, with

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Fig. 7. The mean reduction in the OC when the user is present compared to free space. The -axis labels are in the form Hn/Grip, where ‘Hn’ is the handset and ‘Grip’ is either one hand (OH) or two hand (TH). The four plots represent different MIMO constellations. Top-left: BS1, low band. Top-Right: BS1 , low band. Bottom-left: BS1, high band, Tx1-2. Bottom-Right: BS1, high band, Tx1-4. The measured points are connected by lines only to ease reading.

, and in the ranges (2.7–3.1, 4.4–4.7, 5.9–6.1) bit/s/Hz, respectively. For the HB, 2 2 MIMO can be formed effectively with H1, H2, H3, H4. Here the OCs are similar for H2-4, (1.9–2.4, 3.3–3.8, 4.7–5.3) bit/s/Hz for the 10%-, 50%, and 90%-levels, respectively, but significantly higher for H1, (3.2, 4.8, 6.8) bit/s/Hz for the three levels. This can be attributed to a higher signal to noise ratio due to a larger MEG for this handset compared to the rest. 1) LB/HB Differences: Comparing the obtained OCs for the LB and HB no clear tendency is apparent. For H1, the HB has the higher OCs 0.4–1.0 bit/s/Hz, whereas for H2 the LB has higher OCs by 1.2 bit/s/Hz. For H4 the HB OCs are larger by 0.9–1.1 bit/s/Hz, while for H7 they are about the same with to 0.2 bit/s/Hz. It should be recalled from differences of Section IV.A that compared to the LB, the HB requires about 10 dB higher Tx power to obtain the same SNR. 2) Extra Tx Antennas, Same BS: Comparing the OCs for the two MIMO constellations BS1,Hi1-2 and BS1,Hi1-4 it is found that the two extra Tx antennas do increase the OC, at least for H1-4. Thus, the extra antennas provide more diversity, although the improvement is marginal. H1 benefits the most, 0.3–0.5 bit/s/Hz, while for H2-4 the OC generally increase by about 0.2 bit/s/Hz.

3) Extra BS: Introducing extra diversity by means of an extra BS may also be beneficial. Comparing the results for the BS1,Lo constellation with those of the BS1 2,Lo constellation reveals that for H2 it is improved 1–1.3 bit/s/Hz for the three values OC levels whereas for H1, H4, H5, H7 mainly the are improved by 0.6–0.9 bit/s/Hz, followed by the values by values for H1, H4, and H7 are 0.3–0.6 bit/s/Hz, while the bit/s/Hz. For H5 is larger by 0.6 bit/s/Hz, changed by is but the overall tendency for H1, H4, H5, H7 is that the improved the most and the main effect of the extra BS is to increase the diversity in the channel. D. User Influence on Capacity The CL defined in (6) is shown in Fig. 7 for the handsets measured in the current work. Below these results are analyzed from different viewpoints. 1) Handset Differences in CL: Comparing the CL observed for the different handsets, it is immediately apparent that H1 has the highest CL, about 2.2 bit/s/Hz in mean over all grips, levels, and constellations. H1 is of the PDA type and has one of the antennas at the bottom where it may be affected by the users, as evidenced by a high body loss (see Fig. 5). H3 and H5 have medium CL of about 1.3 bit/s/Hz in mean, despite being relatively small bar types of handsets. The reason

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TABLE IV INCREASE IN OUTAGE CAPACITY (OC) OBTAINED BY ADDING MORE TX ANTENNAS, EITHER ON AN EXTRA BASE (BS2), OR ON THE SAME BASE (BS1). SHOWN VERSUS HANDSET AND OC LEVELS AND COMPUTED AS MEAN OVER GRIPS

may be that both antennas are located at the top of the handsets, and thus somewhat protected from user influence. Handsets H2, H4, and H7 have low CL. H2 is a relatively long (when open) clamshell type that seems to protect the antennas from the influence of the users, with a CL of about 0.8 bit/s/Hz in mean. Again, Fig. 5 shows that this handset also has a relatively small BL. H4 is of the PDA type, but unlike H1 with both antennas at the top where the users are unlikely to touch. For H4 the mean CL is about 0.8 bit/s/Hz. H7 is effectively a single antenna handset, where only the top mounted antenna is receiving significant power. This may explain why this handset in the mean has a CL of only 0.5 bit/s/Hz, the lowest of the handsets. 2) Dependence of CL on Level: Comparing the CL for the and are different OC levels it appears that sometimes changed more than the corresponding mainly for H1 in all constellations, but also, e.g., for H4 and H5 in the LB. Thus, in these cases there is a tendency that high instantaneous capacity values are reduced more than low values. 3) Frequency Dependence of CL: Regarding dependence of the CL on the frequency band, H1, H2, H4, H7 are interesting since they are dual band. Comparing results for BS1,Lo and BS1,Hi1-2, there is a tendency that the CL is higher for the HB than for the LB, in mean by about 0.5 bit/s/Hz. 4) CL for Extra Tx Antennas on the Same Base: Comparing the CLs for BS1,Hi1-2 and BS1,Hi1-4, i.e., when using two or four Tx antennas for the HB, it seen that the CL is generally larger for the BS1,Hi1-4 constellation. The overall mean difference is about 0.16 bit/s/Hz, but for H1 they are generally larger, about 0.3 bit/s/Hz. The overall increase in OC by adding the two extra Tx antennas is shown in the right half of Table IV, where the CLs due to the users are included. From the table it is clear that the OC improve marginally. 5) CL for Extra Base Station: Similarly, the CLs for the constellations with or without the extra BS is compared, i.e., results for BS1,Lo and BS1 2,Lo. The general tendency is that the CL is larger for the BS1 2,Lo constellations with an overall average of about 0.25 bit/s/Hz. The overall gain by using the extra BS2 transmitter is shown as the left part of Table IV, where it is clear that there is a gain. The question is obviously whether this gain of maximally 0.7 bit/s/Hz justifies the extra cost and

difficulties associated with implementing a distributed MIMO system. The capacity variation (CV) is defined above in (7) and Fig. 8 shows the computed values for the different combinations of handsets, probability levels, and MIMO constellations. 6) Dependence of CV on Level: A first observation is that , i.e., large there is a clear tendency that capacity values are more sensitive to the variations that the users introduce. 7) Handset Differences in CV: On average , and bit/s/Hz but there are some variations around these mean values depending on both the handset and band. On the LB the CV for H2 is in general larger than for H1, perhaps explained by the smaller size of H2 in the part of the clamshell with the user grip. Both H1 and H2 have an antenna at the bottom, and the smaller size could allow for more variation in the grip style. Also H4, with only top antennas, has roughly the same or less variation as does H1. On the other hand, H2 has significantly less variation on the HB, whereas H1 and H4 have roughly the same variation as on the LB. Thus, although size and location of antennas could explain some of the CV, specific design of the antennas seems to be important too. Comparing the results for BS1,Lo and BS1,Hi1-2, the CV tend to be a bit lower for the HB than for the LB, about 0.1 bit/s/Hz in the mean. A possible explanation for this is that the whole handset tends to act as antenna for the LB, where for the HB the radiating parts are more confined to the antenna element area. The difference is more pronounced for H2 and H7 than for H1, since the latter has one antenna at the bottom where the user holds and the antennas on H2 and H7 are located where they allow more freedom for variations in the influence of the user. 8) CV for Extra Tx Antennas: The CV values obtained for the two MIMO constellations at the LB, i.e., BS1,Lo and BS1 2,Lo, are roughly the same. Also the CV values for BS1,Hi1-2 and BS1,Hi1-4 are roughly the same. E. Repeatability In the preceding sections the performance of the mobile handsets is studied in terms of OC obtained from the measurements. In order to reach conclusions, it is important to address the repeatability of the combined measurement and processing. In principle a repeated measurement with the same user should yield the same OC, but in practice this will not be the case for several reasons, including the following. • Noise and other errors in the measurement system. • Differences in the handling of the handset, such as exact location of the user’s fingers. Even if the user is instructed to use the same grip, small changes are inevitable. • Similarly, minor changes in, e.g., the user’s route, orientation, and walking speed must be expected. • Changes in the surrounding environment. The repeated measurements allow to investigate the repeatability of the derived channel capacity statistics. Every combination of MIMO constellation, user, and grip results in repeated samples of OC. Based on these values (in total 96), percentiles

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Fig. 8. The STD of the OC when the user is present. The -axis labels are in the form Hn/Grip, where “Hn” is the handset and “Grip” is either one hand (OH) or two hand (TH). The four plots represent different MIMO constellations. Top-left: BS1, low band. Top-Right: BS1 2, low band. Bottom-left: BS1, high band, Tx1-2. Bottom-Right: BS1, high band, Tx1-4. The measured points are connected by lines only to ease reading. TABLE V PERCENTILES OF DEVIATIONS FROM MEAN IN REPEATED MEASUREMENTS. THE ROWS OF THE TABLE REPRESENTS THE OUTAGE CAPACITY (OC). THE COLUMNS SHOW THE PERCENTILES OF THE DEVIATIONS FROM THE MEAN OF THE REPEATED OC. THE VALUES ARE IN BIT/S/HZ

were computed to obtain an overview of the repeatability. Similar to the measurements with users, statistics were computed from the in total 64 combinations in free space. The percentiles regarding accuracy are shown in Table V for both free space and H1. It is noticed that 90% of the observed differences are 0.26 bit/s/Hz or below, and that the deviations tends to increase with the OC level. Similarly, the repeatability of the measured MEG was studied. Every combination of base, band, Rx antenna, grip, and person resulted in repeated samples of power, in total 144 samples. For the free space case in total 48 combinations are available. Table VI shows the percentiles of the absolute differences for both the free space and user measurements. From the

TABLE VI PERCENTILES OF DEVIATIONS FROM MEAN IN REPEATED MEG MEASUREMENTS. ALL VALUES ARE IN DB

table it is noticed that 90% of the observations are within about dB and dB of the mean value in the free space and user cases, respectively. Furthermore, in all cases the free space percentiles are smaller than those for the user cases, indicating, as expected, that the user introduces extra variability in the measurements. However, the largest part of the variation is due to other sources. V. CONCLUSION The user influence on the channel power gain was investigated in terms of the body loss (BL). Similar to previous findings for talk mode, the BL in data mode was found to depend highly on the design of the handset and the usage, with approximate mean values ranging from 0 dB to 10 dB.

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In free space the outage capacity (OC) is generally similar for the handsets, but a high MEG also results in a higher OC, as this effectively gives a higher SNR. Measured values of the 50% OC were 3.3–4.7 bit/s/Hz for an SNR of 10 dB, depending on handset and frequency band. The path loss is about 10 dB higher on the high band (HB) than on the low band (LB). As expected, the OC is reduced the most when users are likely to touch areas near the antennas. A reduction of up to about 2.2 bit/s/Hz was found for a handset with an antenna at the bottom, compared to about 0.8 bit/s/Hz for a relatively large handset with top mounted antennas. In mean the OC reduction is 0.5 bit/s/Hz higher on the HB than on the LB. Using more Tx antennas on the base than on the mobile may in free space introduce extra diversity, increasing the 10% OC about 0.2 bit/s/Hz, but when users are introduced the increase is only marginal. Using an extra BS (distributed MIMO) can provide some extra diversity in the free space case, with a 10% OC increase of up to about 0.9 bit/s/Hz, which is reduced to a maximum of about 0.7 bit/s/Hz when the user is present. Note that these numbers are for the best case with no path loss differences between the BSs. ACKNOWLEDGMENT The authors would like to thank Prof. C. Luxey and this colleagues at the University of Nice Sophia-Antipolis, France for developing the special decoupling technique and designing the antennas used in two of the handsets. REFERENCES [1] L. M. Correia, Wireless Flexible Personalised Communications. COST 259: European Co-Operation in Mobile Radio Research. New York: Wiley, 2001. [2] M. Murase, Y. Tanaka, and H. Arai, “Propagation and antenna measurements using antenna switching and random field measurements,” IEEE Trans. Veh. Technol., vol. 43, no. 3, pp. 537–541, Aug. 1994. [3] G. F. Pedersen, J. Ø. Nielsen, K. Olesen, and I. Z. Kovacs, “Measured variation in performance of handheld antennas for a large number of test persons,” in Proc. VTC, May 1998, pp. 505–509, IEEE. [4] K. Boyle, “Mobile phone antenna performance in the presence of people and phantoms,” in Technical Seminar: Antenna Measurement and SAR, May 2002, pp. 8/1–8/4, IEE Antennas and Propagation Professional Network. [5] J. Ø. Nielsen and G. F. Pedersen, “In-network performance of handheld mobile terminals,” IEEE Trans. Veh. Technol., vol. 55, no. 3, pp. 903–916, 2006. [6] M. Pelosi, O. Franek, M. B. Knudsen, M. Christensen, and G. F. Pedersen, “A grip study for talk and data modes in mobile phones,” IEEE Trans. Antennas Propag., vol. 57, no. 4, pp. 856–865, 2009. [7] D. A. Sánchez-Hernández, Multiband Integrated Antennas for 4G Terminals. Norwood, MA: Artech House, Inc., 2008. [8] D. Astély, E. Dahlman, A. Furuskär, Y. Jading, M. Lindström, and S. Parkvall, “LTE: The evolution of mobile broadband,” IEEE Commun. Mag., vol. 47, no. 4, pp. 44–51, Apr. 2009. [9] D. Gesbert, M. Shafi, D. Shan Shiu, P. J. Smith, and A. Naguib, “From theory to practice: An overview of MIMO space-time coded wireless systems,” IEEE J. Sel. Areas Commun., vol. 21, no. 3, pp. 281–302, Apr. 2003. [10] W. Kotterman, G. Pedersen, and K. Olesen, “Capacity of the mobile MIMO channel for a small wireless handset and user influence,” in Proc. 13th IEEE Int. Symp. Personal, Indoor and Mobile Radio Commun., Sep. 2002, vol. 4, pp. 1937–1941. [11] K. Sulonen and P. Vainikainen, “Performance of mobile phone antennas including effect of environment using two methods,” IEEE Trans. Instrum. Meas., vol. 52, no. 6, pp. 1859–1864, Dec. 2003. [12] J. Ø. Nielsen and G. F. Pedersen, “Mobile handset performance evaluation using radiation pattern measurements,” IEEE Trans. Antennas Propag., vol. 54, no. 7, pp. 2154–2165, 2006.

[13] V. Plicanic, B. K. Lau, A. Derneryd, and Z. Ying, “Actual diversity performance of a multiband diversity antenna with hand and head effects,” IEEE Trans. Antennas Propag., vol. 57, no. 5, pp. 1547–1556, May 2009. [14] V. Plicanic, B. K. Lau, and Z. Ying, “Performance of a multiband diversity antenna with hand effects,” in Proc. iWAT, 2008, pp. 534–537. [15] P. Suvikunnas, J. Villanen, K. Sulonen, C. Icheln, J. Ollikainen, and P. Vainikainen, “Evaluation of the performance of multiantenna terminals using a new approach,” IEEE Trans. Instrum. Meas., vol. 55, no. 5, pp. 1804–1813, 2006. [16] F. Harrysson, J. Medbo, A. Molisch, A. Johansson, and F. Tufvesson, “Efficient experimental evaluation of a MIMO handset with user influence,” IEEE Trans. Wireless Commun., vol. 9, no. 2, pp. 853–863, Feb. 2010. [17] F. Harrysson, A. Derneryd, and F. Tufvesson, “Evaluation of user hand and body impact on multiple antenna handset performance,” in Proc. APSURSI, Jul. 2010, pp. 1–4. [18] T. Zervos, K. Peppas, F. Lazarakis, A. Alexandridis, K. Dangakis, and C. Soras, “Channel capacity evaluation for a multiple-input-multipleoutput terminal in the presence of user’s hand,” IET Microw. Antennas Propag., vol. 1, no. 6, pp. 1137–1144, Dec. 2007. [19] A. Michalopoulou, T. Zervos, A. Alexandridis, K. Peppas, F. Lazarakis, K. Dangakis, and D. Kaklamani, “The impact of the user’s body on the performance of a MIMO terminal in “pocket position”,” in Proc. EuCAP, Nov. 2007, pp. 1–7. [20] Y. Okano and K. Cho, “Dependency of MIMO channel capacity on XPR around mobile terminals for multi-band multi-antenna,” in Proc. EuCAP, 2007. [21] P. Suvikunnas, J. Salo, L. Vuokko, J. Kivinen, K. Sulonen, and P. Vainikainen, “Comparison of MIMO antenna configurations: Methods and experimental results,” IEEE Trans. Veh. Technol., vol. 2, no. 57, pp. 1021–1031, Mar. 2008. [22] K. Sulonen, P. Suvikunnas, L. Vuokko, J. Kivinen, and P. Vainikainen, “Comparison of MIMO antenna configurations in picocell and microcell environments,” IEEE J. Sel. Areas Commun., vol. 21, no. 5, pp. 703–712, Jun. 2003. [23] J. Valenzuela-Valdés, M. García-Fernández, A. Martínez-González, and D. Sánchez-Hernández, “The influence of efficiency on receive diversity and MIMO capacity for Rayleigh-fading channels,” IEEE Trans. Antennas Propag., vol. 56, no. 5, pp. 1444–1450, May 2008. [24] D. Gesbert, H. Bolcskei, D. Gore, and A. Paulraj, “Outdoor MIMO wireless channels: Models and performance prediction,” IEEE Trans. Commun., vol. 50, no. 12, pp. 1926–1934, Dec. 2002. [25] 3GPP TS 36.101 [Online]. Available: http://www.etsi.org version 8.11.0 release 8 [26] W. A. T. Kotterman, G. F. Pedersen, and P. Eggers, “Cable-less measurement set-up for wireless handheld terminals,” in Proc. PIMRC, Sep. 2001, pp. B112–B116. [27] C. Icheln, J. Ollikainen, and P. Vainikainen, “Reducing the influence of feed cables on small antenna measurements,” Electron. Lett., vol. 35, no. 15, pp. 1212–1214, Jul. 1999. [28] C. Icheln, J. Krogerus, and P. Vainikainen, “Use of balun chokes in small-antenna radiation measurements,” IEEE Trans. Instrum. Meas., vol. 53, no. 2, pp. 498–506, 2004. [29] B. Yanakiev, J. Ø. Nielsen, and G. F. Pedersen, “On small antenna measurements in a realistic MIMO scenario,” in Proc. EuCAP, Apr. 2010, pp. 1–5. [30] J. Ø. Nielsen, G. F. Pedersen, K. Olesen, and I. Z. Kovács, “Statistics of measured body loss for mobile phones,” IEEE Trans. Antennas Propag., vol. 49, no. 9, pp. 1351–1353, Sep. 2001. [31] J. Ø. Nielsen, J. B. Andersen, P. C. F. Eggers, G. F. Pedersen, K. Olesen, E. H. Sørensen, and H. Suda, “Measurements of indoor 16 32 wideband MIMO channels at 5.8 GHz,” in Proc. ISSSTA, 2004, pp. 864–868. [32] L. Ozarow, S. Shamai, and A. Wyner, “Information theoretic considerations for cellular mobile radio,” IEEE Trans. Veh. Technol., vol. 43, no. 2, pp. 359–378, May 1994. [33] J. B. Andersen and F. Hansen, “Antennas for VHF/UHF personal radio: A theoretical and experimental study of characteristics and performance,” IEEE Trans. Veh. Technol., vol. 26, no. 4, pp. 349–357, Nov. 1977. [34] C. Waldschmidt, C. Kuhnert, M. Pauli, and W. Wiesbeck, “Integration of MIMO antenna arrays into hand-helds,” in Proc. 5th IEE Int. Conf. 3G Mobile Commun. Technol., 2004, pp. 16–23. [35] J. Ø. Nielsen, J. B. Andersen, G. Bauch, and M. Herdin, “Relationship between capacity and pathloss for indoor MIMO channels,” in Proc. PIMRC, 2006, pp. 1–5.

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Jesper Ødum Nielsen received the M.S. degree in electronics engineering in 1994 and the Ph.D. degree in 1997, both from Aalborg University, Denmark. He is currently employed at Department of Electronic Systems, Aalborg University, where his main areas of interests are experimental investigation of the mobile radio channel and the influence on the channel by mobile device users. He has been involved in channel sounding and modeling, as well as measurements using the live GSM network. In addition he has been working with handset performance evaluation based on spherical measurements of handset radiation patterns and power distribution in the mobile environment.

Morten Christensen was born in 1973. He received the M.Sc. degree in electrical engineering from Aalborg University, Denmark, in 1998. In 1998, he joined Bosch Telecom A/S, Pandrup, Denmark (acquired by Siemens Mobile Phones in 2000) where he designed integrated antennas for mobile terminals. In 2006 he joined Motorola A/S, Mobile Devices Aalborg where he was heading the EMC and Antenna Department. He is now with Molex Antenna Business Unit responsible for the RF Research activities. His areas of interests includes handset antenna design, performance evaluation methods and radio propagation models.

Boyan Yanakiev received the B.S. degree in physics from Sofia University, Bulgaria, in 2006 and the M.S. degree in wireless communication from Aalborg University, Denmark, in 2008 where he is currently pursuing the Ph.D. degree. His current position is as an industrial Ph.D. student in cooperation with Molex Antenna Business Unit. His primary interests are in the area of small integrated mobile antennas, optical antenna measurement techniques and radio channel measurements. He has been involved in the design and development of multiple RF-to-optical convertors, for onboard handset measurements.

Gert Frølund Pedersen was born in 1965. He received the B.Sc.E.E. degree (hons) in electrical engineering from the College of Technology, Dublin, Ireland, and the M.Sc.E.E. and Ph.D. degrees from Aalborg University, Aalborg, Denmark, in 1993 and 2003, respectively. He has been employed by Aalborg University since 1993 where he is now a Full Professor heading the Antenna, Propagation and Networking Group and is also the Head of the Doctoral School on Wireless which some 100 Ph.D. students enrolled. His research has focused on radio communication for mobile terminals especially small antennas, diversity systems, propagation and biological effects and he has published more than 75 peer reviewed papers and holds 20 patents. He has also worked as consultant for developments of more than 100 antennas for mobile terminals including the first internal antenna for mobile phones in 1994 with lowest SAR, first internal triple-band antenna in 1998 with low SAR and high TRP and TIS, and lately various multi antenna systems rated as the most efficient on the market. He has been one of the pioneers in establishing over-the-air measurement systems. The measurement technique is now well established for mobile terminals with single antennas and he was chairing the COST2100 SWG2.2 group with liaison to 3GPP for over-the-air test of MIMO terminals.

Ivan B. Bonev was born in Yambol, Bulgaria, in April 1980. He received the B.Sc. and M.Sc. degrees (hons.) in telecommunications from the Technical University of Varna, Varna, Bulgaria, in 2002 and 2004, respectively, where he also received the M.Sc. degree in electrical engineering in 2007. He is currently pursuing the Ph.D. degree in wireless communications at Aalborg University, Aalborg, Denmark. He has been a Visiting Researcher at Ecole Politechnique de luniversite de Nantes, Nantes, France; Tampere University of Technology, Tampere, Finland; and Atlantic Cape Community College, Cape May Court House, NJ. In 2007, he joined the Antennas, Propagation, and Radio-Networking (APNET) Group at Aalborg University. His current research interests include small antennas, antenna interactions with a human body, computational electromagnetics, numerical techniques, hearing aid compatibility of mobile phones, specific absorption-rate evaluation issues, performance evaluation of multiple-antenna terminals. Mr. Bonev is a member of Sigma Xi and the Hearing Loss Association of America. He is the recipient of the URSI young scientist award for 2011.

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Exposure Compliance Methodologies for Multiple Input Multiple Output (MIMO) Enabled Networks and Terminals Nicholas Perentos, Member, IEEE, Steve Iskra, Antonio Faraone, Senior Member, IEEE, Ray J. McKenzie, Giorgi Bit-Babik, Member, IEEE, and Vitas Anderson, Member, IEEE

Abstract—Multiple input multiple output (MIMO) enabled handsets and base-stations feature antenna systems that generate electromagnetic fields for which relevant exposure standards and guidelines do not explicitly define compliance testing methodologies. Here, through computational modeling, we explore several field summation schemes for evaluating such exposures and propose compliance testing methodologies that limit the degree of exposure under/over-estimation for both base stations and handsets. The methodologies rely on scalar field probe measurements thus avoiding significant equipment upgrades and are applicable to cases where access to signals from each MIMO antenna element can be arranged. Index Terms—Dosimetry, electromagnetic analysis, multiple input multiple output (MIMO) systems, Mobile antennas, safety.

I. INTRODUCTION

M

ULTIPLE INPUT multiple output (MIMO) refers to the use of multiple antennas at the radio transmitter and receiver to improve the performance of a wireless communication system. Recent technology standards have defined MIMOenabled networks including the IEEE 802.11n (WiFi), IEEE 802.16 (WiMAX), 3GPP Rel 7 (HSPA+) and 3GPP Rel 8 (LTE) [1]–[4]. As is the case with other wireless equipment of similar transmit power levels, MIMO enabled devices are required to comply with standards [5] or internationally recognized guidelines [6] for limiting human exposure to radio-frequency (RF) fields. A pertinent feature of MIMO technologies in this regard is the possibility of correlated signal transmissions at the same frequencies from multiple antennas leading to constructive or destructive interference effects in the RF exposure field of the antenna array. The RF exposure assessment guidance in current safety guidelines and product compliance standards may not be suitable for assessing such exposures.

Manuscript received July 05, 2011; revised September 29, 2011; accepted September 30, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. This work was supported by the GSM Association and the Mobile Manufacturers Forum under Grant BS123456. N. Perentos, S. Iskra, and R. J. McKenzie are with Swinburne University of Technology, Hawthorn, VIC 3181, Australia. A. Faraone and G. Bit-Babik are with Motorola Solutions, Inc., Fort Lauderdale, FL 33309 USA. V. Anderson is with Swinburne University of Technology, Melbourne, VIC 3122, Australia (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173453

This paper explores the issues that may arise when assessing exposures from MIMO enabled networks from both the perspective of the user equipment as well as the base station. Methodologies to deal with the identified issues are proposed, and procedures for exposure compliance assessment are presented in the form of flowcharts suitable for inclusion in appropriate standards. II. MIMO BACKGROUND A. MIMO Technology Multiple antennas at both the transmitter and receiver can improve system performance by improving coverage, system capacity, or improved service provisioning [7]. There are three ways in which multiple antennas can be utilized to achieve these objectives. Spatial Multiplexing: Here, the spatial dimension is reused to achieve higher overall data rates by transmitting distinct data streams from each antenna. It is also possible to continually optimize signal transmission for specific users based on feedback from the receiver. In this case, different MIMO antenna elements transmit uncorrelated waveforms since they carry uncorrelated data streams. Transmit Diversity/Cyclic Delay Diversity: Copies of the same data stream are transmitted from each antenna element (sometimes time delayed) leading to signal diversity at the receiver. The diversity provides an improved signal to noise ratio which in turn allows for higher data rates to be used. In this case, different MIMO antenna elements transmit correlated time-domain waveforms since they feature the same information content. Classical Beamforming: Here energy focusing in a subsector of a cell achieves an improved signal to noise ratio. To achieve classical beamforming different antenna arrangements are required to those typically used in MIMO enabled transceivers. For instance, co-polarized, regularly spaced column arrays are frequently required to achieve the desired pattern shape and angular scan agility. Closely spaced antenna elements experience high mutual fading correlation and thus are unable to provide the necessary signal diversity that is commonly desirable to achieve the performance improvements of MIMO. For this reason classical beamforming arrays are sometimes not included among MIMO transmitters, although classical beamforming is another case of correlated time-domain waveforms emitted by each antenna element, thus leading to interference patterns in the corresponding spatial field distribution as for

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PERENTOS et al.: EXPOSURE COMPLIANCE METHODOLOGIES FOR MIMO ENABLED NETWORKS AND TERMINALS

MIMO. Compliance assessment for classical beamforming arrangements has been previously considered [7]. A different kind of beamforming is achievable with low mutual correlation antennas, which is sometimes called pre-coding [7]. B. MIMO Enabled Base Stations Typically when a MIMO antenna system is to be implemented at a base station, it is required that independent fading conditions are experienced by each antenna element. The mutual fading correlation can be used to assess this, where a low value implies that the sources experience independent channels while a high value implies that the sources experience similar channels. One way of achieving low mutual fading correlation is to place the antenna elements sufficiently far apart. In typical urban environments a distance of a few wavelengths apart is sufficient. Another way is to co-locate antenna elements but use a different polarization for each.

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monitoring periods will eventually capture the true maximum exposure level. Such approaches are resource and time consuming so can be impractical. B. Total RF Exposure From Multiple Uncorrelated Sources Because they protect from excessive temperature rise that may be produced by RF exposure, safety standards and guidelines [5], [6] define RF exposure limits on the basis of timeaveraged metrics which depend on RMS fields. Consequently, the superposition of exposures from time-domain uncorrelated fields is readily performed by straight summation of the individual exposures. Considering two uncorrelated field sources transmitting signals and in the same frequency band, the combined exposure is the sum of the respective squared magnitudes (2)

C. MIMO Enabled User Equipment Contrary to the case for base station, user equipment typically operates in close vicinity to multiple scatterers, including the human body, which can provide good multipath fading conditions even with relatively closely spaced antenna elements . III. APPLICABILITY OF CURRENT COMPLIANCE METHODOLOGIES TO MIMO ANTENNAS

Should summation according to (2) be applied to correlated fields, the result is expected to sometimes overestimate and sometimes underestimate exposure depending on the spatial location under consideration. IV. METHODS A. Field Summation Schemes

MIMO antenna elements used in diversity or beamforming, thus transmitting time-domain correlated waveforms, belong to the broader category of correlated sources. Current assessment methodologies adequately cover multiple uncorrelated sources (spatial multiplexing MIMO) since the resulting exposure can be calculated by the summation (sometimes linearly scaled) of the individual exposures [5], [6]. However the same does not apply for correlated sources. A. Total RF Exposure From Multiple Correlated Sources Consider two correlated sources in close vicinity to each other (i.e. a few apart or closer) transmitting signals and in the same frequency band. According to the principle of superposition the resulting combined field distribution at any point in space and time will be the phasor vectorial combination of the two fields, so that the magnitude may be calculated as

Assuming that access to identifiable, correlated signals from each MIMO element is possible, several field summation schemes are proposed in the following, which provide conservative estimates of the true exposure assessed according to (1). Whereas the application of (1) would entail the use of vector field probes capable of measuring magnitude and phase for each field component, the summation schemes that we propose can be implemented with scalar field probes since they do not require knowledge of any phase information. This is a significant advantage since scalar probes and associated readout instrumentation are less complex, broadband in frequency response, easier to operate, and less expensive. For correlated source signals and , the proposed summation schemes are as follows. 1) summing the squares of the sums of local field component magnitudes (3)

(1) Since signals are expected to combine constructively or destructively at different spatial locations, the spatial distribution of RF energy will be dictated by the resulting interference patterns. The dynamic relation between MIMO elements will lead to as many distinct interference patterns as amplitude/phase combinations between elements. It follows that if field assessments through probe measurements are to be performed, at any spatial location, an equal number of measurements as interference patterns will need to be performed in order to guarantee capturing the maximum achievable exposure level. Alternatively it can be argued that adequately long field level

2) the square of the sum of local field magnitudes (4) Summations according to (3) and (4) are mathematically shown [9] to overestimate the true field level provided by (1). Our aim is to quantify the degree of typical over- and under-estimation associated with each summation scheme, including the case when (2) is (improperly) used to estimate the combined exposure from correlated sources.

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Fig. 1. Base station antenna setup. The panels are separated by distance and each has five dipoles. The elevation from the ground is . Fig. 2. An LFMA handset against a sphere volume representing the head.

B. Modeling Strategy In this study, the field summation schemes described above were applied to the field outputs of computational models representing a sample of MIMO enabled base stations and portable devices. Comparisons of the actual combined exposure level given by (1) with that of (2), (3) and (4) provide indications on the typical degree of overestimation and underestimation of each summation scheme. We consider the case of MIMO enabled base stations and the cases of MIMO enabled handset devices and laptop devices. It is important to consider these three categories of devices since standards define distinct methodologies of exposure compliance assessment for each. Base station compliance is usually demonstrated versus electric field (E) reference levels while handheld and portable devices are tested against the specific absorption rate (SAR) basic restrictions through E-field scans in the dielectric media of head and flat phantom models [8], [10], [11]. C. Base Station Modeling A typical urban scenario was modeled using the EMSS FEKO Electromagnetic Software Analysis Tool (v5.4) where two panel antennas, each featuring five dipoles fed by impedance matched distance apart, 6 m above 75 sources, are placed at a ground and excited with a 900 MHz signal (Fig. 1). Three simulations were performed for the same arrangement with the phase difference between the two elements set at 0 , 90 , and 180 , illustrating the dependence of the radiation and interference pattern on the phase difference. Two more simulations were performed where the antenna panels were excited one at a time in separate simulations. The two models were otherwise identical so as to allow for field combination based on the superposition principle. For this reason all active and inactive antennas were loaded with passive resistive loads of 75 . The two E-field vector outputs were then processed and combined and the power density at a distance of 100 m from the antenna was calculated as . The percentage deviation of the calculated power density for the (2), (3) and (4) scalar combinations was compared to the benchmark vector phasor combination (1).

D. Modeling of Portable Devices XFDTD version 6.5 modeling software (REMCOM) was used for simulations described in this section. This computational tool allows easy access and manipulation of output files and for SAR calculations to be performed independent of the FDTD computation therefore allowing SAR calculations after superposition of fields. The MIMO antenna elements were excited one at a time in separate simulations. The same approach described for the base station antennas, where one simulation per antenna element was performed while loading the others with their source impedances, was followed to compute the fields. The electric field output files of the FDTD solutions were combined to obtain according to (1)through to (4) while the phase difference between the MIMO elements was varied from 0 to 180 in 15 steps (Appendix A describes how the field components were combined numerically). From the combined electric field values SAR was then calculated. SAR values were subsequently imported into XFDTD where averaged SAR calculations (peak point SAR, 1 g and 10 g SAR) were performed. Percent deviation from (1) for the other summation schemes ((2)–4) was then calculated. Handset Models: Two handset models were simulated against a sphere with tissue equivalent dielectric medium and specific mass density properties according to the IEEE 1528 standard ( , , ) [10]. We opted for this simple geometric structure instead of the more complex SAM phantom [10] or any inhomogeneous models so as to more clearly seethe influence of the interference between MIMO elements on the SAR value without the added clutter of additional field scattering that may result from more complex geometrical shapes or dielectric boundaries. The first model was a pair of parallel dipoles ( , , ) placed 10 mm away and tangentially to the surface of the sphere. The second model (Fig. 2) was a multimode antenna presented by Kim et al. [12] called a Low Profile Folded Monopole Antenna (LFMA) operating at 2 GHz with a ground plane of dimensions

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Fig. 3. The two simulated orientations of the laptop model against the standard flat phantom are depicted. Distance d represents the separation between the two MIMO elements. Distance d is varied as 87 186 and 286 mm.

comparable to mobile phones. Antenna and ground plane dimensions were identical to those in [8]. SAR was calculated in the section of the sphere closest to the active elements of the antennas in a volume of and , for the dipole and LFMA antenna models respectively. Laptop Models: According to the IEC 62209-2 standard [11], handheld and body mounted devices should be tested against a standard flat phantom representing the torso of a human body. This standard also describes an elliptical flat phantom and distinct testing orientations of devices in relation to it. Accordingly, a laptop model was simulated against this flat phantom with orientations as shown in Fig. 3. The laptop model was made of two ground planes representing the conventional clamshell structure of laptops. Planar Inverted F-type antennas (PIFA’s) were situated on the top part of the lid as shown in Fig. 3(a). The separation distance between the PIFA antennas was set at 33,87,186 and 286 mm for orientation 1 and at 286 mm for orientation 2. The selected antenna separation distances cover a representative range of possible antenna configurations on laptops. For orientation 1, the maximum point, 1 g and 10 g SAR was calculated in the high SAR region that was observed in the phantom nearby to the antennas and the region in between. For orientation 2, the maximum SAR was calculated in the high SAR region nearby to the front edge of the laptop where it was abutting the phantom.

Fig. 4. Electric field (normalized to unity) 100 meters away from two-panel . The antenna (see Fig. 1). Panels separated by a distance of shift in peaks and troughs is clearly seen among the three patterns. Observation angle 0 corresponds to the direction of the x-axis (Fig. 1). ; 0 , ; 90 and ; 180 .

V. COMPARISON OF SUMMATION SCHEMES A. Base Station Transmitting Correlated Waveforms The dependence of the MIMO base station radiation pattern on the phase difference between the antenna elements is seen in Fig. 4. Some lobes are seen to shift by around 10 which corresponds to a distance of 17 m at a radius of 100 m away from the center point of the two panels. The true value of the combined normalized power densities according to (1) are compared to the alternate field summation schemes (2) (3) (4) 100 m away from the base station and 1 m above the ground in Fig. 5 with phase difference between MIMO elements set to 0 . When using (2) the exposure level is overestimated or underestimated depending on the fields phase relationship at the evaluation point. For (3) and (4) results are almost identical with the exposure never being underestimated.

Fig. 5. Power density (normalized to unity) at a radius of 100 m from the center point of the antenna arrangement of Fig. 1 versus observation angle. Observation angle 0 corresponds to the direction of the x-axis. ; true value, i.e. summation according to (1), ; summation according to (2), ; summation according to (3) and ; summation according to (4).

B. Portable Devices Transmitting Correlated Waveforms Handset Models: Table I summarizes the findings for the dipole and LFMA handset placed against the sphere phantom. For the dipoles model, at worst there is a 3% overestimation of maximum SAR using (4) and underestimation using (2) associated with the three scalar summation schemes. Significantly different values are recorded for the LFMA MIMO handset. An underestimation range of 16–33% is observed using (2) and an overestimation range of 32–67% using (3) and (4).

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TABLE I OVER OR UNDER ESTIMATIONS COMPARED TO (1): HANDSET MODELS

TABLE II OVER OR UNDER ESTIMATIONS COMPARED TO (1): LAPTOP MODELS

Fig. 6. The 10 g averaged SAR normalized to the vector phasor addition maximum versus the phase variation is displayed here for the PIFA laptop with antenna separation of 300 mm: true value, i.e. summation according to (1); summation according to (2); summation according to (3), and; summation according to (4). It is seen that (2) can overestimate or underestimate, while (3) and (4) always overestimate exposure.

summation scheme (2) for the 286 mm antenna separation in orientation 2. VI. COMPLIANCE ASSESSMENT METHODOLOGIES A. Field Summation for Base Stations

Antenna separation distance

Laptop Models: Table II summarizes how the ((2)–(4)) scalar summation schemes differ from the true value (1) for SAR estimates in the laptop models for both device orientations against the elliptical flat phantom (Fig. 3). For each summation scheme, the trends for maximum point, 1 g and 10 g SAR were very similar. For 10 g SAR, using (2) led to under estimations in the range of 11–42%, using (3) led to overestimations in the range of 8–20% and using (4) led to similar overestimations of 11–23%. An example of an SAR plot versus phase shift between the PIFA antennas is shown in Fig. 6 for an antenna separation of 286 mm and the laptop device oriented as in Fig. 3(a). For orientation 1, the maximum SAR occurred nearby to each of the two PIFA antenna elements, and so the interference interaction between them generally decreased as the separation distance, , increased as each had progressively less field contribution to the other. For orientation 2, the maximum SAR occurred in the phantom region adjacent to the front edge of the laptop, due to currents induced in the laptop base from both antenna elements. In this case there is a more balanced contribution of field strength from each antenna for the maximum SAR, since both are roughly equidistant from the laptop front edge. This is reflected in the higher underestimation percentages for

In Figs. 5 and 6 it can be seen that the scalar summation according to (2) tends towards the average of the vector phasor summation (1). Actual time-averaged exposure will tend towards that predicted using (2) if the variation in phase, and consequently the interference pattern, is rapidly and randomly varying. The IEEE C95.1 standard [5] and the ICNIRP Guidelines [6] specify that the average power density over any 6-minute exposure interval should be used to demonstrate compliance to reference levels. In this context, a rapid time frame is any time interval substantially shorter than 6 minutes. However, the assumption of rapid and random phase change may not always hold. For example in a static environment with no moving scatterers, small number of fixed users and no spatial multiplexing or diversity coding implemented, a fairly constant radiation pattern maybe expected, whereas in highly variable environments with moving users and scatterers where a base station switches between beam forming to diversity transmission schemes, a variable exposure may be observed. Fig. 5 shows that field summation by (3) and (4) leads to an average overestimation of approximately 70% compared to the true value (1). The summation results of (3) and (4) are very similar to each other because the electric field produced by the simulated MIMO antenna is predominantly z-polarized due to the vertical orientation of the dipoles. In such cases it is easily seen that (3) can be approximated by (4) since:

If the MIMO transmitter had significant field components in more than one Cartesian direction, as would be the case with two cross-polarized dipole antennas or multi-reflection environments, distinctly different results would be observed. The summation scheme defined by (3) is observed to be sensitive to the local frame of reference used for the measurement of the field components (see Appendix B). In practical terms

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Fig. 7. Flow chart for the assessment of MIMO base stations.

this implies that when fields are recorded by an isotropicprobe and combined according to (3) the outcome will depend on the orientation of the probe in relation to the MIMO antenna. This introduces a source of uncertainty on the amount of overestimation in the exposure evaluation using (3). B. Field Summation for Portable Devices LFMA and Dipole Handsets: Table I lists the range of results for handheld devices. The results are consistent with expectations where summation according to (2) tends towards the average (see also Fig. 6) whereas (3) and (4) overestimate exposure with (4) more so than (3). First we note that the simplistic model of the twin dipoles results in small over and under estimations. However this canonical model does not share many common features with probable implementations of MIMO antenna systems in real handsets. One basic feature that is missing is the common ground that the antenna elements are likely to share on handsets where as this is adequately addressed in the LFMA model handset. Significantly different results are observed for the LFMA handset where over estimation was up to 67%. The summation scheme defined by (3) leads to no significant reduction in overestimation for all determined SAR quantities ( 1%). An interesting trend observed in Table I is that the level of SAR increases (i.e. under-estimation is reduced or over-estimation is increased) with an increasing averaging mass for sum-

mation schemes (2–4) relative to (1). Our explanation for this is that scalar summations according to (2), (3) and (4) remove any phase information and as a result assume constructive interference at all spatial locations within the averaging mass. For a10 g SAR averaging cube, the cube dimensions are comparable to the wavelength inside the tissue at 2 GHz . Accordingly, each 10 g cube should always contain areas of destructive interference, but for summation schemes ((2)–4) these areas are summed constructively. As a result the mass averaged SAR is inflated leading to an increase in the degree of over estimation as the averaging volume is increased. Laptops: Large underestimations are observed for the summation scheme of (2) for both laptop orientations (see Table II). Overestimations resulting from the summation techniques given by (3) and (4) do not exceed 23%. It is observed that overestimation decreases when antenna separation is increased. This is so because the contribution of the one element in the vicinity of the other is minimized due to increased field decay. There is an exception however for the separation distance of 186 mm which may be a result of standing wave patterns being formed on the ground plane of the laptop. Consistent with the respective observation in the handset modeling, an increasing SAR level is observed for increasing averaging volume. Summation scheme (3) appears to provide a benefit of a few percent decreased overestimation when compared to the results of (4). Although this

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improvement may appear marginal (less than 10%), where exposure approaches the compliance limit this summation scheme can be of benefit. However the sensitivity of this scheme to the E-field probe local reference frame will need to be assessed further to quantify the likely benefit. C. Exposure Assessment Protocols for Base Stations The proposed summation schemes rely on access to distinguishable field recordings from each MIMO element. In the case of base station assessments this could be achieved by switching off all MIMO antenna elements but one and performing field measurements according to established methodologies for example as defined in the IEC 62232 standard [8]. The same procedure is then repeated for all MIMO elements and finally fields are combined according to the chosen summation scheme. This approach is inconvenient since the normal operation of the base station will need to be disrupted to perform the measurement. There are alternatives however. For example consider the case of an LTE MIMO enabled base station. Each MIMO antenna element carries its own unique pilot signal. Pilot signals of each MIMO element occur in distinct resource blocks (a unique combination of an orthogonal frequency sub carrier and time slot) and are therefore uncorrelated (see [7, pp. 324–330]). It is therefore feasible that through the use of suitable protocol analyzers, one can measure all pilot signal levels ‘simultaneously’, scale the measured field level according to the maximum transmitter output bandwidth and power and then sum the field contributions according to the preferred summation scheme. A possible approach to measurement for MIMO base stations is detailed in the form of a flow chart in Fig. 7. Owing to the limited benefit in terms of reduced overestimation and the increased complexity and potential uncertainty of using summation scheme (3), scheme (4) has been recommended in the proposed protocol as the best compromise while maintaining a conservative approach. D. Exposure Assessment Protocols for Portable Devices In the case of portable terminal devices simpler procedures can be envisaged where special software testing routines are incorporated into the MIMO enabled device where one element is switched on and all others are off while the entire area of interest is being scanned with a SAR probe. In such protocols it would be necessary to ensure that the physical dimensions of the device are scanned in entirety to ensure that the field combination can be estimated at all probable SAR peak locations. This is necessary because antenna locations or accurate prediction of possible SAR peak locations may not be possible. Field combination according to (3) can be problematic since the SAR probe orientation may change with respect to the local reference frame while a measurement is performed. The issue may be avoided if during SAR compliance assessments the orientation of the electric field probe is kept the same between and within SAR scans. This may be difficult to achieve and can lead to results that are not easily reproducible between laboratories. It may be simpler to account for the expected sensitivity through the incorporation of an additional factor into the uncertainty budget. Alternatively it may be determined through physical measurements that the

Fig. 8. A flow chart of a possible routine that can be followed for SAR assessments of MIMO enabled devices. Significant increases in scanning times should be expected as the number of antenna elements increase and as the physical dimensions of the device increase. The terms area scan and zoom scan are defined in [10].

associated uncertainty is simply small enough to be negligible. A possible compliance testing procedure for handheld devices is detailed in the form of a flow chart in Fig. 8. As for base stations, we have recommended summation scheme (4) as the best compromise which always provides a conservative estimate of exposure. E. Future Trends and Opportunities In the case of LTE-enabled portable devices, such as laptops, tablets and PDA-like smartphones, it would be desirable to conduct a SAR assessment using the approach of discriminating concurrent signals with protocol analyzers as described for base stations in Section VI-C. In this way, the device under test could be operated while transmitting from all antennas simultaneously, thereby allowing the completion of a SAR assessment in a single test. However, this approach is not feasible at the present time since SAR probes currently feature low-pass filters and diode-detectors that do not allow discrimination of different resource blocks. Nonetheless, ongoing efforts to develop vector SAR probes that could capture the LTE waveform

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Fig. 10. Two distinct cases of cross-polarized antenna setups. In the first, the orientation of the antennas coincides with the local reference frame defined by is parallel with the -axis and is parallel the chosen x-y coordinates ( to the -axis). In the second case on the right, the cross-polarized antennas are clockwise. rotated by Fig. 9. The twelve electric field components (four for each Cartesian coordinate) that form a valid tissue voxel in the FDTD implementation.

Considering the 12 components that form a valid tissue voxel in the FDTD environment

[13], [14] make it possible to envisage the use of the aforementioned approach in commercial SAR measurement systems once those efforts come to fruition. (6) VII. CONCLUSIONS We have investigated three alternative summation schemes for combining fields from MIMO antenna elements to produce estimates of RF exposure levels for the purposes of safety compliance assessments. The summation schemes rely on scalar field probe measurements thus avoiding significant equipment upgrades. They are applicable to cases where access to uncorrelated signals from each MIMO element source can be arranged, for example, through software control of the RF transmitter function of a device. Two of the summation schemes have been shown to overestimate the true SAR in all cases, and one of these has been recommended because of its relative simplicity. Using the preferred scheme based on the square of the sum of the local field magnitudes, an average over-estimation of 70% compared to the true value may be expected when assessing MIMO enabled base stations, while an overestimation of up to 67% can be expected when assessing SAR compliance of portable devices such as handsets and laptops. The compliance assessment of live traffic-carrying base stations requires ‘simultaneous’ measurement of the fields from all pilot channels and the results combined and scaled according to the preferred summation scheme. Further study is required to identify the practicalities and additional uncertainties associated with the proposed methodologies when applied to live MIMO enabled networks and devices.

where n represents the four vertices that make up any of the x, y or z components of the electric field at the centre of the voxel. Sum of the squares of the sums of local field magnitudes:

APPENDIX

The above equation is only applicable for homogeneous tissue models. Complications arise in the case of inhomogeneous models due to different media properties in adjacent FDTD voxels. However inhomogeneous models are not applicable to assessments in the homogeneous phantoms scenarios specified in SAR compliance standards [5], [6].

A. Summation Formulae for Scalar Combinations In the FDTD computational environment a tissue voxel is formed by twelve Cartesian components, or twelve complex electric fields as shown in Fig. 9, see also [15]. Therefore the scalar superposition of two or more electric fields according to (2), (3) and (4) can be implemented in the following respective ways: Sum of the squared magnitudes (5)

(7) Square of the sum of the local field magnitudes

(8) Taking into consideration the 12 components that form the voxel

(9)

B. Sensitivity of (3) to the Orientation of the Local Reference Frame Consider the case of two sets of cross-polarized antennas as depicted in Fig. 10(a) and 10(b). Assuming that the fields are linearly polarized and orthogonal with complex amplitudes and the

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combined field according to (3), using the probe arrangement in Fig. 10(a), is given by

(10) since . However if we consider the case , depicted by Fig. 10(b) we arrive at a different result, through the use of a rotational transformation matrix, , where (11) After rotation we find

(12) The square of the sum of the local field magnitudes is calculated as

(13)

[8] IEC 62232 Ed. 1 Methods for the Assessment of Electric, Magnetic and Electromagnetic Fields Associated With Human Exposure, IEC/ TC106, The International Electrotechnical Commission, 2009. [9] IEC 62630 Ed.1: Guidance for Evaluating Exposure From Multiple EM Sources, , The International Electrotechnical Commission, 2010. [10] IEEE Recommended Practice for Determining the Peak Spatial-Average Specific Absorption Rate (SAR) in the Human Head From Wireless Communications Devices: Measurement Techniques, IEEE Std 1528-2003, The Institute of Electrical and Electronic Engineers, New York, 2003, IEEE SCC34. [11] Human Exposure to Radio Frequency Fields From Hand-Held and Body-Mounted Wireless Communication Devices—Human Models, Instrumentation, and Procedures Part 2: Procedure to Determine the Specific Absorption Rate (SAR) in the Head and Body for 30 MHz to 6 GHz Handheld and Body-Mounted Devices Used in Close Proximity to the Body, IEC62209-2 Ed 1, The International Electrotechnical Commission, 2010. [12] Y. Kim, T. Hayashi, Y. Koyanagi, and H. Morishita, “Compact built-in handset MIMO antenna using L-shaped folded monopole antennas,” IEICE Trans. Comm., vol. E91-B, pp. 1743–1751, 2008. [13] T. Onishi, H. Togo, N. Shimizu, K. Kiminami, S. Uebayashi, and T. Nagatsuma, “SAR measurement employing electro-optic (EO) probe without using metal,” presented at the Bioelectromagnetic Society Annual Meeting, Dublin, June 2005, P-C-21. [14] H. Togo, N. Shimizu, and T. Nagatsuma, “Near-field mapping system using fiber-based electro-optic probe for specific absorption rate measurement,” IEICE Trans., vol. E90-C, no. 2, pp. 436–442, Feb. 2007. [15] K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’a equations in isotropic media,” IEEE Trans. Antennas Propag., vol. 14, pp. 302–307, May 1966.

When comparing (13) with (10) it is clear that except when sin , thereby indicating variable results for field summation according to (3) depending on the orientation of the local reference frame. ACKNOWLEDGMENT The authors thank J. Cambell and Prof. Q Balzano for useful discussions. REFERENCES [1] IEEE Standard for Information Technology—Telecommunications and Information Exchange Between Systems—Local and Metropolitan Area Networks—Specific Requirements Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications Amendment 5: Enhancements for Higher Throughput, 802.11n-2009 IEEE Standard, Jun. 12, 2007. [2] IEEE Standard for Local and Metropolitan Area Networks—Part 16: Air Interface for Broadband Wireless Access Systems, New York, 802.16-2009, May 29, 2009. [3] 3rd Generation Partnership Project; Technical Specifications and Technical Reports for a UTRAN-Based 3GPP System, 3GPP TS 21.101 V7.5.0 (2009-12) 2009. [4] 3rd Generation Partnership Project; Technical Specifications and Technical Reports for a UTRAN-Based 3GPP System, 3GPP TS 21.101 V8.2.0 (2009-12) 2009. [5] IEEE Standard for Safety Levels With Respect to Human Exposure to Radio Frequency Electromagnetic Fields, 3 kHz to 300 GHz, IEEE Std C95.1, The Institute of Electrical and Electronics Engineers, International Committee on Electromagnetic Safety, New York, April 19, 2005. [6] ICNIRP, “Guidelines for limiting exposure to time-varying electric, magnetic, and electromagnetic fields (up to 300 GHz),” Health Phys., vol. 74, pp. 494–522, Apr. 1998. [7] E. Dahlman, S. Parkval, J. Sköld, and P. Beming, 3G Evolution: HSPA and LTE for Mobile Broadband, 2nd ed. Burlington: Academic Press, 2008.

Nicholas Perentos (M’09) received the Bachelor degree and the Ph.D. degree in engineering telecommunications from RMIT University, Melbourne, Australia, in 2005 and 2008, respectively. In 2009, he joined the Australian Centre for Radiofrequency Bioeffects Research (ACRBR) as a Postdoctoral Research Fellow and in 2010 he joined the University of Cambridge, Cambridge, U.K., as a Research Fellow. He is interested in the development of medical implants as well as interference issues of electromagnetic exposures to such devices.

Steve Iskra received the B.E. (Hon.) degree in electrical engineering from the University of Melbourne, Australia, in 1982. In 1982, he joined the Electromagnetic Compatibility (EMC) Group, Telstra Research Laboratories (TRL). In 2001, he moved to TRL’s Electromagnetic Energy Safety Research Group and has been involved in the measurement of electromagnetic fields, computational electromagnetics, and RF interference effects on medical devices. He has published in peer reviewed journals in the areas of EMC, human exposure to electromagnetic fields and RF personal dosimetry. Mr. Iskra is a Past Chairperson of Standards Australia (SA) Committee TE/3 (EMC), is a member of committees SA TE/7/2 and TC106 WG4 of the International Electrotechnical Commission (both in the area of human exposure to RF fields).

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Antonio Faraone (M’97–SM’05) was born in Rome, Italy, in 1966. He received the Ph.D. degree in applied electromagnetics from the University of Rome “La Sapienza,” in 1997. He then joined the Motorola (now Motorola Solutions Inc.) Corporate EME Research Laboratory, Fort Lauderdale, FL, engaging in mobile antenna technology and RF dosimetry research. He is a Motorola Scientific Advisory Board Associate member, Motorola Distinguished Innovator, and. Fellow of the Technical Staff within the Chief Technology Office. He holds 18 patents in antenna technology and has coauthored more than 30 refereed journal publications. Dr. Faraone is actively involved in IEEE and IEC standards related to human exposure to RF energy and the Convener of the IEC Technical Committee 106 (Methods for the assessment of electric, magnetic and electromagnetic fields associated with human exposure), Working Group 4.

Ray J. McKenzie received the B.S. degree in applied science (with first class honours) in physics from RMIT University in Melbourne, Australia, in 1996. He was the Project Leader of the EME Safety Research Group, Telstra Research Laboratories (TRL), Clayton, Australia, until 2005, joining Telstra’s Chief Technology Office in 2006. He was also the Research Director, Dosimetry, at the Australian Centre for RF Bioeffects Research (ACRBR) until its closure in 2011. He specializes in electromagnetic propagation and physical interactions, in particular, the dosimetry and measurement of ambient fields and SAR, as well as computational electromagnetic modeling. He has spent 23 years in the area of electromagnetic energy and has coauthored over 50 publications and conference papers in RF dosimetry, radiation protection, and electromagnetic interference. Mr. McKenzie is active on Standards Australia, IEEE and IEC RF exposure standards committees, and is a Technical Assessor for the National Association of Testing Authorities (NATA) in the area of RF measurements. He is a member of the Applied Computational Electromagnetics Society and the Bioelectromagnetics Society.

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Giorgi Bit-Babik (M’97) was born in Tbilisi, Georgia, in 1972. He received the M.Sc. and Ph.D. degrees in radio physics and electronics from Tbilisi State University (TSU), Tbilisi, Georgia, in 1994 and 1998, respectively. Until 2000, he was an Associate Professor at TSU, where he was engaged in research on computational electromagnetics. From 2001 to 2008, he was with Motorola Corporate Electromagnetic Energy Research Laboratory, Fort Lauderdale, FL. He is currently a Distinguished Member of the Technical Staff within the Chief Technology Office at Motorola Solutions, Inc. His research interests in applied and computational electromagnetics include antenna technology, numerical techniques and RF exposure and dosimetry. He is actively involved in the IEEE and IEC standards related to human exposure to RF energy and is chairing the working group developing the computational methods for evaluation of exposure from mobile radio antennas. He has coauthored 16 peer reviewed journal publications and over 70 conference papers and holds nine patents in antenna technology.

Vitas Anderson (M’00) was born in Melbourne, Australia, in 1960. After studying medicine for three years, he changed to engineering and completed his mechanical engineering degree (Hons) at the University of Melbourne, in 1985 and received the Ph.D. degree in biophysics from Swinburne University of Technology (SUT), Australia, in 2001. His main professional area of interest has been in bioelectromagnetics (especially electromagnetic and thermal dosimetry) which he began in 1989 at the Telstra Research Laboratories in Melbourne, and continued as a Research Engineer until 2000. From 2001 to 2008, he was mainly engaged as a consultant in electromagnetic safety policy, training and research. In 2008, he was appointed as an Associate Professor of bioelectromagnetics at SUT, and returned to consulting in late 2011. Since 1995, he has been an active contributor to radiofrequency (RF) safety and exposure assessment standards for the ICES/IEEE, Standards Australia and the International Electrotechnical Commission (IEC). He has coauthored 28 peer reviewed journal publications or book chapters and 53 conference papers.

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MIMO Transmission Using a Single RF Source: Theory and Antenna Design Osama N. Alrabadi, Member, IEEE, Julien Perruisseau-Carrier, Member, IEEE, and Antonis Kalis, Senior Member, IEEE

Abstract—An approach for transmitting multiple signals using a single switched parasitic antenna (SPA) has been recently reported. The idea there is to map the signals to be transmitted onto a set of basis functions that serve as “virtual antennas” in the beamspace (i.e., wavevector) domain. In this paper, we generalize the derivation of the antenna pattern basis functions regarding a three-element SPA of arbitrary radiating elements, within a symmetric array topology, for multiplexing signals in the wavevector domain (using different beampatterns) rather than in the hardware antenna domain with multiple feeding ports. A fully operational antenna system example is modeled, optimized regarding its return loss and the power imbalance between the basis functions, and finally realized. The measurements of the SPA show good agreement with the simulated target values, revealing an accurate design approach to be adopted as a fast SPA prototyping methodology. The SPA has been successfully employed for multiplexing two binary phase-shift-keying (BPSK) datastreams over-the-air, thus paving the way for practically compact and highly efficient MIMO transceiver designs. Index Terms—Basis functions, MIMO, reconfigurable antenna, switched parasitic antenna.

I. INTRODUCTION

M

ULTI-INPUT MULTI-OUTPUT (MIMO) communication has gained lots of attention over the last decade as it enhances the spectral efficiency by exploiting the precious spatial resource dimension [1], [2]. Since the emergence of this technology, the classical approach has been assuming a transmitter with a number of transmit RF chains in order to independently map a set of signals onto a corresponding set of antennas. The receiver on the other hand performs some complex signal processing so as to decode the linear mixture of the signals and extract the useful data. However, having multiple RF

Manuscript received May 14, 2010; revised August 29, 2011; accepted September 02, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. The work of J. Perruisseau-Carrier was supported by the Swiss National Science Foundation (SNSF) through its Professorship program. O. N. Alrabadi is with the Antennas, Propagation and Radio Networking (APNet) Group, Department of Electronic Systems, Aalborg University, DK-9220 Aalborg, Denmark (e-mail: [email protected]). J. Perruisseau-Carrier is with the Group for Adaptive MicroNano Wave Systems, LEMA/Nanolab, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne CH-1015, Switzerland (e-mail: [email protected]). A. Kalis is with the Broadband Wireless and Sensor Networks (BWiSE) Group, Athens Information Technology (AIT), GR-19002, Athens, Greece (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173429

chains at the user mobile terminal is rather costly. For example, the LTE–Release 8 standard supports a single antenna for the uplink transmission and two antennas for the downlink reception [3], [4]. The asymmetry in the number of antennas is mainly intended for avoiding the costly power amplifiers in the transmit RF chains. Although antenna selection is a terminal option, it requires instantaneous channel state information from the receiver back to the transmitter, which is a burden on the wireless communication system. Consequently, classical MIMO transmission especially in uplink scenarios may not be supported due to the practical limitations of the portable RF units. To overcome these challenges, the authors in [5] describe how a half rate space-time (ST) code is transmitted with a single radio. In fact, a simple time-switched ST code [6] will outperform the approach in [5] regarding both performance and complexity. In [7], the authors propose an antenna system of two RF sources and four antenna elements. The proposed antenna system is capable of changing its polarization state (at the modulation rate), and thus transmitting the 4 4 Jafarkhani code. However, having two transmit RF chains may still be costly for low-end terminals. On the other hand, the authors in [8] proposed a MIMO-like system using a switched parasitic antenna (SPA) with a single RF source. The SPA was shown to have a throughput potential comparable to that of conventional MIMO systems by switching the SPA far-field at the modulation rate, however no specific multiplexing techniques were proposed. In fact, parasitic antenna systems have been proposed over the past as a promising solution for addressing the problems associated with the difficulty of integrating multiple RF chains in compact portable units [9]. Such antenna systems comprise a single RF branch and multiple antenna elements loaded by variable reactive impedances. By controlling the reactance via a dc control, basic antenna properties, like the beampattern, can be reconfigured. Parasitic antennas have been widely used for providing receive angular (or pattern) diversity (examples are given in [10] and [11]) and have recently been proposed for analogue beam and null steering [12]. The use of a compact-sized SPA for emulating open-loop MIMO transmission has been first proposed in the work of Kalis et al. in [13] followed by work of Alrabadi et al. [14]. The idea of using an SPA as a MIMO terminal is to drive the central active antenna with a high frequency RF signal modulated by the first datastream, while simultaneously driving a set of parasitic elements (PEs) strongly coupled to the active one with a baseband (low frequency) control signal as shown in Fig. 1. The baseband control signal has information about the other datastreams to be

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complex conjugate transpose (Hermitian) operators, respectively. The notation indicates an identity matrix of size . The operator returns a square matrix with the elements of the vector laid across the main diagonal of the matrix. Moreover, we consider a classical uniform three-dimensional angular power spectrum seen by the transmitter (the mobile terminal), which is approximately the case when the mobile unit is surrounded by many scatterers. The rest of the paper is organized as follows. In Section II, we describe a technique for transmitting two BPSK signals simultaneously via a single RF front end. Section III expresses the basis functions of a three-element SPA based on full-wave electromagnetic modeling and optimizes the SPA for BPSK signaling regarding the average rate of transmission. Section IV describes an SPA example of printed dipoles and explains its design implementation. Section V shows both simulation and measurement results, and finally Section VI concludes the paper. II. MIMO TRANSMISSION WITH A SINGLE RF SOURCE

Fig. 1. Schematic diagram of the proposed technique where the first bitstream is modulated, up converted and fed into the central active element whereas the second bitstream is XORed with the first one. The output control signal is used for swapping the loads of the PE.

transmitted over the air. By this way, it has been shown that the input datastreams are mapped onto an orthogonal set of basis functions in the wavevector domain via a single radio and compact array dimensions. In this paper, we focus on binary phase-shift-keying (BPSK) signaling format (the extension to all phase-shift keying (PSK) is straightforward by following the approach in [14]) where we first generalize the derivation of the bases from mirror image pattern pairs (MIPPs) i.e., when one beampattern is a mirrored version of the other, regardless of how the MIPPs are expressed. We therefore extend previous findings by decoupling the wavevector domain [15] from the antenna domain and thus enabling MIMO functionality through any antenna system capable of creating MIPPs. At the receiver side, we prove that the receive antenna response to a beampattern that is a linear mixture of basis functions is nothing more than the linear combination of the receive antenna responses to the different basis functions. By this way, the receiver decodes the transmitted data symbols by estimating the basis responses using classical training techniques. A practical antenna system example of printed dipoles is proposed, modeled, optimized regarding the average rate of transmission, and finally designed and demonstrated. The measured return loss and radiation patterns are in good agreement with the target parameters, revealing a fast and accurate designing methodology. Throughout the paper, a bold small letter designates a vector, and a bold big letter designates a matrix. The operators and designate complex conjugate, transpose, and

In this section, we first prove the existence of an orthogonal basis whenever an MIPP can be formed. Based on this, a technique for transmitting two BPSK signals using an arbitrary single radio based antenna system capable of forming an MIPP is described. A. Orthogonal Bases Using an MIPP The correlation between two arbitrary beampatterns and is given by

(1) where

(2) are the spatial integration of the power beampatterns of and over the space, respectively. Whenever , the two beampatterns are called “balanced.” Lemma 1: For an MIPP and , the set of the angular functions defined as

(3) form an orthogonal basis. Proof: For two beampatterns that form an MIPP, we have since one beampattern is just a mirrored version of the other. Moreover, the correlation between the two beams is real

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(see the proof in the Appendix), and thus . Based on these observations, the proof is straightforward and is given as follows:

TABLE I TWO BPSK SIGNALS COMBINATIONS

compactness. Letting the sole RF port be fed by the signal the antenna beampattern in the far-field becomes either

(4)

Corollary 1: A balanced basis is obtained by designing the two beampatterns and described in Lemma 1 and are to be orthogonal to each other, i.e., if orthonormal, and are orthonormal too.1 Proof: Letting , the proof is straightand are the spatial inteforward, as shown in (6). In (6), gration of the power beampatterns of and , over the space, given, respectively, by

,

State 1

or State 2

or generally as (7a) (7b)

(5)

(6)

B. Transmission Technique Description In this part, we show that an arbitrary antenna system that has a single RF input but has the capability of creating an MIPP will be capable of transmitting two BPSK signals and , simultaneously. The two BPSK signals are mapped onto an orthogonal set of basis functions; thus, independent fading between the two signals is almost always guaranteed regardless of the transceiver 1The reason that we acquire an orthonormal basis and from an MIPP is that the MIPP by itself represents a linear combination (desired multiplexing relation) of the basis onto which the signals are mapped. The diversity action of the system directly depends on the transmit covariance of the basis (proportional to the identity matrix when the basis is orthonormal).

is State where is the antenna system state such that and 1 within which the antenna system transmits over is State 2 within which the antenna system transmits over . From (7b), it is obvious how the two BPSK signals: , which is modulated in the baseband, upconverted, and fed into the input RF port and , which is spatially modulated on the antenna far-field by controlling the antenna state , are mapped onto the space of and , respectively. In general, for any PSK modulation of order is a set of complex numbers evenly distributed over the unit circle, as discussed in Section IV of [12]. Table I shows the state required for transmitting according to the value of , where is input vector of bits modulated into . Fig. 1 shows a schematic diagram of the proposed technique, where the XORing of the two bitstreams gives the required , i.e., giving 0 and 1, which correspond to and , respectively. C. System Training The two BPSK signals that are transmitted in the beam-space domain and received using a classical uniform linear array (ULA) of antenna elements ( -element ULA), can be decoded by first estimating the receive antenna responses to the proposed basis. Proposition 1: A beampattern comprising a linear mixture of basis functions (at the transmitter side) triggers a linear combination of the individual channel responses to the different basis functions (at the receiver side).

ALRABADI et al.: MIMO TRANSMISSION USING A SINGLE RF SOURCE: THEORY AND ANTENNA DESIGN

Proof: This directly stems from the principle of superposition in linear systems. To have a deeper insight, we first define 2 1 column vectors , and , where the first and the second elements of every column vector represent the and polarizations of the corresponding pattern, respectively. We also define as the vector of the polarization components of the th receiver an. As in [16], we assume that the propatenna pattern gation channel between the transmitter and the receiver consists of a set of plane waves, with the th wave characterized by a , and complex voltage gain , angle of departure . We also assume that each plane angle of arrival wave undergoes a polarization transformation due to scattering that can be expressed as the unitary matrix (8) when ilThe response of the th receive antenna luminated by the beampattern is the complex channel gain representing the ratio of the received voltage signal to the transmitted voltage signal and may be written as shown in (9), where is a constant that depends on the receiver and the transmitter active gains and impedances [17], and are the responses of the th receive antenna to and , respectively. By applying the same analysis, the response of the th receive antenna when illuminated by becomes .

(9)

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III. ANTENNA MODEL AND OPTIMIZATION In this paper, we adopt the antenna topology proposed in [14], i.e., a symmetrical three-element SPA, where the central element is the active one, while the other two are passive. The two parasitic elements are loaded with pure imaginary loads as the real part of a complex load degrades the efficiency of the antenna system. Obviously, the antenna system can create an MIPP (the plane in Fig. 1) by simply permuting the reactive loads of the PE as , based on image theory. In other words, having the first beampattern at , the beampattern is obtained at . Consequently, by feeding the central active element with the first BPSK datastream and permuting the loads according to the second datastream, the two streams are simultaneously transmitted out of a single radio and mapped onto an orthogonal basis according to Lemma 1, irrespective of and . Having the two loads and as a degree of freedom when considering BPSK signaling, we can optimize the loads according to a specific criterion as shown in Section III-C.

A. Generalized Derivation of Antenna Basis Functions Although the beampattern of thin electrical dipoles (or monopoles) can be practically approximated as an array factor by the superposition of the retarded currents induced on the wire antenna elements such as in [14, eq. (6)], this is not true when considering general2 radiating elements, e.g., flat or fractal dipoles, slot antennas, etc. To overcome this problem, we implement full wave electromagnetic modeling based on the SPA scattering parameters (S-parameters) denoted by , as well as the 3D complex active port patterns3 of the antenna elements 0, 1, and 2 shown in Fig. 1, denoted by and , respectively. An expression of the electric far-field beampattern of a three-element SPA based on the aforementioned quantities and the variable antenna loading has been derived in [19] using Mason’s rule. From [19] and after correcting the equations to properly adhere to Mason’s rule, the two basis functions obtained when swapping the imaginary loads of the two parasitic elements become

Based on this, the receiver can decode the two BPSK signals by estimating the channel responses of the basis as (10a) (10b) By constructing the matrix of the receive antennas’ responses, the receiver can zero-force the received signal by inverting the channel matrix (or using any other reception techniques) for decoding and .

(11) 2Again, we emphasize that the arbitrariness of the elements is limited to the center element being a self mirror image, and the outer two being respective mirror images of each other, both about a vertical plane that divides the left and right sides of the SPA structure. 3The active port pattern is defined as the beampattern obtained when driving the corresponding port (whether being active or passive) with a unit excitation voltage signal while terminating the other ports with reference impedances [18].

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where

vector matrix5

, the transmit covariance is obtained as

(16) (12)

and

such that

(13)

which is simply the power distribution across the basis functions since according to Lemma 1. Notice that , which is easily obtained from (2) and the basis definition in (3), where is the average transmit power. Defining the power imbalance ratio between the basis functions as , we can write as , where is the normalized power distribution across the basis functions such that . can be written as such that and . From the above, the received signal model becomes

(14) where we assumed by having the source impedance at the central driven port equal to the reference impedance . The basis coefficients in (12) are derived with respect to a general scattering matrix. Swapping the two reactive loads as , swaps the coefficients in (11), thus phase-shifting by 180 without affecting . By this way, the factor in (7a) is obtained. The two functions and are the basis functions that are used to transmit two PSK signals of any modulation order [14]. B. Received Signal Model Considering a narrowband, flat-fading, point-to-point communication link where the two BPSK symbols are transmitted in the beam-space domain over two basis functions (equivalent to two uncorrelated virtual antennas) and received using an -element ULA of uncorrelated and uncoupled antenna elements. Assuming independent fading statistics at the transmitter and the receiver, the Kronecker product [20] can be assumed and thus the channel transfer function can be written as4

(17) where

is the power into the transmitter (input power) and is the efficiency of the transmit antenna system being equal to , where is the SPA return loss derived in [19]. Finally, is the vector of the modulated BPSK signals (see Table I), and is a vector representing the white Gaussian noise, with zero mean and variance. C. Optimization Criterion In this paper, we define the optimal SPA loads as the ones that maximize the average rate of transmission. However, in MIMO communications, average rate computation often demands tackling calculations of expectations with respect to random matrices rather than random scalar variables. For this reason, we derive an upperbound on the average rate and deploy it as an optimization criterion. We assume open-loop operation where the channel is known to the receiver but unknown to the transmitter. The ergodic capacity of a MIMO random channel, denoted by , is the ensemble average of the information rate over the distribution of the elements of the channel matrix . By using the formula [22], the upper bound that comes from the Jensen’s inequality and the concavity of ,6 we get

(15) where the elements of the matrix are independent and identically distributed (i.i.d.) complex Gaussian random variables with zero mean and unit variance. The correlation at the receiver side is ignored by the aforementioned assumptions regarding the receiving ULA. Defining the row 4In [21], the correlation based channel model accounts for the mutual coupling by explicitly incorporating the coupling matrices. However, in (15), the mutual coupling is implicitly taken into consideration within the calculation of the basis functions in (11).

5Since the basis functions are imbalanced, the transmit covariance matrix rather than the transmit correlation matrix is considered. 6The

is concave over positive semi-definite matrices [23]. Since is positive semi-definite, the term is positive semidefinite too, as it is a one-to-one mapping of , thus preserving the positive definiteness.

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(18) In (18), the average transmitted power is not divided by the number of the basis functions (the number of the virtual antennas), since the trace of is normalized to a unity rather than to the number of the basis functions (both forms are equivalent). The optimal loading is defined as the one that maximizes the average throughput upperbound in (18), i.e., Fig. 2. Schematic diagram of the SPA initially proposed in [24].

(19) In (19), is made part of the optimization criterion by constraining rather than as the SPA efficiency is a key design parameter when considering portable RF units with limited storage batteries. IV. ANTENNA SYSTEM DESIGN In this section, we consider the three-element SPA shown in Fig. 2, where the radiating elements are thin printed dipoles. The planar topology of the SPA makes it better fit in compactnessconstrained mobile units as compared to the majority of the wire parasitic antennas already proposed in the literature. The current SPA was proposed earlier in [24]; however, in this paper, we complete the work by describing the implementation and the measurements of the prototype. A. Design Parameters and Optimal Loading The first design steps consist of making some initial choices on the antenna materials and the basic topology. We consider a three-element SPA of flat dipoles as radiating elements as shown in Fig. 2, designed on an 1.5-mm-thick substrate of relative permittivity . The dipole lengths and spacing are 48.3 and 11 mm, respectively. The spacing is at the desired operational frequency of 2.6 GHz. The SPA was simulated using HFSS, with ports at the locations of the variable loads. The resulting scattering matrix is given by

(20) where the matrix is symmetric by the reciprocity theorem i.e., by the usual assumption of employing antennas with electrically reciprocal materials, thus . Moreover, the symmetric topology of the SPA shown in Fig. 1 ensures that and . The antenna system is lossy as when compared to the lossless four-port network (expressed by ) in [19] as by the energy conservation principle when including the radiated beams in the network structure. Further, the diagonal elements of are nonvanishing as we aim at diminishing the return loss of the central active element rather than . The resulting three-port S-parameters and the complex

Fig. 3. An optimization contour map regarding the upperbound on and . respect to

with

3D active port patterns were exported to Matlab, where a computer routine scans the realizable range of the reactance space searching for given by (19). Fig. 3 shows an optimization contour plot of at a transmit signal to noise ratio7 (SNR) 10 dB. The figure shows that is maximized at . At such loading, the upperbound on is 5 b/s/Hz, the power imbalance between the two basis functions is 0.56 dB, and the SPA efficiency is 97%. B. Reconfigurable Impedance Implementation The design of the variable load, explained in more detail in the earlier partial work of [24], consists of the following steps: First, an adequate layout for the reconfigurable load area, to be controlled using a PIN diode, is selected [“Reconfigurable Load Area” in Fig. 4(a)]. The parasitic capacitance ( , and ) between the different pads are extracted from full-wave simulations. Here the inductive effect in the pads can be neglected in the design. Subsequently, the surface-mounted elements to implement and are deduced from the circuit of Fig. 4 so that the overall impedance in each state and 7In fact, the transmit SNR is commonly used in the literature when evaluating the system performance. However, as the SPA loading will affect the transmit SNR through the matching efficiency, it seems more reasonable , which is simply the transmit SNR before the mismatch effect to use . On the other hand, the way of calculating the receive SNR represented by is different and is shown later in (20).

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Fig. 4. Reconfigurable dipole load impedance: (a) Layout and elements view, including biasing network; (b) target two-state variable impedance; and (c) detailed implementation circuit, including layout parasitic capacitances.

[see Fig. 4(b)] match the target values deduced in the previous section, namely and . Finally, a dc biasing network was designed using large RF-block inductors and a resistor to precisely control the diode biasing current. As can be seen in Fig. 6, the dc paths are then driven to the other side of the substrate by vias, where they can conveniently be connected to the dc voltage references in the antenna environment (see Section V). The PIN diode (Aeroflex Metelics MPN7310A-0805) serves as a low capacitance fast switch, with a negligible transient switching time (orders of nanoseconds). and are capacitors of 0.5 and 0.8 pF, respectively. The biasing network elements are 22 nH and 910 . In order to experimentally validate the reconfigurable load design prior to its insertion in each of the SPA parasitic dipoles, it was fabricated and measured using a thru-reflect-line (TRL) calibration kit, which allows placing the measurement reference planes at the desired locations, as required here. It is then possible to extract the desired impedances and from the measured S-parameters and microstrip line impedance, as shown in Fig. 5 for each of the diode states. The imaginary parts of the measured impedance and at the design frequency of 2.6 GHz are 38 and 108 in the ON and the OFF states, respectively. These values are close to the target reactances of 27 and 100 , considering the tolerances of the SMD elements and the impact of the biasing network. The real parts of and are not exactly zero due the diode and SMD components finite resistances, which were neglected in the design procedure (their measured average values are only 5 and 3 in the OFF and the ON states, respectively). The target basis functions (at ) and the achieved ones are compared in Fig. 7, showing very good agreement. V. SIMULATION AND MEASUREMENT RESULTS The current section presents the measurements of the different SPA parameters and compares them to the corresponding parameters obtained by computer simulations.

Fig. 5. Measured load impedance in each diode state of the PIN diode, extracted from the S-parameter measurements on a dedicated microstrip TRL calibration kit, from [24]. The OFF and ON diode states correspond to a reversed 0 V and forward ( 9 mA) bias, respectively.

Fig. 6. Photograph of the fully operational SPA, optimized for the proposed aerial MIMO approach.

A. Antenna Demonstration A photograph of the fully operational fabricated antenna is shown in Fig. 6. It was observed that a good balanced excitation of the active dipole is simply obtained by connecting the central and the outer conductors of a coaxial connector to each of the dipole arms. The variable load designed and characterized in Section IV-B was introduced in each parasitic dipole of the SPA, including the dc biasing network. The dc ground pad of each variable load on the backside of the substrate is connected by a printed line to the coaxial connector outer conductor (which thus serves as a dc ground), whereas each actuation pad (shown as “ ” in Fig. 4) is connected by a thin wire to the

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Fig. 7. The magnitude of the H-plane co- polarized basis functions at the target and at the practically achieved loads of . loads of The two basis functions resemble the omni and the angular sine functions, which are orthogonal to each other. Fig. 9. Return loss (dB) of the SPA for both loading states, i.e., .

Fig. 8. Setup of the antenna for reconfigurable radiation pattern measurements, with a 9-V battery places behind the absorber cone in a direction of the low field intensity.

bias voltages for controlling the states of the diodes. In order to improve the antenna performance and provide pure measured patterns, the dc wires are driven along the coaxial feed, which is oriented toward the minimum radiation of the SPA (i.e., parallel to the dipoles, see Fig. 6). A standard 9-V battery is used as a dc source in the radiation pattern measurements. The battery is placed behind a piece of an absorber (located in the direction of minimum radiated power density), as can be seen in Fig. 8. Therefore the antenna states were simply selected by connecting each of the two dc wires to the 0 or 9 V references. The impact of the biasing voltages on the antenna performance was investigated, showing similar responses for 10 to 0 V as the OFF (or “reverse-biased”) state, while 3 V to 10 V are acceptable for the ON (or “forward-biased”) state. B. Return Loss Fig. 9 shows the simulated and measured return loss of the SPA around the design frequency of 2.6 GHz. The graph only shows the response in the operational states of the antenna, namely when it is loaded by the reactance load pairs and . As explained earlier in Section IV, the return loss is the same for both states due to the SPA symmetry, which is confirmed here by the similarity between the two measured

and

curves in Fig. 9. The SPA was found to have poor matching in the two (unused) states and ), which are not shown here. The agreement between simulations and the measurements is moderate, since the measured bandwidth is larger than the one obtained by simulation and is not exactly centered around the design frequency of 2.6 GHz. Nevertheless the measurements show good return loss at 2.6 GHz. The 10-dB measured bandwidth is 5.6% and 7.1% for a reference of 10 dB, for and , respectively. C. Radiation Patterns Fig. 10 shows the H-plane co- and cross- polarized far . Note fields in the first operational antenna state that the maximum of the co-polarized beampattern, located at 90 , corresponds to the direction of the load in the OFF state. The simulated and measured co- and cross- polarized beampatterns are in good agreement, as shown in Fig. 10. Because of the SPA symmetrical structure and the reactance pair antisymmetry, the other antenna beampattern should simply be a mirror image of the first beampattern around the 0 180 axis, which is well verified by the measured prototype, as can be seen in Fig. 11. D. Experimental Results The proposed antenna prototype has been successfully used for spatially multiplexing two BPSK datastreams over the air at 2.6 GHz. The experiments constitute to the best of the authors’ knowledge the first MIMO transmission with a single RF source yet to be proposed. The first train was modulated into a BPSK symbol stream (using a raised-cosine waveform with 0.3 roll-off factor) and upconverted to 2.6 GHz. The high frequency signal was modulated to the central element within a modulation bandwidth of 533 kHz. The second binary train was XORed with the first binary train in the baseband domain and the output baseband control signal was amplified and used for

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Fig. 10. Simulated and measured co- and cross- polarization components of the in the H-plane, i.e., , at 2.6 GHz. beampattern Fig. 12. Scatter plot of received signal constellation after equalization.

Fig. 11. Measured co- and cross- polarization components of the beampatterns and at 2.6 GHz. Notice that , resulting in an MIPP.

switching the SPA loads. A simple zero-forcing decoding was implemented by the receiver which was equipped with two distant omnidirectional monopole antennas separated from each other by 23 cm or , and both are located several wavelengths from the SPA (the receiver is located in the broadside direction of the SPA, but completely blocked from the transmitter in the sense that no line-of-sight between the transmitter and the receiver exists). The receiver first estimates the receive antennas’ responses to the two beampatterns and using classical training, then the response to the basis is obtained from (10a)–(10b). Finally, the 2 2 complex channel matrix is inverted and used for equalizing the received signal. A total bit rate of 820 kb/s was obtained with arbitrarily low error; thus, a spectral efficiency of 1.54 b/s/Hz can be claimed. Although this seems far from the target upperbound of 5 b/s/Hz, it is well justified by the fact of using real signaling with uniform distribution rather than complex signaling with Gaussian distribution. The details of the experiments’ setup are detailed in [25]. Fig. 12 shows the received signal constellations after equalization (spatial separation), onto which the transmitted signals

Fig. 13. Probability of error versus the transmit SNR (per bit).

(red dots) are also projected, for comparison reasons. Every demodulated signal comprises of two noisy clouds such that and . The receive SNR of the th cloud is calculated as

SNR

(21)

returns the sample mean of the operand, and returns the sample variance of the operand. The four clouds have almost the same SNR, and the mean of the four SNRs is finally considered. The bit SNR referred to as is calculated by adding to the average SNR (in decibels), where is the number of samples per one symbol, whereas the 0.5 factor is due to using real signaling. In this experiment, was set to five samples per symbol such that each transmission has 410 symbols or equivalently 2048 samples. On the other hand, Fig. 13 shows the bit probability of error versus obtained by measurements as well as the performance of a 2 2 BPSK-MIMO with a Rayleigh channel of independent and identically distributed coefficients, and where

ALRABADI et al.: MIMO TRANSMISSION USING A SINGLE RF SOURCE: THEORY AND ANTENNA DESIGN

zero-forcing decoding.8 The figure shows that the performance of the beamspace MIMO is comparable to the conventional one, thus validating the importance of such a new approach for realizing single radio compact-sized MIMO transceivers. VI. CONCLUSION The paper generalized a previously reported approach for transmitting multiple signals using a single RF source. The idea is to obtain an orthogonal or orthonormal basis out of MIPPs. The paper also provided design steps for an example of a threeelement SPA, capable of forming an MIPP that are mirror images of each other. The SPA was optimized for BPSK signaling by deriving a criterion that maximizes the SPA efficiency and minimizes the power imbalance between the basis functions, simultaneously. A reconfigurable impedance was designed and a fully operational SPA for single radio MIMO transmission was demonstrated for the first time. The measured SPA parameters are in good agreement with the target values, regarding the SPA return loss and the radiation patterns in the different SPA states. Finally, the SPA has been successfully used for multiplexing two BPSK datastreams with a total bit rate of 820 kb/s. APPENDIX In this part, we prove that the cross-correlation of an MIPP in a uniform field is real. Proof: Assuming an MIPP over the angular domain, where is the azimuth polar system of coordinates with a reference axis taken from the MIPP axis of symmetry (the can be dropped for simplicity). The MIPP can generally be written as and . The can be further written as , where and are the real and imaginary parts of . The cross-correlation of the MIPP becomes

ACKNOWLEDGMENT The authors like to thank P. Pardo for fabricating and measuring the variable load circuit, and P. Miskovsky for his help in 8Theoretically, of a 2 2 BPSK-MIMO under Rayleigh fading and a zeroforcing receiver is unsurprisingly identical to the performance of 1 1 BPSK[26]. SISO i.e.,

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the antenna measurement, both at Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Barcelona, Spain. Finally, the authors express their deepest gratitude to the editor and to the anonymous reviewers for their helpful and constructive comments and suggestions. REFERENCES [1] J. H. Winters, “On the capacity of radio communication systems with diversity in a Rayleigh fading environment,” IEEE J. Sel. Areas Commun., vol. SAC-5, pp. 871–878, Jun. 1987. [2] G. J. Foschini and M. J. Gans, “Limits of wireless communication in a fading environment when using multiple antennas,” Wireless Pers. Commun., vol. 6, no. 3, pp. 311–335, 1998. [3] Overview of 3GPP Release 8 V0.0.3, Nov. 2008 [Online]. Available: http://www.3gpp.org/Release-8, available online at [4] J. Kotecha, “LTE:MIMO techniques in 3GPP-LTE,” Freescale Semiconductor, Inc., Jun. 2008, available online. [5] M. Okoniewski, S. V. Hum, A. Sutinjo, and G. G. Messier, “A spacetime coding scheme utilizing phase shifting antennas at RF frequencies,” IEEE Antennas Wireless Propag. Lett., vol. 4, pp. 369–372, 2005. [6] J. Yuan and B. Vucetic, Space-Time Coding. New York: Wiley, 2003. [7] A. Grau, J. Romeu, M. Lee, S. Blanch, L. Jofre, and F. De Flaviis, “A dual-linearly-polarized MEMS-reconfigurable antenna for narrowband MIMO communication systems,” IIEEE Trans. Antennas Propag., vol. 58, no. 1, pp. 4–17, Jan. 2010. [8] M. Wennstorm and T. Savantesson, “An antenna solution for MIMO channels: The switched parasitic antenna,” in Proc. 12th IEEE Int. Symp. Pers., Indoor, Mobile Radio Commun., Sep. 2001, vol. 1, pp. 159–163. [9] R. Vaughan, “Switched parasitic elements for antenna diversity,” IIEEE Trans. Antennas Propag., vol. 47, no. 2, pp. 399–405, Feb. 1999. [10] T. Sawaya, K. Iigusa, M. Taromaru, and T. Ohira, “Reactance diversity: Proof-of-concept experiments in an indoor multipath-fading environment with a 5-GHz prototype planar ESPAR antenna,” in Proc. Consumer Commun. Netw. Conf., Jan. 5–8, 2004, pp. 678–680. [11] M. Yamamoto, M. Taromaru, H. Sadamichi, and A. Shimizu, “Performance of angle switch diversity using ESPAR antenna for mobile reception of terrestrial digital TV,” in Proc. IEEE 64th Veh. Technol. Conf. (VTC–Fall 2006), 2006, pp. 1–5. [12] C. Sun, A. Hirata, T. Ohira, and N. C. Karmakar, “Fast beamforming of electronically steerable parasitic array radiator antennas: Theory and experiment,” IIEEE Trans. Antennas Propag., vol. 52, no. 7, pp. 1819–1832, Jul. 2004. [13] A. Kalis, A. G. Kanatas, and C. B. Papadias, “A novel approach to MIMO transmission using a single RF front end,” IEEE J. Sel. Areas Commun., vol. 26, no. 6, pp. 972–980, Aug. 2008. [14] O. N. Alrabadi, C. B. Papadias, A. Kalis, and R. Prasad, “A universal encoding scheme for MIMO transmission using a single active element for PSK modulation schemes,” IEEE Trans. Wireless Commun., vol. 8, no. 10, pp. 5133–5142, Oct. 2009. [15] A. S. Y. Poon, R. W. Brodersen, and D. N. C. Tse, “Degrees of freedom in multiple-antenna channels: A signal space approach,” IEEE Trans. Inf. Theory, vol. 51, no. 2, pp. 523–536, Feb. 2005. [16] M. L. Morris and M. A. Jensen, “Network model for MIMO systems with coupled antennas and noisy amplifiers,” IEEE Trans. Antennas Propag., vol. 53, no. 1, pp. 545–552, Jan. 2005. [17] C. Waldschmidt, S. Schulteis, and W. Wiesbeck, “Complete RF system model for analysis of compact MIMO arrays,” IEEE Trans. Veh. Technol., vol. 53, no. 3, pp. 579–586, May 2004. [18] D. M. Pozar, “The active element pattern,” IEEE Trans. Antennas Propag., vol. 42, no. 8, pp. 1176–1178, Aug. 1994. [19] L. Petit, L. Dussopt, and J. Laheurte, “MEMS-switched parasitic-antenna array for radiation pattern diversity,” IIEEE Trans. Antennas Propag., vol. 54, no. 9, pp. 2624–2631, Sep. 2006. [20] D. S. Shiu, G. J. Foschini, M. J. Gans, and J. M. Kahn, “Fading correlation and its effect on the capacity of multielement antenna systems,” IEEE Trans. Commun., vol. 48, no. 3, pp. 502–513, Mar. 2000. [21] Y. Fei, Y. Fan, B. K. Lau, and J. S. Thompson, “Optimal single-port matching impedance for capacity maximization in compact MIMO arrays,” IEEE Trans. Antennas Propag., vol. 56, no. 11, pp. 3566–3575, Nov. 2008.

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[22] A. Paulraj, R. Nabar, and D. Gore, Introduction to Space-Time Wireless Communications. Cambridge, U.K.: Cambridge Univ. Press, 2003. [23] R. A. Horn, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1996. [24] J. Perruisseau-Carrier, O. N. Alrabadi, and A. Kalis, “Implementation of a reconfigurable parasitic antenna for beam-space BPSK transmissions,” in Proc. Eur. Microw. Conf. (EuMA), Paris, France, Sep. 2010, pp. 644–647. [25] O. N. Alrabadi et al., “Spatial multiplexing with a single radio: Proof-of-concept experiments in an indoor environment with a 2.6 GHz prototype,” IEEE Commun. Lett., vol. 15, no. 2, pp. 178–180, Dec. 17, 2010. [26] D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge, U.K.: Cambridge Univ. Press, 2005.

Osama N. Alrabadi (M’10) was born in Jordan in 1979. He received the Electrical Engineering Diploma from the University of Jordan (JU), Amman, in 2002, the Master’s degree in information and telecommunications (M.S.I.T.T.) (with highest hons.) from Athens Information Technology (AIT), Greece, in 2007, and the Ph.D. degree from Aalborg University (AAU), Denmark, in 2011. In 2001, he joined Orange Mobile (previously MobileCom) for undergraduate training in the Microwave and GSM Network Maintenance Department. From 2002 to 2006, he was working at the National Electrical Power Company (NEPCO) and the Jordan Electrical Power Company (JEPCO) in remote control, metering, and communications. He is currently a Postdoctoral Fellow at the Antennas, Propagation and Radio Networking (APNet) group at AAU. He is currently working on the Smart Antenna Frontend (SAFE) project, in cooperation with the antenna company Molex, the tuner company Wispry, Irvine, CA, and Intel Mobile Communications. His research interests include design and modeling of small antenna arrays, space–time signal processing, as well as MIMO and cognitive radio transceiver architectures. Dr. Alrabadi has been a member of the Jordan Engineering Association since 2002.

Julien Perruisseau-Carrier (S’07–M’09) was born in Lausanne, Switzerland, in 1979. He received the M.Sc. and Ph.D. degrees from the Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland, in 2003 and 2007, respectively. In 2003, he was with the University of Birmingham, U.K., first as a visiting EPFL M.Sc. student and then as a short-term researcher. From 2004 to 2007, he was with the Laboratory of Electromagnetics and Acoustics (LEMA), EPFL, where he completed his Ph.D. while working on various EU funded projects. From 2007 to 2011, he was an Associate Researcher with the Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Barcelona, Spain. Since June 2011, he has been a Professor at EPFL funded by the Swiss National Science Foundation (SNSF), where he leads the group for Adaptive MicroNano Wave Systems. He has led various projects and work packages at the National, European Space Agency, European, and industrial levels. He has authored more than 50 conference papers and more than 20 journal papers. His main research interest concerns interdisciplinary topics related to electromagnetic micro- and millimeter-waves: dynamic reconfiguration, application of micro/nanotechnology, metamaterials, and joint antenna-coding techniques. Prof. Perruisseau-Carrier was the recipient of the Young Scientist Award of the URSI-EMTS 2007 conference (Ottawa, Canada), of a Torres Quevedo Grant awarded by the Spanish government, and of the Raj Mittra Travel Grant 2010 presented by the IEEE Antennas and Propagation Society.

Antonis Kalis (A’01–M’03–SM’10) received the Electrical Engineering Diploma degree from the Electric Engineering Department of the University of Patras, Greece, in 1997 and the Ph.D. degree from the University of Patras in 2002. In 1997, he joined the Laboratory of Electromagnetics at the University of Patras, participating in various R&D projects for the Greek Government and the European Union, as a Member of Research Staff. In 2000, he worked as a Research Engineer and an Assistant Research Unit Manager at the Computer Technology Institute. He joined Athens Information Technology (AIT) in January 2003. During the summer semester of the same year, he taught the course Network Design and Evaluation at Carnegie Mellon University, Pittsburgh, PA. In 2004, he supervised the work of D. Leang in Pittsburgh, PA, which received the Kennametal Fellowship Award. Since 2005, he has been an Adjunct Professor at Carnegie Mellon University. He is also currently a Professor at AIT. From June to November 2009, he spent a semester in the Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Barcelona, Spain, as a Visiting Scientist. Since 2003, he has also worked as a consultant for a number of small enterprises in Cyprus and the United States. His research interests are in the areas of radio communications, antenna design, and wireless networks. He has numerous journal and conference publications and a U.S. patent. Dr. Kalis received the Chester Sall Memorial award of the Consumer Electronics Society in the areas of radio communications, antenna design, and wireless networks in 2000. His research output has drawn the interest of the scientific community, underlined by a significant number of invited talks (e.g., in Bell Labs, Princeton University, Carnegie Mellon University, University of Trento, University of Piraeus, etc.) and one IEEE tutorial in PIMRC 2007, entitled “Developments in ESPAR Antennas.” A paper that he coauthored appeared in the October 2010 issue of the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, and was nominated for the Marconi paper award. Other recognitions include numerous invitations to act as an organization chair, session chair, and member of the technical program committee in major IEEE conferences in the field of communications. He has been a member of the Technical Chamber of Greece since 1998.

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MIMO Capacity Enhancement Using Parasitic Reconfigurable Aperture Antennas (RECAPs) Rashid Mehmood, Student Member, IEEE, and Jon W. Wallace, Member, IEEE

Abstract—The capacity of multiple-input multiple-output (MIMO) systems employing reconfigurable apertures (RECAPs) is carefully analyzed with a realistic thermal noise model for three different power constraints: average receive signal-to-noise ratio (SNR), maximum effective isotropic radiated power (EIRP), and average transmit power. Performance is studied not only for a noise-limited single link, but also in the presence of interference and multiple RECAP-equipped users. The impact of loss and finite bandwidth on the operation of the RECAP is also considered. For the practical EIRP constraint, results show that a compact MIMO RECAP provides 30%–50% capacity improvement for a single link. It is also found that RECAPs are even more beneficial in interference-limited and multiuser scenarios, where capacity is increased by 50% to 800% depending on the severity of the interference, indicating that RECAPs are an attractive solution for future wireless systems employing aggressive spectral reuse. Index Terms—Information rates, interference suppression, multiple-input multiple-output (MIMO) systems, reconfigurable antennas.

I. INTRODUCTION

R

ELIABLE and high performance transmission continues to be a major goal of wireless communication systems, which is significantly enhanced by arrays employing beamforming and diversity techniques. Multiple-input multiple-output (MIMO) wireless technology emerged in the 1980s and has gained increasing attention due to the significant gains in channel capacity [1], [2], possible by exploiting channel multi-path with spatial multiplexing. In a communication system, the channel matrix includes effects of the physical propagation environment and antenna radiation and reception characteristics. Antennas can be viewed as transmit and receive filters that are ideally matched to the physical channel, enhancing signals of interest and mitigating noise and interference to maximize capacity [3]. Although for a single fixed antenna, no adaptation of spatial filtering is possible, multiple fixed antennas connected to multiple radio frequency (RF) and digital signal processing (DSP) chains can employ the “smart

Manuscript received July 21, 2010; revised November 30, 2010; accepted January 15, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. The authors are with the School of Engineering and Science, Jacobs University Bremen, Bremen 28759, Germany (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173445

antenna” concept [4] to provide dynamic spatial filtering. However, the increased RF and DSP resources may be prohibitive for many applications. The term reconfigurable aperture (RECAP) antenna [5], [6] refers to a large array of analog reconfigurable elements (REs), which can be manipulated in order to support beam-steering, signal-to-noise (SNR) maximization, interference suppression, and dynamic matching. In contrast to smart antennas, RECAPs adapt directly in the analog radio-frequency (RF) domain and require only a single RF chain and modest DSP resources, potentially providing lower cost. RECAPs are also interesting for MIMO systems, where the optimal antenna array exploits the multi-path to provide peak capacity while using as few active RF chains as possible. Also, for multi-user systems RECAPs can adapt patterns to dynamically partition spatial reuse of spectral resources. Optimal antenna selection for MIMO has been considered (e.g., [7]), where only a few antennas out of a set of antennas are chosen for capacity maximization with lower complexity. The improvement in the channel capacity using a reconfigurable antenna is presented in [8], where moderate sized switched parasitic arrays with relatively few REs are used. A practical antenna solution providing multiple patterns with a single fixed antenna is presented in [9], exhibiting improved performance compared to spatially separated dipoles. Capacity maximization using planar RECAPs at transmit and receive is investigated in [10], where each antenna acts as a single RECAP. A reconfigurable MIMO array consisting of two dipole elements is introduced in [11], where by adaptively changing the length of the dipoles, modest increases in single-user capacity are possible. The important study in [12] shows that MIMO systems with reconfigurable antennas have a maximum diversity order equal to the product of the number of transmit antennas, receive antennas, and the reconfigurable states. This idea is expanded in [13], where not only practical space-time coding methods that code over the antenna state to maximize diversity are developed, but also practical aspects like antenna switching time are considered. This previous work on reconfigurable MIMO systems has some limitations. First, only simple termination-independent receiver noise has been considered, which is known to be inaccurate for analyzing MIMO systems with variable termination [14]. Second, limited reconfigurability has been considered, which may be insufficient to exploit the degrees of freedom of the occupied aperture. Third, the role of the power constraint has not been studied in detail, where typically only an average transmit power constraint has been assumed. Finally, capacity maximization for a single link limited by thermal noise has been

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considered, but multi-user systems with interference are more realistic for today’s wireless scenarios. This work provides a more comprehensive analysis of capacity enhancement possible with reconfigurable antennas by addressing these previous shortcomings. To this end, we study a RECAP consisting of a 9 9 parasitic array having sufficient complexity to exploit a compact aperture as studied in [15]. In contrast to [10], the complete aperture is exploited rather than using separate RECAPs for each MIMO antenna. A realistic noise model is considered in order to take into account the effect of matching on amplifier noise. Three realistic but distinct power constraints are also considered, indicating where RECAPs are most effective: 1) average signal-to-noise (SNR), where transmit and receive power are normalized and the focus of optimization is on channel orthogonality and multi-path enhancement; 2) effective isotropic radiated power (EIRP), which allows power enhancement at receiver but not at transmitter, which is more practical for many of today’s communication systems; and 3) average transmit power, which is a commonly assumed constraint allowing power enhancement at both transmit and receive. In addition to considering a single link limited by thermal noise, we also consider fixed interference and multiple RECAP-equipped links. The remainder of the paper is organized as follows: Section II explains the simulation method that was used to study RECAPs, followed by Section III that defines MIMO capacity with power constraints. Section IV studies the MIMO channel capacity using RECAP antennas in comparison with non-RECAP arrays, and Section V concludes the paper. II. ANALYSIS OF PARASITIC RECAP STRUCTURE The structure considered in this study is depicted in Fig. 1(a), which is a 9 9 dipole array consisting of -oriented half-wave dipoles constrained to an area of in the plane. Each dipole is either an active “feed” (connected to a transmit or a receive chain) or terminated with a reconfigurable element (RE), each of which has 8 possible reconfigurable states (RSs) to ensure sufficient control over the aperture [15]. The top view of the structure is shown in Fig. 1(b), where REs and feeds are indicated by squares and circles, respectively. In this work, we consider propagation in the plane, where the two-dimensional array can generate patterns with both endfire and broadside characteristics. REs are assumed to be variable capacitances, such that the reflection coefficient presented at the th port is , where . We have assumed that is uniformly distributed on as presented in [15]. Although planar RECAPs with realistic RE biasing are arguably more practical, this study employs this simple structure, since it can be simulated efficiently and its performance is not constrained by practical limitations of existing switch technologies, biasing, substrate losses, etc. Time required for RE switching for a dynamic reconfigurable antenna was treated in [13] for MEMS switches, indicating that this overhead can significantly impact system throughput. For our analyzed structure employing variable capacitances (i.e. varactor diodes), the switching time is expected to be a few ns, which is on the order of a symbol for existing modulation

Fig. 1. Configurations for non-RECAP and RECAP arrays: (a) perspective view of the parasitic RECAP with 2 feeds. (b) Top view of RECAP configurations, where red boxes show RE positions, blue stars and circles show feed 2 and 4 4 MIMO respectively. (c) Top view of antenna locations for 2 positions for non-RECAP for 2 2 MIMO (stars) and 4 4 MIMO (circles), where boxes are empty locations.

standards. Thus, switching at the beginning of a transmission frame should incur negligible overhead. On the other hand, if tunable MEMS devices are used, switching times could be higher, requiring longer block lengths to mitigate overhead as explained in [13]. Although a detailed analysis of switching time for dynamic adaption in time-varying channels is beyond the scope of this paper, this remains an important consideration for practical systems. Thus, this present work demonstrates the benefit of the RECAP concept for MIMO systems, and practical aspects are to be treated in future work. A. Efficient Simulation of RECAP Structure Efficient simulation of the RECAP is accomplished by combining full-wave simulation of the array with network analysis for RE loading. The structure is first analyzed using the Numerical Electromagnetics Code (NEC), which yields the admittance matrix and short circuit embedded radiation patterns of the arrays, where gives the radiation into polarization for unit voltage excitation on port , when the other ports are short-circuited. S-parameter analysis is more convenient for this study, where the S-parameter matrix and matched ( -terminated) patterns are computed as (1) and (2) is the real scalar normalizing impedance, respectively, where and is the identity matrix. Note that the matched circuit patterns in (2) are embedded patterns, where the entry gives the pattern radiated into polarization when port is

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Fig. 2. MIMO system model and noise matching for LNAs. (a) System model; (b) LNA matching.

driven with a unit incident wave and the other ports are terminated in loads . Next, network analysis is used to find radiation patterns and the input reflection matrix of the feeds for arbitrary RE termination. Defining and as the vectors of incident and reflected waves on the feed ports and and as the corresponding vectors on the RE ports

with internal impedance . The insource voltage cident traveling waves on the feed ports are simply , and radiated far fields are given by (7). The RE-terminated receive array is modeled in a similar manner, expect that due to external incident field, a source wave term must be included, such that . Assuming a plane wave arriving at angle and reciprocity

(3) (8) where has been partitioned according to feeds and REs. Terminating RE ports with loads having reflection matrix , we have , where is a diagonal matrix with . Combined with (3) (4) (5) is the input reflection coefficient matrix looking where into the feed ports for the given termination at the REs. In this work, we choose to be closely matched to a single half-wave dipole. The field radiation pattern of the RECAP with RE termination is

gives the polarization and complex amplitude of the where plane wave. A multi-path model is assumed consisting of clusters and paths (or rays) within the th cluster, where the th path in the th cluster has angle of departure , angle of arrival , complex amplitude , and time of arrival , or , where is frequency. Although depolarization of the paths is not considered in this work, this could be included by making a matrix. Superimposing the waves due to all paths

(6)

(9) C. Noise Modeling

where and represent matched patterns corresponding to feeds and REs respectively. Substituting (4) into (6) yields

(7) where represents matched patterns of feed ports with RE port termination . B. System Model Next, we consider using RECAPs at transmitter (Tx) and receiver (Rx) to form a complete system, as depicted in Fig. 2(a). Note that unprimed and primed RECAP quantities denote those at Tx and Rx, respectively. At Tx the th feed is connected to

In order to consider a realistic system, where noise from the low-noise amplifier (LNA) at the receiver depends on the feed reflection, we employ an LNA model equivalent to [14], where equivalent forward and reverse traveling noise waves at the LNA input are needed to properly model real transistors. The receiver consists of a matching network, forward and reverse noise sources, and LNA as shown in Fig. 2(a). The multiport LNA is assumed to consist of multiple uncoupled LNAs with optimal reflection coefficient , normalized equivalent noise resistance , and minimum noise figure , available from a standard LNA data sheet. Straightforward analysis at the connection of array and matching network reveals (10)

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where

where (11) (12) The incident wave

into the amplifier is found to be, (13)

In this work, a fixed (non-RECAP) array is used as a reference case for gauging performance improvement, and an identical uncoupled matching network is assumed on each of the receive feeds such that for the reference, where is the source reflection coefficient that provides optimal noise performance. The same uncoupled matching network is employed for the RECAP, and noise coupling from one feed to the next and deviation of can lead to reduced SNR. Fig. 2(b) shows the uncoupled matching arrangement on each branch that transforms to using , a reciprocal lossless matching network, such that where is a 2 2 matrix. The required conditions are satisfied with (14) (15) is a 2 2 block matrix, where the th block is equal to from (14) and (15), and is an identity matrix. Note that the fixed matching network can also be lumped into the LNA to form the effective LNA shown in Fig. 2(b), with new optimal reflection coefficient and equivalent noise resistance . Plugging (9) into (12) and the result into (13) yields

, is the equivalent-noise resistance, is the noise voltage covariance, , is Bolzmann’s constant, is reference temperature, and is bandwidth. Since is the same for the reference and RECAP systems and SNR of the reference system is fixed, has no effect on capacity and is set to 1. Note that since a data sheet typically assumes , which is different from the value used in our analysis, the transformation (21) is required, where and are optimal reflection and reference impedance from the data sheet. Summarizing, the MIMO input-output relationship is given by (16), where RE-dependent noise covariance is computed from (17)–(20), where parameters , , and are available from a standard LNA specification. Although computation of the noise covariance in this way seems cumbersome compared to MIMO analyses that directly specify , the added complexity is necessary to capture noise coupling of the active ports and variable input impedance of the receive array, which both affect capacity when thermal noise is significant compared to interference. D. LNA Specification This analysis uses the MAXIM MAX2656 LNA, having , noise-equivalent resistance , and optimum reflection coefficient (at ) [17]. Since the specific LNA may 1960 MHz and affect the simulations and conclusions, we briefly consider the impact of the LNA choice. Analysis of the RECAP mainly depends on how sensitive the noise figure of the LNA is to the reflection coefficient presented by the RECAP. Noise figure for uncoupled LNAs is [16] (22)

(16) is from (9), is noise, where is the channel matrix, and and are input and output signals. The linear term applied to both signal and noise does not change capacity and is omitted. The noise covariance is

is the reflection coefficient looking into the output of where one of the matching networks. Assuming a lossless matching network shown in Fig. 2(b) that transforms the source reflection to of the LNA, it can be shown that for , (23)

(17) where

,

, and

are [16] (18) (19) (20)

where is the the equivalent LNA noise resistance referenced back to the input of the matching network where . Fig. 3 shows noise figure degradation in dB for difand using (23), where . ferent values of As increases, the penalty of mismatch can increase dramatically. However, our chosen amplifier (as indicated in the figure) has moderate sensitivity to mismatch, making it a good candidate for this initial study. Amplifiers with much higher would

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Although RECAPs that can adapt to each instantaneous value of , and are optimal, this rate of adaptation may be unrealistic for practical implementation. Thus we also consider a system that adapts average RECAP performance when the and are fixed, but only the are random. We refer to the former and latter cases as instantaneous and average RECAP optimization, where average performance is computed in the latter case using 10 realizations of . F. Genetic Algorithm

Fig. 3. Effects of

and

on

.

simply increase mismatch penalty, which would more strongly constrain the set of useful RECAP states, possibly resulting in reduced capacity. E. MIMO Channel Modeling The channel matrix is given by (16), where is found according to the path-based model in (9). In this work we consider models where attention is restricted to the azimuthal plane ( and are 90 ). Two propagation models are assumed for the paths between Tx and Rx: 1) Uniform Model: In this simple model, a single cluster is assumed with rays having arrival times . Angles of arrival and departure are uniformly distributed on and has a unit variance complex normal distribution. 2) SVA Model: The more realistic Saleh-Valenzuela angular (SVA) model [18] assumes clusters, where the arrival of the th cluster has the conditional pdf (24) where is the arrival rate of the clusters. Relative arrival time of the th ray within the th cluster has the pdf (25) where is the arrival rate of rays. The complex amplitude of the th ray in the th cluster is complex gaussian, where the variance decays exponentially with arrival time according to (26) and and are the cluster and ray decay time constant, respectively. The azimuthal angle of the th cluster at transmit and receive is and , respectively, which are uniformly distributed on . The relative transmit and receive angles of the th ray in the th cluster are and , which follow a double-sided Laplacian distribution with pdf , where is the angular spread.

Due to the large number of RE combinations, obtaining the optimal solution with an exhaustive search is not feasible, and a genetic algorithm (GA) is employed. The GA employed in this work is basically equivalent to that described in [15], except that REs at both transmit and receive end are jointly optimized to maximize the capacity. Note that the purpose of using genetic algorithms in this work is only to explore the peak potential of RECAP-enabled MIMO, since such algorithms may be too expensive for in-situ optimization due to the extensive training overhead and computation time required. The development of direct RECAP optimization methods more suitable for real-time optimization is a long-term goal of this research, to be treated in later work. III. MIMO CAPACITY WITH CONSTRAINTS For the analysis of MIMO channel capacity, we have used the RECAP structure explained in Section II, for both Tx and Rx, forming a MIMO system. In order to properly scale power and assess RECAP capacity gain, a reference non-RECAP antenna array is considered, having the same number of feeds and area as the RECAP, but consisting of matched dipoles. Although antennas were placed as far apart as possible for the reference case, some initial experiments were required to find the best placement of feeds for the RECAP to give peak capacity. Having feeds too close to the aperture center or edge reduced the capacity of the RECAP, and a balanced arrangement gave the best performance. Channel capacity is computed from (27) , where is and for equal power allocation the total Tx power, and is the number of Tx feeds. Lumping noise covariance into the channel matrix results in (28) where

is computed using (17). Plugging (28) into (27) (29)

which can be interpreted as the capacity of an effective channel for i.i.d. noise (unit variance) and transmit power . A convenient way of enforcing the different power constraints in this study is to first define the average single-input single-output (SISO) gain of a given system as (30)

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where is Frobenius norm and is the number of feeds at Rx, which indicates the average power gain provided by channel matrix with respect to all active ports. The desired SNR of a system can then be fixed by normalizing that system by its SISO gain according to and setting transmit power as , resulting in the equivalent capacity expression (31) where represents the normalized quantity. Below we explain how this normalization can be used to implement power constraints for three realistic cases. Fixed SNR Constraint (Case 1): The total amount of transmitted/collected power is the same for both the non-RECAP and RECAP structures. This constraint ensures that the RECAP can only increase capacity by improving channel orthogonality or conditioning. For Case 1, channel matrices corresponding to a non-RECAP reference (REF) and the RECAP are normalized as (32) (33) Normalizing each system individually by its own SISO gain forces the RECAP and reference case to both have average SISO SNR when computing capacity with (31). Max EIRP Constraint (Case 2): Here we constrain the EIRP of the RECAP to be no larger than that of the reference (non-RECAP) system. This is accomplished by setting transmit power such that a prescribed SNR is obtained for the reference system, and this same transmit power is also used for the RECAP system. Maximum EIRP of the RECAP system is then limited to be equal to or lower than that of the reference system by scaling the embedded RECAP radiation patterns according to

Fig. 4. Instantaneous and average MIMO channel capacity for a simple nonRECAP array (dashed lines) and RECAP (solid lines): (a) 2 2 MIMO with , (b) 4 4 MIMO with .

Average Transmit Power Constraint (Case 3): In this case, only average transmit power is constrained such that a prescribed SNR is obtained for the reference system, and no constraint is placed on directional gain of Tx or Rx antennas. Specifically, channel matrix normalization is done using (32) and (35), allowing the RECAP to obtain a power advantage through both transmit and receive beamforming. IV. MIMO CAPACITY ANALYSIS Since the advantage of RECAP may depend on the number of antennas, we consider both 2 2 and 4 4 MIMO systems. Fig. 1 shows the top view of transmit/receive antennas for the RECAP and non-RECAP structures for the analyzed 2 2 and 4 4 MIMO systems. Results are for the uniform path-based model and reference SNR , unless otherwise noted. A. Single User MIMO Capacity

(34)

refers to the radiation pattern of the th feed at where Tx, refers to the one corresponding to the th feed of the reference (non-RECAP) Tx, and is used in place of when computing in (9) when is less than or equal to 1 (i.e. when a RECAP feed provides higher maximum gain than a non-RECAP feed). The non-RECAP and RECAP channels are normalized respectively with (32) and (35) Note that although the advantage of transmit beamforming by the RECAP is removed due to the maximum EIRP normalization, both channels are normalized by the SISO gain of the reference system, preserving possible enhanced power collection with receive RECAP beamforming.

Channel capacity for single user communication is computed using (31) where is computed using the cases in Section III. 1) 2 2 MIMO System: Fig. 4(a) plots the capacity for the RECAP and non-RECAP structures for average and instantaneous optimization. Note that capacity for the non-RECAP does not change with constraint type, since the reference has constant SNR, and the slight difference with respect to optimization type is due to different Monte Carlo realizations. For fixed SNR (Case 1), RECAP capacity is only marginally better than that of the non-RECAP, indicating that two channels of sufficient quality are obtained without reconfigurability, and the RECAP cannot significantly improve this. The main advantage of RECAP is power, with significant improvements seen when moving to the EIRP constraint (Case 2) and the transmit power constraint (Case 3). It is also apparent that average optimization is only slightly worse than instantaneous optimization, which is reasonable for power enhancement, since multi-path directions are mainly important, not the phases of signals sent in those directions.

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2) 4 4 MIMO System: Fig. 4(b) shows that RECAP performance is more flat with respect to the constraint type for the 4 4 MIMO system, suggesting that power advantage is less important and more opportunity for improving channel conditioning exists. Also a more significant gap is seen between average and instantaneous optimization, indicating not only mutli-path directions but also phases are important to attain peak capacity. Finally it is interesting that the transmit power constraint for the 2 2 RECAP system gives almost the same performance as the 4 4 system with the EIRP constraint. B. Single User MIMO Under Interference Constraint Most practical systems for personal wireless communications are interference limited, and we therefore study the effect of interference on single-link capacity in detail. In order to model the effect of interference, we extend to be the covariance matrix of noise and interference, or

Fig. 5. Channel capacity for single user 2 2 MIMO with fixed interference for a simple non-RECAP array (dashed lines) and RECAP (solid lines): (a) uni, (b) SVA model. form multi-path

(36) where represents the channel matrix between the interferer and receiving antennas, other quantities are for interferer, analogous to those at Tx, and we assume . Plugging (36) into (27) and simplifying yields

(37) where is interference-to-noise ratio. Since depends on proximity of the interferer, values of between 0 to 20 dB are considered. We assume that the interfering node employs a non-RECAP structure and is computed as

(38) 1) 2 2 MIMO System: Fig. 5(a) plots the capacity of a 2 2 system with multi-path for both non-RECAP and RECAP. The case for , is similar to no interference. As increases, non-RECAP capacity steadily drops towards zero, since for interference with rank , it is not possible for the non-RECAP to null the effect. Although capacity for both the non-RECAP and RECAP is falling with increasing , closer inspection reveals that the capacity gain of using the RECAP over the non-RECAP actually increases with increasing . Performance degradation is much smaller for the RECAP since REs can be used to null interference, suggesting the possibility of aggressive spectral reuse. 2) 4 4 MIMO System: The results for varying are shown in Fig. 6(a) for . The overall effect is same as that of 2 2 system, but the curves are flatter with respect to the power constraint, indicating that power advantage is less important for more feeds for fixed interference as well. However, improvement relative to the non-RECAP is still very significant, especially for severe interference.

Fig. 6. Channel capacity for single user 4 4 MIMO with fixed interference for a simple non-RECAP array (dashed lines) and RECAP (solid lines): (a) uni, (b) SVA model. form multi-path with

C. Multi-User MIMO Building on the idea of employing aggressive spectral reuse, we next consider a true multi-user scenario where users optimize their RECAPs to maximize sum capacity. This is different from the case of fixed interference, since the role of the transmit RECAP becomes more important to reduce interference to the other user. Although for fixed interference, the user does not have control over interference, he also does not care about how much interference he causes. For the multi-user case, interference can be controlled but users also impact each other. Capacity degradation due to interference depends on proximity, and between 0 and 20 dB is again considered. Two links are considered, where each receiving user experiences interference from the transmitter of the other link and a joint optimization is done in order to maximize the sum capacity

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Fig. 7. Channel capacity for two-user 2 2 MIMO for a simple non-RECAP array (dashed lines) and RECAP (solid lines): (a) uniform mutli-path with , (b) SVA model.

Fig. 9. Effect of losses for a simple non-RECAP array (dashed lines) and , (b) RECAP (solid lines): (a) 2 2 MIMO with uniform multi-path and . 4 4 MIMO with uniform multi-path and

D. SVA Propagation Model

Fig. 8. Channel capacity for two-user 4 4 MIMO for a simple non-RECAP array (dashed lines) and RECAP (solid lines): (a) uniform mutli-path with , (b) SVA model.

The simple path-based model is convenient, but possibly over-simplistic to represent true propagation scenarios, and hence we also consider the Saleh Valenzuela Angular (SVA) model [18]. The parameters of the model are assumed to be , , , and , taken from [18]. The model makes use of a threshold value after which it stops looking for multi-path, which we have assumed to be 10 dB, generating 50 multi-path on average. Results for SVA channel simulations have been plotted next to the respective plots for the simple path-based model in Figs. 5–8. There is not a dramatic impact compared to the simple channel model. For the non-RECAP case, capacity is slightly more degraded in some results with increasing due to more paths. For the RECAP case the curve trends are similar, but curves are shifted up slightly in some results showing that RECAP is more advantageous with increased multi-path. However, in general changes are only marginal. E. Effects of Losses and Bandwidth on Channel Capacity

of both links. Individual capacity of each link is calculated using (37), except now in (38), the Tx RECAP patterns of the other link are employed instead of for a non-RECAP. Fig. 7(a) shows MIMO channel capacity per user for the 2 2 multi-user system with increasing , exhibiting similar RECAP capacity gain as the fixed interference case. The relative gain in moving from Case 1 to Case 2 is higher for multi-user compared the single user case with fixed interference, likely due to the fact that Tx RECAPs can now be controlled to avoid interference. Fig. 8(a) shows the results for the 4 4 MIMO system. By increasing , the improvement with respect to constraint type becomes even flatter than the 4 4 case for fixed interference. Surprisingly, RECAP capacity per user is now lower than that for fixed interference, indicating that jointly suppressing incoming interference and avoiding outgoing interference becomes more difficult for more active feeds.

Bandwidth limitations and RE loss are important considerations in practical RECAP structures, and in this section we study these two effects. First we consider loss by including a series resistance with each RE ranging from 0–10 . Fig. 9(a) shows the results corresponding to the 2 2 single user system without any interference. There is no impact of loss for Case 1 since power differences are removed. Moving to Cases 2 and 3, the impact of loss becomes increasingly prominent, resulting from reduced gain of the RECAP, which decreases the channel capacity. More performance loss is observed for the 4 4 MIMO system as shown in Fig. 9(b). Another important aspect is finite bandwidth, and in order to study its effect a two sided bandwidth of 20 MHz is assumed at a center frequency of 3 GHz. Capacity is computed as the average capacity at the center frequency and two band edges for a single fixed RECAP structure. Channels are normalized as

MEHMOOD AND WALLACE: MIMO CAPACITY ENHANCEMENT USING PARASITIC (RECAPs)

Fig. 10. RECAP capacity for 20 MHz bandwidth and the SVA model for a simple non-RECAP array (dashed lines) and RECAP (solid lines): (a) 2 2, (b) 4 4.

before, except now the largest (worst case) normalization factor of the three frequencies is used. Fig. 10(a) indicates that finite bandwidth results in a small capacity reduction for the 2 2 non-RECAP. Although RECAP performance is minimally impacted in Case 1, for Cases 2 and 3 some reduction is seen, comparable to the difference of average versus instantaneous optimization. Results for the 4 4 system in Fig. 10(b) are similar with a slightly larger gap between single frequency and finite bandwidth curves. V. CONCLUSION This work has analyzed MIMO capacity improvements possible with a simple RECAP structure for different scenarios and system power constraints. The results indicate that very large gains relative to fixed antenna MIMO systems are possible, especially for interference-limited and multi-user environments, suggesting that RECAPs may enable aggressive spectral reuse. Consideration of finite bandwidth and losses has indicated that RECAPs can also provide most of this capacity improvement even with these practical impairments. REFERENCES [1] E. Telatar, “Capacity of multi-antenna Gaussian channels,” Eur. Trans. Telecommun., vol. 10, no. 6, pp. 585–595, 1999. [2] R. S. Blum, “MIMO capacity with interference,” IEEE J. Sel. Areas Commun., vol. 21, no. 5, pp. 793–801, 2003. [3] M. A. Jensen and J. W. Wallace, “Capacity of the continuous-space electromagnetic channel,” IEEE Trans. Antennas Propag., vol. 56, no. 2, pp. 524–531, 2008. [4] A. Alexiou and M. Haardt, “Smart antenna technologies for future wireless systems: Trends and challenges,” IEEE Commun. Mag., vol. 42, no. 9, pp. 90–97, 2004. [5] L. N. Pringle, P. H. Harms, S. P. Blalock, G. N. Kiesel, E. J. Kuster, P. G. Friederich, R. J. Prado, J. M. Morris, and G. S. Smith, “A reconfigurable aperture antenna based on switched links between electrically small metallic patches,” IEEE Trans. Antennas Propag., vol. 52, no. 6, pp. 1434–1445, 2004. [6] J. H. Schaffner, R. Y. Loo, D. F. Sievenpiper, F. A. Dolezal, G. L. Tangonan, J. S. Colburn, J. J. Lynch, J. J. Lee, S. W. Livingston, R. J. Broas, and M. Wu, “Reconfigurable aperture antennas using RF MEMS switches for multi-octave tunability and beam steering,” in Proc. IEEE Antennas Propag. Society Int. Symp, 2000, vol. 1, pp. 321–324.

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[7] A. F. Molisch, M. Z. Win, Y.-S. Choi, and J. H. Winters, “Capacity of MIMO systems with antenna selection,” IEEE Trans. Wireless Commun., vol. 4, no. 4, pp. 1759–1772, 2005. [8] M. D. Migliore, D. Pinchera, and F. Schettino, “Improving channel capacity using adaptive MIMO antennas,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3481–3489, 2006. [9] C. Waldschmidt and W. Wiesbeck, “Compact wide-band multimode antennas for MIMO and diversity,” IEEE Trans. Antennas Propag., vol. 52, no. 8, pp. 1963–1969, 2004. [10] B. A. Cetiner, E. Akay, E. Sengul, and E. Ayanoglu, “A MIMO system with multifunctional reconfigurable antennas,” IEEE Antennas Wireless Propag. Lett., vol. 5, no. 1, pp. 463–466, 2006. [11] D. Piazza, N. J. Kirsch, A. Forenza, R. W. Heath, and K. R. Dandekar, “Design and evaluation of a reconfigurable antenna array for MIMO systems,” IEEE Trans. Antennas Propag., vol. 56, no. 3, pp. 869–881, 2008. [12] A. Grau, H. Jafarkhani, and F. De Flaviis, “A reconfigurable multipleinput multiple-output communication system,” IEEE Trans. Wireless Commun., vol. 7, no. 5, pp. 1719–1733, 2008. [13] F. Fazel, A. Grau, H. Jafarkhani, and F. Flaviis, “Space-time-state block coded MIMO communication systems using reconfigurable antennas,” IEEE Trans. Wireless Commun., vol. 8, no. 12, pp. 6019–6029, 2009. [14] M. L. Morris and M. A. Jensen, “Network model for MIMO systems with coupled antennas and noisy amplifiers,” IEEE Trans. Antennas Propag., vol. 53, no. 1, pp. 545–552, 2005. [15] R. Mehmood and J. W. Wallace, “Diminishing returns with increasing complexity in reconfigurable aperture antennas,” IEEE Antennas Wireless Propag. Lett., vol. 9, pp. 299–302, 2010. [16] G. Gonzalez, Microwave Transistor Amplifiers. Englewood Cliffs, NJ: Prentice-Hall, 1997. [17] MAXIM, July 2004, “Low-Noise Amplifier (LNA) Matching Techniques for Optimizing Noise Figures,” MAXIM [Online]. Available: http://pdfserv.maxim-ic.com/en/an/AN3169.pdf [18] Q. H. Spencer, B. D. Jeffs, M. A. Jensen, and A. L. Swindlehurst, “Modeling the statistical time and angle of arrival characteristics of an indoor multipath channel,” IEEE J. Sel. Areas Commun., vol. 18, no. 3, pp. 347–360, 2000. Rashid Mehmood (S’05) received the B.Sc. degree (cum laude) in communication systems engineering from the Institute of Space Technology (IST), Pakistan, in 2007 and the M.Sc. degree in electrical engineering from Jacobs University Bremen (JUB), Bremen, Germany, in 2010. From 2007 to 2008, he worked as a Research Associate at IST and supervised various undergraduate laboratories. From 2008 to 2010, he worked as a Research Assistant in several laboratories at JUB and external companies. His current research interests include reconfigurable aperture antennas, antenna optimization and wireless and optical communications. Mr. Mehmood was a recipient of the 2009 IEEE AP-S Undergraduate Research Award.

Jon W. Wallace (S’99–M’03) received the B.S. (summa cum laude) and Ph.D. degrees in electrical engineering from Brigham Young University (BYU), Provo, UT, in 1997 and 2002, respectively. He received the National Science Foundation Graduate Fellowship in 1998 and worked as a Graduate Research Assistant at BYU until 2002. From 2002 to 2003, he was with the Mobile Communications Group, Vienna University of Technology, Vienna, Austria. From 2003 to 2006, he was a Research Associate with the BYU Wireless Communications Laboratory. Since 2006, he has been an Assistant Professor of electrical engineering at Jacobs University, Bremen, Germany. His current research interests include MIMO wireless systems, physical-layer security, cognitive radio and UWB systems. Dr. Wallace is serving as an Associate Editor of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION and is a Co-Guest Editor of the Special Issue on Multiple-Input Multiple-Output (MIMO) Technology.

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Eigen-Coherence and Link Performance of Closed-Loop 4G Wireless in Measured Outdoor MIMO Channels Matthew Webb, Mythri Hunukumbure, Member, IEEE, and Mark Beach, Member, IEEE

Abstract—Employing feedback in multiple-input-multiple-output (MIMO) systems offers the potential to significantly increase data rates over open-loop schemes. However, the impact the propagation channel has on the behavior and performance of the scheme must be considered and, where appropriate, the signaling designed to suit. In this paper, measured outdoor MIMO propagation data is used to evaluate initially the distributions and statistics of the coherence of the eigenmodes of the channel, for a wide range of mobility scenarios and user devices. Then, the impact on link performance of the differing coherences in time and frequency is evaluated in terms of the feedback delay and spectral spacing of pilots in a practical feedback scheme used in mobile WiMAX. It is found that not only mobility and physical environment, but also the directivity of the antenna array affect the eigen-coherence and also, therefore, the performance of a feedback scheme. Bit-error rate and information capacity are both shown to be sensitive to increased feedback delay and pilot spacing, however, the closed-loop system always outperforms its open-loop counterpart. Index Terms—Coherence, eigenmode, feedback, MIMO, pilots.

I. INTRODUCTION

T

HE provision of high-throughput, high-mobility wireless communications over city-size environments offers the possibility of radically improving the user experience and operator business opportunities in such situations. The benefits of multiple-input-multiple-output (MIMO) systems in such situations have long been appreciated in the literature [1], [2]. To reach towards the higher end of MIMO performance, it is necessary to include feedback which provides channel state information (CSI) to the transmitting end of the link, a point well-established in MIMO information theory [3], [4]. In any feedback scheme, there is inevitably a delay between estimating the channel and feeding back the CSI. During this time, the channel will naturally evolve and mobile users may

Manuscript received May 28, 2010; revised September 13, 2011; accepted September 27, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. This work was supported in part by the UK Mobile VCE ‘MIMO Propagation’ Elective. Parts of this work were presented at the IET EuCAP, 2007. M. Webb was with the Centre for Communications Research, University of Bristol, Bristol BS8 1UB, U.K. He is now with Fujitsu Laboratories of Europe Ltd., Hayes UB4 8FE, U.K. (e-mail: [email protected]). M. Hunukumbure is with Fujitsu Laboratories of Europe Ltd., Hayes UB4 8FE, U.K. (e-mail: [email protected]). M. Beach is with the Centre for Communications Research, University of Bristol, Bristol BS8 1UB, U.K. (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173431

move, and this will tend to cause performance loss. Particularly relevant studies of this have been conducted in [5]–[7]. Furthermore, in wideband multicarrier systems popular in emergent wireless standards, such as mobile WiMAX [9] and 3GPP LTE [10], spectral pilots are used to allow the same CSI feedback to be used on a number of subcarriers even though they do not have identical channel responses. Given these two limitations, performance of a feedback-based algorithm depends on the channel’s coherence time [11], [12] and coherence bandwidth [13]. Conditions for feedback to be beneficial are derived in [14] in terms of the coherences of the channel, and the throughput of MIMO spatial multiplexing (SM) schemes is considered in terms of the coherence of an eigenmode in [15]. Thus, the nature of the propagation channel, particularly its coherence time and bandwidth statistics, is critically important to the system’s correct functioning, as are reductions in performance as these channel parameters change. This paper presents results from an extensive wideband outdoor MIMO propagation measurement campaign in an urban cellular scenario to tackle this joint question. While there are numerous studies of the coherence properties of wireless channels, for example in [16]–[18] for coherence time, in [19]–[21] for coherence bandwidth, and in [22], [23] jointly, in this paper the focus is the coherence of the eigenmodes—the ‘eigen-coherence’ (the same terminology has a different definition in [15]). This spatial structure of the channel holds the key to the SM capability of such systems. Having considered the distribution and implications of the eigen-coherence, the time/frequency structure of the propagation data is used to allow the simulation of a pilot-based CSI feedback scheme and thus the loss for incorporating feedback delay and increasing spectral pilot spacing. The analysis in this paper offers four main contributions. • The distribution and statistics of the eigen-coherence times and bandwidths of a measured outdoor MIMO propagation channel, investigated for users who are standing, walking or driving, and carrying a personal digital assistant (PDA), a laptop or non-device antenna array. • The implications of different antenna arrays on user devices in terms of their effect on perceived eigen-coherence and thus feedback load. • The impact on bit-error rate (BER) and information capacity of feedback delay and spectral pilot spacing in a closed-loop spatial multiplexing MIMO system. • A demonstration that, in the environment measured, feedback is always useful, even in the presence of considerable delay or spectral offset. The setting for this is codebook-based quantization of the channel matrix—a popular means of providing CSI feedback

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WEBB et al.: EIGEN-COHERENCE AND LINK PERFORMANCE OF CLOSED-LOOP 4G WIRELESS IN MEASURED OUTDOOR MIMO CHANNELS

with manageable computational complexity and limited feedback load. Such codebook schemes are prevalent across many wireless standards: the one used here will be that specified for IEEE 802.16e ‘mobile WiMAX’ [8], but versions are also included in 3GPP LTE [10], IEEE 802.16m [9], and 3GPP2-UMB [24]. The scheme used in [8] is designed to approximate singular value decomposition (SVD) feedback [25] and the performance is thus tightly related to the behavior and coherence properties of the eigenmodes. Previous work on the performance of mobile WiMAX includes [26] which covers some aspects of this codebook scheme, but in an 802.16m setting focusing on the throughput of various feedback methods; [27] which considers many different physical-layer aspects, but not codebook feedback; and [28] which presents codebook design for system configurations not supported in [8]. Section II summarizes the measurement campaign and data, and Section III describes its use to study the eigen-coherence properties of the channels. Section IV presents the analysis of BER and capacity changes according to feedback delay and frequency pilot spacing, and Section V summarizes the work. II. MIMO PROPAGATION MEASUREMENT CAMPAIGN An extensive outdoor MIMO measurement campaign was carried out around Bristol city center, U.K. [29], [30], using a multichannel wideband channel sounder [31]. The center frequency of the measurements was 2 GHz (wavelength, cm), with a 20 MHz signal bandwidth. A periodic transmit signal with a repetition period of 6.4 s was carried through 128 discrete frequency fingers with 156.25 kHz spacing. A 4 4 MIMO configuration was used throughout. Measurements were conducted at 56 point locations in Bristol city-center, U.K., and along 10 vehicular drive routes (see [29] for a map). At each point location, 6.1 s of measurements with each of the three devices described in Section II-A were collected whilst the mobile user was standing facing in each of four directions separated by successive approximate 90 rotations, followed by the user walking at 1 m/s for 6 s in each of two approximately perpendicular directions. The vehicular measurements lasted 8.1 s each at an approximately constant speed of 30 mph (48 km/h). A. Prototype Device and Antennas The measurement campaign deployed three different devices shown in Fig. 1: some head-mounted ‘reference’ dipoles, a personal digital assistant (PDA), and a laptop. The purpose was to capture propagation data relevant to possible realistic deployments of MIMO technology on user devices, and to study the fundamental properties of the channel without the variable impacts of physical device form-factor and human body shadowing. The four head-worn halfwave dipoles were located in two pairs in orthogonal planes around the cycle helmet, with to the plane’s the two elements in each pair oriented at vertical. The linear slots in the PDA were arranged around the face and edges of the device, and the printed inverted-F antennas (PIFAs) in the laptop on the lid’s two inside edges. Table I summarizes the devices’ characteristics; values are the averages across the four individual, almost-identical antennas in each case. dual polarized The base station (BS) antennas were two UMTS antennas (a total of four transmit chains) mounted atop a

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Fig. 1. The three devices used in measurements: laptop, PDA, and dipoles.

TABLE I SUMMARY OF MEASUREMENT DEVICE ANTENNA CHARACTERISTICS

30 m high five-storey building overlooking the city center where the measurements were conducted. The antennas were fitted to metal railings, and given 3 m horizontal separation and an 8 downtilt to improve coverage. B. Data Pre-Processing In each standing and walking measurement there were 4096 samples of each frequency finger in the 6.1 s measurement period. To improve the measured signal-to-noise ratio (SNR), the complex gains comprising 4 consecutive samples (collected within the channel’s physical coherence time) were averaged, taking advantage of the zero-mean white noise statistics. There are thus 1024 time samples at each of the 128 frequency fingers, for the giving a spacing of approximately walking cases. In the vehicular measurements, there were 7944 samples of each frequency finger in an 8.1 s measurement period, with consecutive pairs of measurements averaged. Thus there were 3972 samples over a distance of approximately 108 . The channels are then m, giving a spacing of normalized in the time-domain such that they have unit average gain over the bandwidth and all transmit-receive links. III. COHERENCE OF EIGENMODES Eigen-coherence time, , and bandwidth, , defined precisely below, are used here to measure how quickly the spatial modes of a MIMO channel change in their respective domains. This is essential to a feedback-based SM system, since performance is governed by how often feedback is updated compared to the eigen-coherence in that domain. In that respect, eigen-coherence is a parameter of significant interest in such schemes as compared to classical coherence which deals only with the overall channel matrix. We have studied relations between classical quantities and eigen-coherences in [30]. Eigen-coherences are calculated based on the autocovariance functions (ACFs) of the eigenvalues of the channel. Define to be the variation of eigenvalue over time and frequency , and its ACF in the time-domain to be

(1)

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Fig. 2. Eigen-coherence times of the largest eigenvalue across all locations.

TABLE II EIGEN-COHERENCE TIME STATISTICS FOR VEHICULAR ROUTES

where is the expectation over and denotes complex conis the earliest lag such that , jugation. Then . An equivalent procedure in the frequency and . Figures are shown for only the largest domain is used for eigenvalue for the sake of clarity. A. Coherence Time Fig. 2 shows the cumulative distribution function (cdf) of for the largest eigenvalue of the channel matrix over all point locations. Statistics for the vehicular routes are summarized in Table II since the range of coherence times is too small to depict in Fig. 2. As expected, coherence times while walking are distributed at significantly lower values than when standing: the walking median is 35 ms compared to the standing median at 110—140 ms and the vehicular medians are an order of magnitude lower again at around 5 ms. In the standing measurements, the PDA’s coherence times are smallest, and the reference dipoles the largest. Since the PDA antennas are much more directional than the dipole array (see Table I), this suggests that having a directional antenna in a scattering, changing environment (but with a stationary user) tends to estimate coherence time only in the direction(s) it can see, whereas a wider angular ‘view’ averages out the signals arriving from low- and high-coherence time directions. Since most of the locations considered were in a densely scattering city center, for antennas sensitive to a smaller angular spread there is a higher probability that a stronger LOS component is not detected (bringing down the coherence time) versus a less-directional antenna which is more likely to see both LOS and NLOS multipaths, and higher average coherence time. The situation in the walking and vehicular measurements is different, due to the dominant effect of the user’s motion. With

Fig. 3. Eigen-coherence bandwidths of the largest eigenvalue across all locations.

TABLE III EIGEN-COHERENCE BANDWIDTH STATISTICS FOR VEHICULAR ROUTES

the multipath environment changing more quickly in all directions, having a wider azimuth view tends to decrease the coherence time and so the dipole array gives the lowest eigen-coherence time distribution and the PDA the highest. B. Coherence Bandwidth The distribution of eigen-coherence bandwidth over all point locations is shown in Fig. 3, where there was found to be virtually no difference between the curves for standing and walking measurements. The driving measurements are shown in Table III. In each case, the median eigen-coherence bandwidth is 400 kHz, although the smaller range of values in the driving case implies a different distribution there, tending to be to the left of the standing/walking cdfs at the higher percentiles. Even so, only some 15% of the values for standing/walking are above the driving laptop’s maximum of 625 kHz, showing that the distributions are broadly similar. The reference dipoles show the smallest eigen-coherence bandwidths, by a small margin. Similarly to in Section III-A, the wide azimuth view of the head-mounted dipoles means their delay response contains more multipath components making the channel more frequency selective and thus reducing coherence bandwidth. IV. FEEDBACK DELAY AND SPECTRAL OFFSET Two major sources of feedback imprecision are using the same feedback over several frequency subchannels distinct from the pilot (referred to here as spectral offset) and the inevitable calculation and transmission delay on the feedback. This section presents results showing how they affect the bit-error rate (BER) and capacity of the SM feedback scheme in mobile WiMAX. A set of standing, walking and driving measurements are compared for the impact of feedback delay, with their changing coherence times. Spectral offset is studied

WEBB et al.: EIGEN-COHERENCE AND LINK PERFORMANCE OF CLOSED-LOOP 4G WIRELESS IN MEASURED OUTDOOR MIMO CHANNELS

by comparing an NLOS to a LOS location, as these have contrasting coherence bandwidths. The measurements from the reference dipoles mounted on the user’s head are used throughout this section, eliminating the ‘body shadowing’ in the laptop and PDA measurements. A. System Model The closed-loop SM scheme used here is a codebook quantization method from mobile WiMAX [8]. The codebooks defined in [8] approximate the ideal singular value decomposition (SVD) feedback scheme described in [25]. Define a channel ma, then the precoding needs to trix to have SVD of posapproximate . A codebook sible quantizations, or codewords of the right singular matrix of the channel is specified, among which one, , is chosen for optimizing a suitable metric. Call the transmitted signal , receive combiner , the received signal , and additive white Gaussian noise (AWGN) , then (2) In the case of exact feedback, , and the , and there channel is diagonalized. With a codebook, is no diagonalization. To optimize the SNR, is the linear minimum mean squared error (MMSE) combiner for (3) where the total transmit power is and the AWGN has covari. ance or codewords, requiring, respecCodebooks with , tively, 3 or 6 bits of feedback, are provided in [8] for , or streams between or antennas transmitting . A full exposition of the scheme is them, subject to left to [8], with the simulations here taking: and throughout, offering a mid-way 1) tradeoff between SM and diversity gain. Comparisons to an open-loop system will use the same for consistency, with (arbitrarily) the third antenna disabled, i.e., the precoder [100;010;000;001] is statically applied; disabling a different antenna alters the results only slightly. 2) 6-bit codebooks, to outer-bound performance. will be selected from to minimize the mean 3) squared error as in [32] (4) This is a likely realistic metric if a system operator is targeting quality-of-service improvement. 1) Capacity: Denote the original channel, on which and are calculated as , and the delayed or spectrally-offset channel actually used for transmission as . To simplify notation, re-express (2) as (5) with stream

. The received SNR on is (6)

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. The fact that giving a total capacity , along with codebook precoding, results in residual inter-stream interference. In (6) this is modeled as additional white i.i.d. Gaussian noise, a worst-case assumption as the interstream interference is in fact correlated. computed this way is not capacity in the strict sense, being instead a lower bound on the actual capacity, since the self-interference is not i.i.d. Gaussian and its specific structure could be used to obtain a higher mutual information. In (6), a simple receiver without knowledge of the noise structure is implied. The SNR for all such analysis will be 20 dB. At each location, the wideband capacity averaged over frequency at each time sample will be reported as cdfs. 2) BER: For BER performance, QPSK with a half-rate convolutional forward error-correcting code (FEC) with the octal generator (247, 371) is used. This is a constraint-length 8, maximal free-distance code [33]. Enough random binary bits are generated to allow each sample, subcarrier and stream to carry a QPSK symbol following half-rate encoding. These bits are randomly interleaved before being coded and modulated. Viterbi hard decoding is used in the receiver.

B. Feedback Delay Standing and walking measurements at the same physical location will be used in this section, with an additional driving and is perroute. The curves assume that calculation of formed correctly for the channel on the pilot tone and time slot , and then actually applied to a later time slot (but still on the pilot tone) when the channel has evolved to become . The feedback delay increments, , are therefore multiples of the measurement interval of 6.14 ms. For the standing was 144 ms and for walking it was case, the coherence time 21.6 ms (to 0.7 autocorrelation). To facilitate comparisons, the in both cases, meaning that the inratio crement in feedback delay on adjacent BER curves represents approximately the same multiple of coherence time. Thus, in , so each curve is disFig. 4, placed by 7 measurement samples relative to its neighbors, and . in Fig. 5, 1) BER Performance: Fig. 4 shows, for the standing measurement, BER curves for increasing estimation delay. The long coherence time of 144 ms means that even large feedback delays only degrade performance by around 1 dB for the codebook system over the range considered. The feedback load induced by such a channel would therefore be low, as updates could be widely spaced in time. By comparison, when walking at about 1 bbm/s in Fig. 5 the curves spread out significantly, with acceptable SNR losses of 1.5 dB after a 6 ms delay, but increasing quickly, meaning that feedback would have to be much more rapid if performance close to ideal was desired. Fig. 7 shows the initial parts of the ACFs. Since the ACFs for walking and driving are much steeper than for standing, moving an equal along the curve will produce greater decorrelamultiple of tion and poorer performance. There is an error-floor appearing at the longer delays in Fig. 5; discussion of this is deferred to Section IV-C1 where it also appears. The open-loop performance is always worse than any of the closed-loop cases and shows slightly greater SNR loss, and more pronounced onset of

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Fig. 4. Impact of feedback delay on BER for standing measurements. .

Fig. 5. Impact of feedback delay on BER for walking measurements. .

error-floors with delayed feedback. This implies that most of the SNR loss with precoding is actually from the spatial equalization being unable to suppress inter-stream interference successfully; and also that the approximately-diagonalising effect of the precoder can partially mitigate this problem. Clearly, more sophisticated channel estimation schemes would perform better and could relax these delay constraints. To capture data appropriately in the driving measurements, the channel sounder’s sample spacing was reduced to 2.05 ms. ms in this case, ; sigSince nificantly different to that in the earlier figures, but it was not . Fig. 6 practically possible to move this ratio toward shows the results for the driving measurement (the closed- and open-loop 2.05 ms delayed curves coincide). The effect of delay is decisive: the system as modeled here clearly requires significantly shorter delays than twice the coherence time; an observation familiar from the above results. Inferring from the standing/ walking results that equalization failure is the more significant effect, a vehicular scenario will benefit most from using rapid channel estimation techniques, or closer-spaced temporal pilots.

Fig. 6. Impact of feedback delay on BER for driving measurements. .

Fig. 7. Autocorrelation functions of the three measurements, with the 0.7 level indicated.

2) Capacity Performance: The capacity response (on the basis of (6)) to feedback delay is shown in Fig. 8, for the vehicular measurement. The capacity loss is about 66% after just one in this quickly-decordelay step—even the smallest delay is relating scenario—but is relatively less severe than the BER result. The losses diminish after the first delay, since the channel has already largely decorrelated. The open-loop curves are always lower than their closed-loop counterparts indicating that, as with BER, the feedback scheme provides at least some benefit. Comparing the BER and capacity effects suggests that the principal performance losses will result from BER degradations leading to a reduced useful throughput as a result of re-transmission (e.g., via hybrid automatic repeat request (HARQ)), but that the capacity losses are also meaningful if the BER can be repaired. These results could be viewed as performance degradations due to imperfect precoding and equalization, if the rate is perfectly adapted with respect to the resulting channel including imperfect precoding. An alternative view of capacity is the outage probability. Then, since transmission is always at the

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Fig. 8. Impact of feedback delay on capacity for driving measurements.

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Fig. 9. BER performance with spectral offset for NLOS location.

capacity limit, if the capacity of the precoded channel with delay is smaller than the rate implied by the original channel and precoder there is an outage. We have found that for the wideband capacity, at all delays in Fig. 8 the channel is always in capacity outage. Looking at individual subcarriers, 75–77% of them are in outage (depending on the delay). C. Spectral Offset Most configurations in mobile WiMAX have pilots with a spectral spacing of 2–4 subcarriers [8]. The subcarrier spacing is 10.84 kHz, so feedback and equalization information is applied to subcarriers with about 20–40 kHz spectral offset from a given pilot. This section studies the performance of the precoding scheme as the feedback is applied to subcarriers with increasing spectral offset from the pilot. The channel has become , with the codeword and equalization from the pilot channel still in use. The frequency response of the channel was interpolated to reduce the spacing of the measured data from 156.25 kHz by zero-padding the end of the time-domain response. Since in this region the response is only zero-mean noise, it negligibly alters the temporal and spectral properties of the response, while giving more frequency points following a fast Fourier transform. In this way, the frequency resolution was increased by a factor of 8 to 19.5 kHz per finger. kHz) and LOS Results are shown for NLOS ( kHz) walking measurement locations. ( 1) BER Performance: The BER performance at the NLOS location is shown in Fig. 9. Curves for both the closed-loop system using the 6-bit codebook and an open-loop system with no feedback are shown. The “pilot” curves show the BER if the feedback information were to be used to transmit data on the pilot subcarrier itself, i.e., with no spectral offset. For a 19.5 kHz , the loss from the case of transmitting on offset the pilot channel is small; much less than 1 dB at all BERs. The losses are more pronounced for the 2-finger offset curves, , and once the offset has reaching nearly 3 dB at a BER of reached about 60 kHz, the losses from the ideal case are substantial. The curves for open-loop transmission show that the SNR loss caused by a given spectral offset of the receive combiner

Fig. 10. BER performance with spectral offset for LOS location.

is approximately the same as for the precoded system but that precoding performs better at all the offsets considered here, so that feedback is always useful. For the LOS channel, in Fig. 10, BERs are substantially higher due to the less-scattering conditions resulting in poorer MIMO channels, but degradations under spectral offset are , much smaller: almost zero with a 19.5 kHz offset corresponding to higher coherence bandwidth implying slower changes in the channel over frequency. Whereas at 40 kHz offset in NLOS the loss was 3 dB, here it is less than 1 dB. At the largest offsets an error-floor appears. In a LOS situation particularly, BER behavior will be dominated by the weakest spatial stream(s), all of which have the same modulation and coding scheme, and increasing SNR also increases the residual, post-MMSE, inter-stream interference, resulting in an error floor. A similar effect is analyzed in [34]. These results suggest the 20 kHz spacing used in 802.16e is suitable in both NLOS and LOS environments in terms of kHz BER performance, where a pilot carrier is used over a range. However, the 2.5–3 dB loss in the NLOS environment at a 40 kHz offset would have to be considered in the system design, and could call for other techniques to reduce the headline

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that in a LOS environment, the principle system performance degradation will be from gradual BER losses rather than capacity losses, but in NLOS, the two will interact much more strongly, thus limiting the scope for feedback-load reduction in such cases. Even though system performance will degrade, the precoded capacity distributions are again always better than the open-loop curves, so that feedback is always useful. The outage probability behavior is as with feedback delay: the wideband channel was found to be always in outage at the delays considered here. At the individual subcarrier level, this is also true in NLOS, but in LOS it reduces slightly to 90%, 97%, and 99% of subcarriers at 1, 2, and 3 subcarrier offsets. V. SUMMARY AND CONCLUSIONS

Fig. 11. Capacity performance with spectral offset for NLOS location.

Fig. 12. Capacity performance with spectral offset for LOS location.

error-rate, such as stronger FECs. In LOS, wider spaced pilots could be tolerated in such an environment, suggesting that a dynamically chosen pilot spacing, dependent on prevailing propagation conditions, could yield benefits. Feedback load would steadily reduce as coherence bandwidth increases which could increase the data rate available on the forward link, providing some compensation for the higher BER it will experience under increasingly LOS conditions. 2) Capacity Performance: The impact of spectral offset on capacity as in (6) is shown in Figs. 11 (NLOS) and 12 (LOS). Capacity losses in the NLOS case rise quickly as spectral offset increases, having reduced the median level by 50% with a 60 kHz offset. However, the loss is much smaller at the lower end of the WiMAX spectral offsets: at 20 kHz, it is 3.5 bps/Hz (15%). Comparing to Fig. 8, capacity is less sensitive to spectral offset in NLOS than to feedback delay. The LOS location suffers much less, as in the BER results, because of its higher coherence bandwidth giving greater correlation between successive spectral offsets. The loss is just 2.5 bps/Hz (16%) at a 60 kHz spectral offset, and the decremental steps in capacity are also smaller than in NLOS. These results mean

This paper has studied the statistics of MIMO eigenmode coherence time and bandwidth coupled with the impact of feedback delay and the use of spectral pilots on the performance of a class of closed-loop spatial multiplexing scheme widely adopted in standards. Based on measured data collected in an urban cellular scenario, distributions of eigen-coherence were presented encompassed standing, walking and driving users with a variety of mobile devices. The nature of the antenna array in use also had a distinct impact on coherence properties and thus may be a consideration in mobile unit design in order to avoid higher-than-necessary feedback loads. Then, the performance of the codebook-based CSI quantization scheme in mobile WiMAX was evaluated in terms of how quickly the decoherence of the channel in time and frequency degrades BER and capacity performance. Although feedback always provided some benefit, the losses in BER were found usually to be more significant than in capacity, and much more significant under NLOS than LOS propagation conditions. This suggests that future schemes which dynamically respond to the changing propagation, e.g., by controlling the feedback rate, may fare better than schemes that are unaware of it. REFERENCES [1] V. Tarokh, N. Seshadri, and A. Calderbank, “Space-time codes for high data rate wireless communication: Performance criterion and code construction,” IEEE Trans. Inf. Theory, vol. 44, no. 2, pp. 744–765, Mar. 1998. [2] G. J. Foschini, “Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas,” Bell Labs. Tech. J., pp. 41–59, Oct. 1996. [3] I. E. Telatar, “Capacity of Multi-Antenna Gaussian Channels,” Bell Labs, Lucent Technologies, Technical Memorandum, Oct. 1995. [4] D. J. Love and R. W. Heath, “What is the value of limited feedback for MIMO channels?,” IEEE Commun. Mag., vol. 40, no. 10, pp. 54–59, Oct. 2004. [5] A. Khrwat et al., “Feedback delay in precoded spatial multiplexing MIMO systems,” in Proc. IEEE Int. Symp. Personal Indoor and Mobile Radio Commun., Cannes, France, Sep. 2008, pp. 1–4. [6] P. Zhu, L. Tang, Y. Wang, and X. You, “Quantized beamforming with channel prediction,” IEEE Trans. Wireless Commun., vol. 8, no. 11, pp. 5377–5382, Nov. 2009. [7] Y. Isukapalli and B. D. Rao, “Packet error probability of a transmit beamforming system with imperfect feedback,” IEEE Trans. Signal Process., vol. 58, no. 4, pp. 2298–2314, Apr. 2010. [8] IEEE Standard for Local and Metropolitan Area Networks Part 16 Amendment 2: Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands and Corrigendum 1, IEEE Std. 802.16e-2005 and 802.16-2004/COR1-2005, Feb. 2006. [9] DRAFT Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Broadband Wireless Access Systems, IEEE Std. 802. 16Rev2/D6a, Jul. 2008, draft.

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[10] LTE-A; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical Channels and Modulation, Release 10, 3GPP TS 36.211 V10.2.0, Jun. 2011. [11] D. Samardzija and N. Mandayam, “Pilot-assisted estimation of MIMO fading channel response and achievable data rates,” IEEE Trans. Signal Process., vol. 51, no. 11, pp. 2882–2890, Nov. 2003. [12] J. Chena, R. A. Berry, and M. L. Honig, “Performance of limited feedback schemes for downlink OFDMA with finite coherence time,” in Proc. IEEE Int. Symp. Inform. Theory, Nice, France, Jun. 2007, pp. 2751–2755. [13] M. D. Larsen, A. L. Swindlehurst, and T. Svantesson, “Performance bounds for MIMO-OFDM channel estimation,” IEEE Trans. Signal Process., vol. 57, no. 5, pp. 1901–1916, May 2009. [14] D. J. Love, “Duplex distortion models for limited feedback MIMO communication,” IEEE Trans. Signal Process., vol. 52, no. 2, pp. 766–773, Feb. 2006. [15] B. Mielczarek and W. A. Krzymień, “Influence of CSI feedback delay on capacity of linear multi-user MIMO systems,” in Proc. IEEE Wireless Commun. and Networking Conf., Hong Kong, Mar. 2007, pp. 1188–1192. [16] A. M. O. Ribeiro, E. M. M. Barrientos, and E. Conforti, “Spatial correlation function and coherence time characterization of 3.5-GHz microcell propagation,” in Proc. Int. Microwave and Optoelectronics Conf., Belém, Brazil, Nov. 2009, pp. 501–505. [17] A. Sorrentino, G. Ferrara, and M. Migliaccio, “Characterization of NLOS wireless propagation channels with a proper coherence time value in a continuous mode stirred reverberating chamber,” in Proc. Eur. Wireless Technol. Conf., Rome, Italy, Sep. 2009, pp. 168–171. [18] L. Cheng, B. Henty, F. Bai, and D. D. Stancil, “Doppler spread and coherence time of rural and highway vehicle-to-vehicle channels at 5.9 GHz,” in Proc. IEEE Global Commun. Conf., New Orleans, LA, Nov. 2008, pp. 1–6. [19] Q. T. Zhang and S. H. Song, “Exact expression for the coherence bandwidth of rayleigh fading channels,” IEEE Trans. Commun., vol. 55, no. 7, pp. 1296–1299, Jul. 2007. [20] J. Ø. Nielsen et al., “Measurements of indoor 16 32 wideband MIMO channels at 5.8 GHz,” in Proc. Int. Symp. Spread Spectrum Techniques and Applications, Sydney, Australia, Aug. 2004, pp. 864–868. [21] A. M. O. Ribeiro, C. S. Castelli, E. M. M. Barrientos, and E. Conforti, “Coherence bandwidth in a 1.8-GHz urban mobile radio channel,” in Proc. Int. Microwave and Optoelectronics Conf., Salvador, Brazil, Oct. 2007, pp. 599–602. [22] P. Kyritsi, P. C. Eggers, and A. Oprea, “Dual domain coherence measures for FWA channels in the 5–6 GHz band,” in Proc. IEEE Veh. Technol. Conf., Fall, Vancouver, BC, Dec. 2002, vol. 1, pp. 111–115. [23] J. R. Mendes and M. D. Yacoub, “A general bivariate Ricean model and its statistics,” IEEE Trans. Veh. Technol., vol. 56, no. 2, pp. 404–415, Mar. 2007. [24] Physical Layer for Ultra Mobile Broadband (UMB) Air Interface Specification, 3GPP2 Std. C.S0084-001-0 v3.0, Aug. 2008. [25] D.-S. Shiu, G. J. Foschini, M. J. Gans, and J. M. Kahn, “Fading correlation and its effect on the capacity of multielement antenna systems,” IEEE Trans. Commun., vol. 48, no. 3, pp. 502–513, Mar. 2000. [26] K. Sivanesan, J. Xiao, R. Q. Hu, and G. Wu, “Code book based CL-MIMO for DL Wimax Rel. 1.5: System level performance analysis,” in Proc. IEEE Int. Conf. Commun., Dresden, Germany, Jun. 2009, pp. 1–5. [27] S. P. Alex and L. M. A. Jalloul, “Performance evaluation of MIMO in IEEE802.16e/WiMAX,” IEEE J. Sel. Topics Signal Process., vol. 2, no. 2, pp. 181–190, Apr. 2008. [28] V. Raghavan, M. L. Honig, and V. V. Veeravalli, “Performance analysis of RVQ-based limited feedback beamforming codebooks,” in Proc. IEEE Int. Symp. Inform. Theory, Seoul, Korea, Jun. 2009, pp. 2437–2441. [29] M. Hunukumbure and M. Beach, “MIMO channel measurements and analysis with prototype user devices in a 2 GHz outdoor cell,” in Proc. IEEE Int. Symp. Personal Indoor and Mobile Radio Commun., Helsinki, Finland, Sep. 2006, pp. 1–5.

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[30] M. Beach, M. Hunukumbure, and M. Webb, “Dynamics of spatial eigen modes in measured MIMO channels with different antenna modules,” in Proc. European Conf. Antennas Propag., Edinburgh, U.K., Sep. 2007. [31] RUSK Channel Sounder 2010 [Online]. Available: http://www.channelsounder.de, Medav, GmbH. [32] D. J. Love and R. W. Heath, “Limited feedback unitary precoding for spatial multiplexing systems,” IEEE Trans. Inf. Theory, vol. 51, no. 8, pp. 2967–2976, Aug. 2005. [33] J. G. Proakis, Digital Communications, 3rd ed. New York: Wiley, 1974. [34] C. Wang et al., “On the performance of the MIMO zero-forcing receiver in the presence of channel estimation error,” IEEE Trans. Wireless Commun., vol. 6, no. 3, pp. 805–810, Mar. 2007.

Matthew Webb received the B.A. and M.Eng. degrees in electrical and information sciences from the University of Cambridge, Cambridge, U.K., in 2002, and the Ph.D. degree in electrical engineering from the University of Bristol, Bristol, U.K., in 2006. From 2006 to 2011, he was a member of research staff at the University of Bristol. He is currently a Senior Researcher at Fujitsu Laboratories of Europe Ltd., Hayes, U.K. His research interests include multi-antenna wireless information theory, radio propagation measurements and modeling, closed-loop feedback imperfections in MIMO, and the use of information about location and physical surroundings to augment the wireless physical and MAC layers.

Mythri Hunukumbure (M’07) received the B.Sc. degree in electronic and telecommunications engineering from the University of Moratuwa, Sri Lanka, in 1998, and the M.Sc. and Ph.D. degrees from the University of Bristol, Bristol, U.K., in 2001 and 2004, respectively. From 2005 to 2006, he was a member of research staff at the University of Bristol. He is currently a Senior Research Engineer with Fujitsu Laboratories of Europe Ltd., Hayes, U.K. His research interests have included code orthogonality and MIMO technology, as well as network planning and physical layer design of 4G LTE and WiMAX systems.

Mark Beach (M’06) received the Ph.D. degree for research addressing the application of smart antennas to GPS from the University of Bristol, Bristol, U.K., in 1989. After graduation, he joined as a member of academic staff at the University of Bristol, Bristol. He was promoted to Senior Lecturer in 1996, Reader in 1998, and Professor in 2003, serving as Head of the Department of Electrical and Electronic Engineering from 2006 to 2010. His research interests include the application of multiple antenna technology, with particular emphasis on spatio-temporal aspects of the channel, as well as enabling RF technologies for “green radio”.

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Multipath Simulator Measurements of Handset Dual Antenna Performance With Limited Number of Signal Paths Paul Hallbjörner, Juan D. Sánchez-Heredia, Peter Lindberg, Member, IEEE, Antonio M. Martínez-González, and Thomas Bolin

Abstract—Antenna pairs for diversity or MIMO functionality are characterized under the assumption of a certain statistical distribution of the incident signals over angle and polarization, but also assuming a signal environment with a large number of signal paths. In many real-life environments, however, only a few signal paths contain most of the transferred power. A multipath simulator can be used to realize signal environments with a controlled number of signal paths. This paper presents measurements of dual antenna performance using a multipath simulator with 2–16 signal paths. The results are analyzed in terms of statistical power distributions, power imbalance, correlation coefficient, multiplexing efficiency, and diversity gain. Differences in performance depending on the number of signal paths are noted, illustrating the value of considering the number of signal paths in characterization. Index Terms—Antenna measurements, multipath simulator, signal environment, sparse environment, terminal antenna. Fig. 1. MPS in anechoic room, with test object at the center of the MPS array.

I. INTRODUCTION

D

UAL antennas in mobile terminals are used more and more, for diversity or multiple-input multiple-output (MIMO) functionality. There are different opinions regarding the proper way to characterize antenna pairs for diversity or MIMO functionality, involving different parameters [1]. One common way to characterize dual antennas is by their mean effective gains (MEG) and correlation coefficient [2], [3]. These parameters depend on the assumed statistical distribution of the incident signals over angle and polarization. Dual antenna performance is also based on the assumption of a large number of signal paths [4], [5]. When calculating the correlation coefficient from the radiation patterns of the two antennas, the integrals are in effect summations of an infinite number of signal paths. There is, however, nothing in the integral about the number of simultaneous signal paths at any instant. Manuscript received April 20, 2011; revised September 20, 2011; accepted October 10, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. The work was supported in part by MICINN (Project TEC2008-05811) through an FPI doctoral grant (BES-2009-013764). P. Hallbjörner is with SP Technical Research Institute of Sweden, SE-501 15 Borås, Sweden (e-mail: [email protected]). J. D. Sánchez-Heredia and A. M. Martínez-González are with the Universidad Politécnica de Cartagena (UPCT), E-30202 Cartagena, Spain (e-mail: [email protected]; [email protected]). P. Lindberg is with TE Connectivity, SE-175 26 Järfälla, Sweden (e-mail: [email protected]). T. Bolin is with Sony Ericsson Mobile Communications, Nya Vattentornet, SE-221 88 Lund, Sweden (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2011.2173451

In many real-life environments, most of the transferred power is contained in only a few signal paths [6], [7]. The performance of an antenna pair in such environments can be studied by computer simulations using the radiation patterns. Dual antenna performance in multipath environments can also be measured directly, without going via the radiation patterns [8]. Reverberation chambers (RC) [9], [10] is an established technique for this. RCs are usually designed so as to ensure that the test object is subjected to a large number of signal paths. Multipath simulators (MPS) [11]–[13] are an emerging technique that allows better control of the signal environment than RCs. For instance, the number of signal paths is a parameter that can be decided arbitrarily. This paper presents a study in which a multipath simulator is used to characterize dual antenna performance in environments with a limited number of signal paths. The purpose is to have experimental indications of how performance typically differs depending on the number of signal paths, and thereby also indications regarding the need to consider the number of signal paths in characterization. II. SETUP A. Multipath Simulator An MPS comprising 16 antennas is used. The antennas are of vertical and horizontal polarizations, and evenly distributed on a circle around the test object, in a plane, see Fig. 1.

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sweep rates over the MPS antenna array that realize the desired Doppler shifts. Measurements are performed with 2, 4, 8, and 16 MPS antennas active, and the antennas that are switched on all have equal amplitude. Which MPS antennas are active for the respective number of signal paths is also shown in Table I, with reference to Fig. 2 for the physical locations of the antennas. Active antennas are marked in Table I with an “O”. With 2, 4, and 8 paths, there are three different sets of active antennas, given by the three columns. B. Performance Metrics Results are analyzed in terms of the power imbalance , correlation coefficient , and multiplexing efficiency [14], according to the expressions Fig. 2. Block diagram of the setup for S-parameter measurements on dual antennas.

(1) (2)

TABLE I PHASE SWEEP RATE ON THE MPS BRANCHES, AND THE ACTIVE BRANCHES USED FOR THE DIFFERENT NUMBER OF PATHS. FOR 2, 4, AND 8 PATHS, THREE SETS ARE USED, EACH GIVEN BY A COLUMN

(3) In (1)–(3), and are the complex transmission coefficients of the respective test object antenna, each being a sequence of 6401 samples, and denotes average over the whole sequence. The expression in (3) differs from the one in [14] in that normalization to the average radiation efficiency of the two antennas is introduced. This is done because we want to study only the effects of imbalance and correlation, but not the effect of the absolute levels of the efficiencies. Diversity gain [15] is also used as a figure-of-merit. Maximum ratio combining is assumed, and the combined signal is thus (4) After this,

is calculated at the 99% signal reliability levels, %

The MPS thus simulates a 2-D signal environment with up to 16 signal paths. Each MPS antenna is fed via a sweeping phase shifter, which simulates the Doppler shift experienced when the terminal moves in a multipath environment. By setting the sweep rate differently on the antennas, a fast fading signal is received by the test object antennas. Each MPS antenna is also fed via an attenuator, and the antenna is effectively switched on/off by setting its attenuator to minimum/maximum attenuation. Fig. 2 shows a block diagram of the setup, with a network analyzer for simultaneous measurements of the complex transmission coefficients between the MPS port and each of the two antenna ports of the test object. Each measurement in the presented work is a 20 s sequence of 2 6401 values between the MPS port and the two test object antenna connectors. A maximum Doppler shift of 50 Hz is used, to ensure that samples are taken with sufficient density with respect to the fast fading. Table I shows the phase

%

(5)

and ) with each where two values are calculated ( of the two antennas serving as the non-diversity reference case. The reason for doing this, rather than using one specific antenna as the reference, is that we hereby avoid assuming which antenna would be used in a non-diversity case. III. MEASUREMENTS Two experiments are carried out, with different test objects. In the first, a test object with near-ideal performance in an isotropic environment is used. This makes an interesting reference case for the change in performance when going to fewer signal paths. In the second experiment, two terminal prototypes with less ideal and more typical performance are used. They are prototypes of the same terminal, but with different design solutions for the dual antennas. This represents a realistic situation in which different designs are characterized and compared.

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A. Near-Ideal Test Object A terminal antenna model for the 2600 MHz band is used, with measurements performed at 2655 MHz. The model is made of metal only (no plastic housing) and consists of a 100 mm 40 mm ground plane with two PIFA antennas fed by coaxial cables. The cables are routed so as to minimize influence on the antenna performance [16]. Tests with different feed cable arrangements and with ferrite absorbers [17] are performed to ensure that the results are not affected too much. Electrical performance is a return loss of 12 dB and near 100% radiation efficiency on both antennas, and a correlation coefficient of 0.25 in an isotropic environment with a large number of signal paths. In the MPS measurements, the test object is mounted in freespace (no head or hand) at the center of the MPS array. It is measured in three orthogonal planes with each set of active branches according to Table I. It is also measured in a 45 slant orientation (data mode), with 10 different orientations in azimuth. The slant orientation measurements are done only for the leftmost set of active branches for 2 and 4 paths, and the set of 16 branches. The total number of measurements are thus 19/19/9/13 for the respective 2/4/8/16 paths. Fig. 3 shows its performance for the different number of signal paths. Power imbalance, correlation coefficient, and multiplexing efficiency all show a strong increase in the spread when reducing the number of signal paths. The performance with 16 signal paths agrees well with the performance in an isotropic environment with a large number of signal paths, with only small variations. With two signal paths, the correlation coefficient is many times very high, and even with four signal paths it varies over almost all possible values. With few signal paths, the average correlation coefficient is also increased significantly compared to the case of many signal paths. Examples of time sequences and cumulative distribution functions (CDF) of the received power are plotted for a few measurements. The case of two signal paths are shown in Fig. 4(a) and (b), while the case of 16 signal paths are seen in Fig. 4(c) and (d). With 16 paths, time sequences are similar to Rayleigh fading curves, and the CDF curves are all approximately the same, corresponding to the theoretical curves under assumption of a large number of signal paths. With two paths, on the other hand, strong variations are seen in time sequence characteristics and CDF curve shapes. As a result, can be anything from very large to almost none. B. Two Realistic Test Objects Two samples of the same terminal model, with dimensions 115 mm 65 mm, but with different antenna solutions, are measured. The two test objects are referred to as Prototype A and Prototype B. These models are more realistic than the first one, having plastic housing and antennas with less ideal performance. Their antennas are made for the 700 MHz band, and the measurements are performed at 740 MHz. The antennas are accessed via coaxial cables, which exit the test objects on the middle of the long side for minimum interference. As with the near-ideal test object, tests are conducted to ensure that the feed cables have a negligible effect on performance. The respective antenna performance in a 3-D environment with a large number

Fig. 3. (a) Power imbalance of the near-ideal test object, as a function of of the near-ideal test the number of signal paths. (b) Correlation coefficient object, as a function of the number of signal paths. (c) Multiplexing efficiency of the near-ideal test object, as a function of the number of signal paths.

of signal paths is measured in an RC. The power imbalances dB for Prototype A and dB for Prototype B, and are the correlation coefficients are 0.35 for Prototype A and 0.56 for Prototype B. More interesting for comparison with the MPS measurements is the performance in a 2-D environment. These values are calculated from 2-D cuts of the radiation patterns in

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Fig. 4. (a) Examples of time sequences for the case of two signal paths, on the two branches (dotted and dashed). (b) Examples of cumulative distribution functions for the case of two signal paths, with the two branches (dotted and dashed) and the combined signal using maximum ratio combining (solid). The four examples show vastly different diversity gains. (c) Examples of time sequences for the case of 16 signal paths, on the two branches (dotted and dashed). (d) Examples of cumulative distribution functions for the case of 16 signal paths, with the two branches (dotted and dashed) and the combined signal using maximum ratio combining (solid). All four examples are approximately the same. TABLE II POWER IMBALANCE AND CORRELATION COEFFICIENT OF PROTOTYPES A AND B, IN DIFFERENT 2-D ENVIRONMENTS

each of three orthogonal planes. The cuts are measured with a standard far-field antenna test range. Uniform power distribution over angle and polarization is assumed when calculating the performance parameter from these 2-D cuts. As can be seen in Table II, the test objects are well balanced in all three planes. Correlation coefficients are notably higher in the 2-D environments than in the 3-D environment. For the MPS measurements, the test objects are mounted in free-space at the center of the MPS array. They are measured

in three orthogonal planes with each set of active branches according to Table I. The same planes and orientations are used for both test objects. The total number of measurements for each test object are thus 9/9/9/3 for the respective 2/4/8/16 paths. Results are seen in Fig. 5, with circles for Prototype A and triangles for Prototype B. The plots show that also in this experiment, reducing the number of signal paths leads to a much greater spread in the different metrics. Power imbalance is not as symmetrical around 0 dB as in the first experiment, and Prototype A shows a larger spread than Prototype B. For both test is clearly worse with 16 paths than in a 3-D enviobjects, ronment with many paths, but comparable to 2-D environments according to Table II. At 16 signal paths, is higher for Prototype B than Prototype A, and it is significantly higher with fewer signal paths. A correlation coefficient of 0.7 is usually considered the limit for good diversity/MIMO performance. Table III values less than 0.7 for the two shows the proportion of prototypes, indicating that Prototype A is superior. The spread

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TABLE III PROPORTION OF CORRELATION COEFFICIENT VALUES LESS THAN 0.7 FOR PROTOTYPES A AND B, FOR DIFFERENT NUMBER OF SIGNAL PATHS

TABLE IV MEDIAN AND WORST CASE MULTIPLEXING EFFICIENCY OF PROTOTYPES A AND B, FOR DIFFERENT NUMBER OF SIGNAL PATHS

Fig. 6. Diversity gain of Prototype A (circles) and Prototype B (triangles), using maximum ratio combining, as a function of the number of signal paths. TABLE V BEST CASE, MEDIAN, AND WORST CASE DIVERSITY GAIN OF PROTOTYPES A AND B, FOR DIFFERENT NUMBER OF SIGNAL PATHS

Fig. 5. (a) Power imbalance of Prototype A (circles) and Prototype B (triangles), as a function of the number of signal paths. (b) Correlation coefficient of Prototype A (circles) and Prototype B (triangles), as a function of the number of Prototype A (circles) and of signal paths. (c) Multiplexing efficiency Prototype B (triangles), as a function of the number of signal paths.

is however very large for both models, and there are many cases in which the performance difference is reversed. The multiplexing efficiency, being a function of both the efficiencies and the correlation, show better performance for Prototype A in general, and a quicker degradation for Prototype B

as the number of signal paths is reduced. Table IV summarizes the median and worst case multiplexing efficiencies. Diversity gain is shown in Fig. 6 and Table V. From 16 paths down to four, the median remains stable for both prototypes, but with an increase in the spread. With two paths, the median value for Prototype B drops drastically, while it remains approximately the same for Prototype A. The spread increases even more for both, and Prototype B has better best case and worst case values. Best and worst cases are however highly sensitive to random fluctuations. Which model has the best diversity gain performance depends on which number of signal paths and which statistical parameter (median, best/worst case) is considered.

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IV. CONCLUSION Mobile terminal dual antennas are characterized using an MPS, which provides a 2-D signal environment with up to 16 signal paths. Three test objects are characterized with 2, 4, 8, and 16 simulated signal paths. Several conclusions are drawn from the results. The performance with 16 signal paths shows only small variations over different test object orientations. For the test objects used, it is close to the performance in a corresponding 2-D environment with a large number of signal paths, but not necessarily close to the performance in a 3-D environment. As the number of signal paths is reduced, the primary effect is a strong increase in the spread of the different metrics. Some degradation in average performance is also seen. With only two signal paths the correlation coefficient can have any value, with a significant portion of the values being above 0.7, even on a test object with good performance in a 3-D environment with many signal paths. Two test objects of the same type of terminal, but with different antenna solutions, are demonstrated to both have very strong performance variations in an environment with limited number of signal paths, but also somewhat different characteristics in terms of median and worst case performance. Which antenna solution is the better depends on the exact number of signal paths, and the choice of performance parameter. Presented experiments show that characterization in environments with a limited number of signal paths provides a deeper insight into dual antenna performance compared to the traditional characterization assuming a large number of signal paths, and that an MPS is suitable for such characterization. V. FUTURE WORK Future work includes a study of the same type as the presented, but with the application of realistic channel models to the MPS. Further, models and metrics intended specifically for dual antenna performance in sparse environments should be studied, and specific test methods should be developed that enable performance assessment with maximum reliability at minimal cost. REFERENCES [1] J. Villanen, P. Suvikunnas, C. Icheln, J. Ollikainen, and P. Vainikainen, “Performance analysis and design aspects of mobile-terminal multiantenna configurations,” IEEE Trans. Veh. Technol., vol. 57, no. 3, pp. 1664–1674, May 2008. [2] C. B. Dietrich, Jr., K. Dietze, J. R. Nealy, and W. L. Stutzman, “Spatial, polarization, and pattern diversity for wireless handheld terminals,” IEEE Trans. Antennas Propag., vol. 49, no. 9, pp. 1271–1281, Sept. 2001. [3] T. Taga, “Analysis for mean effective gain of mobile antennas in land mobile radio environments,” IEEE Trans. Veh. Technol., vol. 39, no. 2, pp. 117–131, May 1990. [4] M. J. Gans, “A power-spectral theory of propagation in the mobileradio environment,” IEEE Trans. Veh. Technol., vol. VT-21, no. 1, pp. 27–38, Feb. 1972. [5] P. L. Carro, J. de Mingo, and P. G. Ducar, “Analysis of the antenna stochastic effective gain in mobile environments,” presented at the IEEE 69th Veh. Technol. Conf., Barcelona, Spain, Apr. 26–29, 2009. [6] K. Kalliola, “Experimental Analysis of Multidimensional Radio Channels,” Ph.D. dissertation, Helsinki University of Technology, Radio Laboratory Publications, Rep. S 251, Espoo, Finland, Feb. 2002.

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[7] A. M. Sayeed and V. Raghavan, “Maximizing MIMO capacity in sparse multipath with reconfigurable antenna arrays,” IEEE J. Sel. Topics Signal Process., vol. 1, no. 1, pp. 156–166, June 2007. [8] J. S. Colburn, Y. Rahmat-Samii, M. A. Jensen, and G. J. Pottie, “Evaluation of personal communications dual-antenna handset diversity performance,” IEEE Trans. Veh. Technol., vol. 47, no. 3, pp. 737–746, Aug. 1998. [9] T. Maeda, S. Sekine, S. Obayashi, and T. Morooka, “Two methods for estimating the diversity characteristics of built-in antennas for mobile communication equipment,” in Proc. IEEE AP-S Int. Symp., Jun. 1995, vol. 4, pp. 18–23, pp. 1944-1947. [10] J. F. Valenzuela-Valdés, A. M. Martínez-González, and D. A. SánchezHernández, “Diversity gain and MIMO capacity for nonisotropic environments using a reverberation chamber,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 112–115, 2009. [11] T. Sakata, A. Yamamoto, H. Iwai, K. Ogawa, J. Takada, K. Sakaguchi, and K. Araki, “BER evaluation system for a handset antenna in a multipath environment using a spatial fading emulator,” in Proc. ISAP2005, Seoul, Korea, vol. TB1-6, pp. 351–354. [12] L. Rudant, C. Delaveaud, and M. AbouElAnouar, “Synthesizing realistic environments in an anechoic chamber,” in Proc. 3rd Eur. Conf. on Antennas Propag., Berlin, Germany, Mar. 23/27, 2009, pp. 221–225. [13] P. Hallbjörner, Z. Ying, M. Håkansson, C. Wingqvist, T. Anttila, and J. Welinder, “Multipath simulator for mobile terminal antenna characterization,” IET Microw. Antennas Propag., vol. 4, no. 6, pp. 743–750, 2010. [14] R. Tian, B. K. Lau, and Z. Ying, “Multiplexing efficiency of MIMO antennas,” IEEE Antennas Wireless Propag. Lett., vol. 10, pp. 183–186, 2011. [15] D. G. Brennan, “Linear diversity combining techniques,” in Proc. IRE, Jun. 1959, pp. 1075–1102. [16] S. Saario, D. V. Thiel, J. W. Lu, and S. G. O’Keefe, “An assessment of cable radiation effects on mobile communications antenna measurements,” in Proc. IEEE Antennas Propag. Society Int. Symp., Montreal, Canada, Jul. 13/18, 1997, vol. 1, pp. 550–553. [17] C. Icheln, J. Krogerus, and P. Vainikainen, “Use of balun chokes in small-antenna radiation measurements,” IEEE Trans. Instrum. Meas., vol. 53, no. 2, pp. 498–506, Apr. 2004.

Paul Hallbjörner was born in Uppsala, Sweden, in 1966. He received the B.Sc., M.Sc., and Ph.D. degrees, all in electrical engineering, from Chalmers University of Technology, Göteborg, Sweden, in 1988, 1995, and 2005, respectively. Since 1989, he has worked in the telecom industry in the areas of pre-production engineering, product development, and research, mainly in the field of antennas and microwave technology. He has worked with mobile terminal antennas for handsets and vehicles, base station antennas, reconfigurable and steerable antennas, wave propagation, passive microwave circuits, electrical material characterization, and millimeter-wave design. He has been employed by Ericsson, Saab, Allgon, and is currently working an Antenna Researcher at SP Technical Research Institute of Sweden, Borås, Sweden, where his main focus is on antenna measurement techniques for mobile phones and short range communication, in addition to antenna development for various applications. He is the author of more than 70 scientific publications and the inventor of 10 patents.

Juan D. Sánchez-Heredia was born in Lorca, Spain. He received the Telecommunication Engineering degree from the Universidad Politécnica de Cartagena, in 2009, which culminated with the Final Degree Award, and the Master degree in information technologies from Universidad de Murcia, in 2010. He is currently working toward the Ph.D. degree at the Universidad Politécnica de Cartagena, Spain. In 2007, he worked at General Electric, Cartagena, and was involved in several projects in relation with the network infrastructure. In 2009 he joined the Department of Information Technologies and Communications, as a Ph.D. student. His current research areas cover MIMO communications, multimode-stirred chambers and electromagnetic dosimetry.

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Peter Lindberg (M’08) was born in Uppsala, Sweden, in 1974. He received the M.Sc. and Ph.D. degrees in engineering physics from Uppsala University, Sweden, in 2000 and 2007, respectively. Previously, he worked as an RF Engineer at Smarteq Wireless, Enebyberg, Sweden, from 2000 and 2002, and as a Research Engineer in the Microwave Technology Group, Uppsala University, from 2002 and 2003. He is the coauthor of more than 30 scientific publications and co-inventor of over 40 patents. Currently, he is with the Advanced Technology Group, Mobile Antenna Systems Division, Laird Technologies, Sweden, working with antenna design, measurement techniques, technology scouting, and customer engineering support. Dr. Lindberg received the R. W. P. King Best Paper Award from the IEEE Antennas and Propagation Society in 2007.

Antonio M. Martínez-González received Dipl.-Ing. degree in telecommunications engineering from the Universidad Politécnica de Valencia, Spain, in 1998 and the Ph.D. degree from Universidad Politécnica de Cartagena, in early 2004. From 1998 to September 1999, he was employed as a Technical Engineer at the Electromagnetic Compatibility Laboratory, Universidad Politécnica de Valencia, where he developed assessment activities and compliance certifications with European directives related with immunity and emissions to

electromagnetic radiation from diverse electrical, electronic and telecommunication equipment. Since September 1999, he is an Associate Professor at Universidad Politécnica de Cartagena. At present, his research interest is focused on electromagnetic dosimetry, radioelectric emissions and mode stirred chambers. In December 2006, he was one of the founders of EMITE Ing, a technological spin-off company founded by telecommunication engineers and doctors of the Microwave, Radiocommunications and Electromagnetism Research Group (GIMRE), Technical University of Cartagena (Spain). Dr. Martínez-González was awarded with the Spanish National Prize from Foundation Airtel and Colegio Oficial de Ingenieros de Telecomunicación de España for the best final project on Mobile Communications in 1999. In 2006 and 2008, he was a co-recipient (as a co-founder of EMITE) of the i-patentes prize for innovation and technology transfer in the Region of Murcia (Spain).

Thomas Bolin was born in Falun, Sweden, in 1954. He received the M.Sc. degree in electrical engineering from Linköping Technical University in Sweden, in 1979. He is currently working with MIMO antenna design and measurement techniques within Sony Ericsson Mobile Communications, Lund, Sweden. He is one of the pioneers in the mobile handset business having held positions in radio design and management at Ericsson and later Sony Ericsson. Since 1996, he founded and managed an antenna group within his company. From 1979 to 1983, he worked for ITT Standard Radio & Telefon AB in Vällingby, Sweden, with design of short wave radio kW transmitters. He is the author of a number of scientific papers and holds five patents.

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On Small Terminal Antenna Correlation and Impact on MIMO Channel Capacity Boyan Yanakiev, Jesper Ødum Nielsen, Morten Christensen, and Gert Frølund Pedersen

Abstract—Analysis of the antenna correlation at the design stage is made, and then compared to real life performance in a typical propagation environment and in typical use cases. A traditional design flow is followed and conclusions are made on the performance of several handsets. These conclusions are then contrasted to measurements and an explanation is sought for the variations. It is concluded that correlation estimation and optimization at the design stage, using conventional methods, brings little benefit in real life situations. Impact on channel capacity has been the figure of merit. Index Terms—Antenna, correlation, electrically small antennas, handset antennas, MIMO systems, optical fiber, optical fiber measurement applications, propagation measurements.

I. INTRODUCTION

W

ITH the fast approaching worldwide launch of the long term evolution (LTE) system, it is ever more urgent that adequate antenna design specifications are defined. From multiple input multiple output (MIMO) theory point of view, the received power, signal correlation and branch power ratio are all important for the channel capacity and overall system performance. The influence of each one is investigated in the literature [1] and certain requirements and rule of thumb numbers are available [2]. It is not clear, however, how to translate these essentially signal requirements, to antenna specifications. This paper takes a look at the current trends in antenna design and evaluates the relevance to real life performance. The focus is on correlation. A common approach is to evaluate an antenna system in terms of diversity gain, which is known to depend on mean effective gain [3], branch power ratio and correlation [4], [5]. While this can give a very good estimate, of how influential each parameter is, it is not easy to come up with design goals. A large study of the user influence on the mean effective gain done in [6] shows,

Manuscript received June 15, 2010; revised May 18, 2011; accepted August 26, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. The work of B. Yanakiev and J. Ø. Nielsen was supported in part by the Danish Advanced Technology Foundation (Højteknologifonden) as part of the Converged Advanced Mobile Media Platform (CAMMP) project. B. Yanakiev is with the Molex Antenna Business Unit, DK-9220 Aalborg, Denmark and also with the Antennas, Propagation and Radio Networking section at the Department of Electronic Systems, Faculty of Engineering and Science, Aalborg University, DK-9220 Aalborg, Denmark (e-mail: [email protected]). J. Ø. Nielsen and G. F. Pedersen are with the Antennas, Propagation and Radio Networking Section, Department of Electronic Systems, Faculty of Engineering and Science, Aalborg University, DK-9220 Aalborg, Denmark. M. Christensen are with Molex Antenna Business Unit, DK-9220 Aalborg, Denmark. Digital Object Identifier 10.1109/TAP.2011.2173442

that up to 10 dB of variation can be expected from one user to another. In [7] and [8] investigation is done on the measured correlation and branch power ratio around 1.8 GHz, with the presence of the user. It is concluded that the users generally increase the correlation, but also that the branch power difference is a more important parameter for diversity gain. A more theoretical approach is resented in [9] and [10]where rotation properties of the antenna radiation patterns are investigated in details and shown to contribute to the variations reported earlier. An extension to this work is done in [11], for several different environment models, highlighting the need for realistic use cases. A more recent work [12] further develops the concept to include a more realistic estimate of the actual diversity gain in the presence of users and confirms the conclusions. In the current paper the antenna performance, in terms of correlation, is analyzed at two distinct stages, called here—design and real life. • The design stage is defined as the performance evaluation by simulation and initial verification measurements in laboratory. Antenna correlation from simulation tools is usually directly computed from the radiation patterns or S-parameters following the derivations in [4] and [13], respectively. The method for measurement verification depends on the system used—measured radiation patterns for the anechoic chambers or sequences of transmission coefficients for the mode-stirred chambers [14]. The practicalities and capabilities of these two measurement methods are different, so here the computed design stage correlation is only from simulations, assuming that whatever the verification method, it should converge to about the same simulated value. • The real life stage is defined as the evaluation of the performance in a realistic propagation environment and with realistic handling by users. To measure correlation in such realistic conditions, large scale channel sounding campaign was performed in a typical urban environment. In this paper the correlation values presented as achieved in real life scenario, are computed from the recorded channel impulse responses, which include the transmit and receive antennas, and the propagation channel. It is worth noting that currently there is an effort in the scientific community and especially industry, to emulate such conditions in the laboratory with methods based on both chamber types—[15]–[17] or [18]. The focus is primarily on the end-to-end system performance in terms of throughput with the main discussion over the realistic modeling of the propagation channel.

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Currently, rule of thumb numbers exist suggesting that for all other parameters being the same, the envelope correlation of two antennas should be or even depending on the source—[2], [4], [5] and [19],[20], respectively. Such signal correlation value would provide good MIMO performance and is readily adopted by antenna designers as a requirement alongside antenna efficiency, branch power ratio etc. The goal of this paper is to reexamine these signal correlation requirements and evaluate the benefits of adding a particular correlation value to the antenna design requirements. It will be argued here that, while it is always true that low correlation leads to better performance, high correlation is not necessarily leading to noticeably worse performance and that designing for low correlation can even have negative effects. Some potential pitfalls in the current correlation measurement techniques are also discussed. The paper is organized as follows: Section II gives details on the extensive work done to make realistic handset mock-ups. Details on the measurement set-up and use cases are also given. Section III presents the theoretical background for the design stage results. Details on processing of the measured data are given in Section IV. Results from the design stage are presented in Section V and channel sounding results follow in Section VI. The impact on channel capacity is presented in Section VII with some additional discussion. Section VIII concludes the paper.

TABLE I HANDSET OVERVIEW

TABLE II LAB MEASUREMENTS FOR H1, H2 AND H4

II. TEST HANDSETS AND SCENARIOS Since the paper aims at accurately representing both the design process as well as the real life scenarios, special attention has been paid to designing realistic handsets and evaluating them in scenarios as close as possible to a real network. For the design stage evaluation, standard finite difference time domain (FDTD) based [21] software has been used for simulation. Optimizations have been made to achieve typical efficiency, low user influence and low coupling. All handsets have been measured in an anechoic chamber to confirm the simulation results. Since there is a known problem with the coaxial cable when measuring small terminal antennas [22], [23], [24], a special optical unit was developed [25], [26], which allows for both accurate measurements but also natural user handling. A. Handsets Seven handset mock-ups were used for the measurements. Here the focus will be on three of them (H1, H2 and H4) for simplicity, as they present the corner cases and show the main trends well. The conclusions are true for all handsets and Table I gives an overview. In Table I “mono” and “PIFA” stand for monopole and planar inverted F antenna types, respectively. The handsets’ form factors are given along with the electrical sizes in columns 1 and 2 as typically defined in [27]. For example H2 is meant to represent a long, clamshell phone used when open (Fig. 3), while H1 and H4 have sizes similar to modern touchscreen smartphones/PDAs. All handsets have two antennas but not all antennas are dual band. For example, antenna No.1 on H4 covers only the high band, while antenna No.2 is dual band and is used for a SISO reference case on the low band. H4 also has

both antennas on the top, as opposed to top and bottom placement in H1 and H2. Table II gives details on the measured efficiencies and coupling for the selected handsets. The coupling is measured with coaxial cables attached. Some difference can be expected when the cables are removed, however the optical measurement system used does not support optical S-parameter measurements. Simulations suggest another 2–3 dB lower coupling without the coaxial cables. All of the handsets were equipped with optical units and plastic casings from PC-ABS material with grip position engravings for accurate and natural user handling. The finger positions were surrounded with elevated rings to avoid finger movement during measurements. Example of H1 is shown in Fig. 1 and details are given in [26], where the benefits of using the optical links for radiation pattern measurements is confirmed. The sizes listed in column 2 of Table I are the effective electrical sizes or simply the PCB size. The PC-ABS material has a dielectric constant of about and adds 1.5 [mm] in all directions to the overall handset size. The resolution of the 3D rapid prototyping printer used to make the plastics, is around 0.1 [mm], allowing for very accurate mechanical design, antenna positioning and repeatability. Industry grade matching components and gold plated feed springs are used to ensure high quality and durability. During the design process the handsets have been disassembled tens of times without any noticeable performance change. The three selected handsets for this paper are shown in Fig. 2. Overall the design process has followed the traditional mobile phone antenna design path.

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Fig. 1. Handset one (H1). Notice the optical unit in the middle.

Fig. 3. Two grips used in the measurements. (a) One Hand (OH) grip for H2; (b) Two Hands (TH) grip for H2 with the same user.

Fig. 2. Antennas for handsets H1, H2 and H4. Top cover of H4 shown with screw domes and grip marks visible.

TABLE III BASE STATIONS DETAILS

B. Real Life Measurements Once built and verified in the lab, the handsets were measured in a realistic propagation scenario. To represent a realistic network architecture two base stations were built—one high altitude, low band representing an umbrella cell and one low altitude, dual band, equipped with multiple antennas, representing a local high capacity cell—see Table III. The two test frequencies are and . Measurements were made indoor in browsing mode in free space and with twelve users. Aalborg University’s parallel

channel sounder was used to sample the complex channel impulse response. For details on the channel sounding refer to Section IV. C. Use Cases Three main cases were measured—free space (FS), one (OH) and two (TH) hands, all in data mode operation—see Fig. 3. In all cases the data mode is imitated by positioning the handsets at about degrees angle from vertical position. To perform the free space measurements, the handsets were positioned in pockets carved into a Styrofoam block and pushed along the measurement routes on a table with wheels, by a kneeling down person. The pre-defined one hand grips are an attempt to imitate the CTIA grips described in [27] for narrow (H2, H3 and H5-7) and wide (H1 and H4) data mode operated handsets. The case engravings were positioned approximately where the phantom hands would touch the handsets and the distance to the palm is fixed with a Styrofoam piece glued to the back of the handset. The two hands grips are freely chosen since CTIA currently does not specify them. Fig. 3 shows the grips used with H2 and all other narrow bar phones. H1 and H4 are thought to be touch

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III. CORRELATION AT THE DESIGN STAGE It has previously been shown that to achieve some diversity gain the antenna envelope correlation should be below [2], [4], [5]. This is of course not a fixed number but rather a rule of thumb used as a guideline. A more commonly used number in industry is [19], [20]. These have been adopted for MIMO as well. It is thus important to understand how to compute the correlation and what it depends on. A. Antenna Correlation Formulations Antenna correlation was first formulated in [4] as (1) Fig. 4. Measurement site with color coded routes.

screen devices therefore for the two hands grip users were instructed to touch the handset approximately in the middle imitating touch interaction. Twelve users participated in the channel sounding measurements and each handset was measured with each user at each measurement route. Further in the paper, the two distinct grips described above, are combined in a general use case called “with users”. In the statistical analysis later, no differentiation is made between one and two hands grips. This is done for simplicity, since this paper aims only to quantify the general user effect on correlation. All conclusions made for the user influence on correlation when compared to free space, are true for the two grips individually as well as when combined. D. Measurement Site The indoor measurements were taken on the third floor of Aalborg University’s building in downtown Aalborg, Denmark. The propagation is outdoor-to-indoor in a typical urban area. On the floor of the measurement room, a square was drawn with 4 meter long sides—A, B, C and D (Fig. 4) with the arrows indicating the user orientation. The users were instructed to hold the handsets with the predefined grips and walk forward and backward along a single side, twice for each measurement, without turning around. The total distance of 16 meters per measurement, gives about 40 wavelengths of sounding distance on the low band. The order of the user participation is random, and measurement with the same user, were taken within several days to perform all measurement combinations of handsets, square sides and grips. The cable holder in the middle of the square was used to ensure that the optical fibers do not twist or bend too much. Again for simplicity, the four square sides are grouped into one general indoor case and no further differentiation is made unless otherwise noted. In few measurements the window side (B) leads to direct line of sight and some larger variation, most often for H2. It is not observed in all cases most probably due to the slight variations of the user orientation and walking path. Statistical analysis showed that the sides are not equivalent and that side (B) does have higher received power. This is kept in the statistical sampling simply to represent a more general case.

is the cross covariance, and and are the stanwhere dard deviations of the received signals. The cross covariance can also be written in a convenient way as in [28]

(2) where is the cross polarization ratio of the environment as defined in [3]. The variances can be written as (3) and antennas, In the above equations represents both and if stands for both the elevation and azimuth vector components, then and are respectively, the electric fields and gain patterns in the far field of the i-th antenna for both polarizations. is then the power distribution in the environment of both polarizations in spherical coordinates. indicates variation over both and spherical angles, and represents the complex conjugate. It has also been shown [29] that the envelope correlation of Rayleigh fading signals can be written as (4) Equation (4) is known to have less than 10% relative error in the approximation estimated in [19] based on the data from [29]. In the current paper all correlation results presented are of the envelope correlation, since it is the most commonly used. As can be seen clearly from the above formulations, the correlation depends directly on the power distribution in the environment, which can be seen as a weighting function of the radiation pattern differences. The total power received per antenna however is normalized via making the correlation estimate independent of efficiency differences. Very often, the environment is defined as isotropic for simplicity. Assuming no losses and such environment, in [13] a very fast, convenient and broadband way for correlation computation from S-parameters in derived. The isotropic assumption however, rarely holds and many propagation measurements

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have shown, that the incoming power distribution is rather directive or clustered, within several main directions [30]. It will be shown here, that this simplification can compromise the estimation of correlation at the design stage. Here (1)–(4) will be used to compute the envelope correlation, which implies that a power distribution model must be defined as well. When measurement verification in the lab is needed, the typical procedure for anechoic chambers is to replace the simulated radiation patterns with measured ones in (1)–(4). This requires accurate complex pattern measurements, but allows for arbitrary power distribution. Using mode-stirred chambers gives the advantage of directly measuring the signal correlation at the antenna ports, with typically isotropic power model assumed, [14]. Solutions however exist for modeling directive environments [31]. B. Incoming Power Distribution Models For the purposes of this analysis three spherical incoming power models will be used. 1) Isotropic: The power in this case is uniformly distributed on a sphere for both polarizations and . In that case the power is a constant independent of elevation or azimuth and and can come out in front of the integrals in (2) and (3) leading to the most common definition of correlation formulation in literature and practice (e.g., [13])

(5) 2) Gaussian: The power distribution for this model is given in [3] as Gaussian for both polarizations along elevation and uniform along azimuth. The peak of the Gaussian distribution indicates the mean angle of arrival and the variance is an estimate of the angular spread. In this paper the mean angle of arrival used is 0 degrees and the angular spread is 30 degrees for both polarizations. Since the XPR is not defined explicitly here it is set to 1. This is currently the most common model used in industry. 3) AAU: A mobile specific, statistical power model for outdoor to indoor propagation is defined in [28] as a result of extensive measurements in Aalborg city, Denmark. Since the later analysis in this paper relies on similar overall scenario (outdoor bases and indoor mobile in a room with a single window), this channel model should give a very good correlation estimate. It must be noted however that the power distribution model is derived about 10 years before the current measurements took place and is a statistical description of a much richer variety of scenarios—multiple floors, rooms and base stations at various distances. The main feature is a single direction of arrival from the room openings (windows) for each polarization, with different spreads. The model is derived based on work done in [32]. Since the model is based on measurements the cross polarization ratio is given explicitly as and the model parameters used are the ones listed in [28]. Alternative, directive power models can be found in [33].

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IV. MEASUREMENT DATA PROCESSING The channel sounding was done for both bands, all transmitters and four handsets simultaneously. Some parameters include: spatial sampling frequency of , chosen for the indoor walking speed. The impulse response sampling is done with corresponding to impulse response (IR) resolution. The total IR sampling time is (or IR samples) corresponding to frequency domain resolution of . The total measurement time was , which in turn produces spatial samples for the 16 meters measurement route for each square side. The sounding frequencies are given in Table III and the corresponding low and high band bandwidths are and . The result is a complex channel impulse response with about 2 GB per measurement. In total around 300 measurements were done, each with four handsets at a time on the four sides of the measurement square. A. Correlation from Measurement Data The algorithm for computing the correlation from the measurement data is described in the following steps for each antenna/Tx combination. • Perform a Fast Fourier Transform on the complex resulting in the frequency dependent channel Transfer Function , with complex channel gain coefficients . • Take the absolute value for the selected frequencies (here only the center sounding frequency is presented) resulting in vectors of the narrowband signal envelopes. • Pearson’s correlation coefficient is then computed as defined in [34] for a large sample from every two envelope vectors corresponding to the two antennas receiving from a particular transmitter. The exact treatment for a discrete sample is given in (6), (6) and are the instantaneous discrete samples where (envelope samples in this case) and and are the means. The summation index runs through the complete sample length . The result is a single number for the envelope correlation for each antenna pair and transmitter. Essentially, the procedure is the same as the one used in a mode-stirred chamber. The advantage of the sounding data is the inherent realism and true propagation environment. With adequate channel power modeling however, the mode-stirred chamber can be a significantly cheaper and faster solution. B. Advanced Signal Processing It is well known that the correlation computation defined as above is not a robust measure, see [35] with practicalities related to channels given in [19]. Slow fading variations due to body shadowing for example [36], can create periodic mean

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power variations within the measurement, equally for both antennas, essentially violating the assumptions, under which (6) is derived. This leads to a correlation number dominated by the slow fading pattern rather than the fast fading and should be avoided. The solution is to perform a demeaning procedure [19]. For the results presented here, simple moving average filter is used. The chosen window has width of 50 measurement samples, which corresponds to several wavelengths at the low band for the spatial sampling used. The number of samples has been determined by investigating some of the worst case measurement examples, where the slow fading variation is very strong. Demeaning was performed with various window sizes and the optimal number was selected corresponding to a value that gives stable estimate. Taking few window samples more or less does not influence the correlation estimation significantly. From a physical point of view, since the route is 16 meters, but split in four equivalent sections, the variation within each 4 meters is expected to be similar. Assuming constant speed, the window size should be smaller than the 300 samples for each 4 meter section. Details on assumptions, procedures and practicalities of performing demeaning can be found in [19]. It must be noted that in simulations there is no slow fading effect. This step is essential when trying to make sense of measurement data compared to simulations.

where is the transmit power, is the number of transmit antennas and are the eigen values of the matrix of rank r and

leading to different parameters being highlighted. Some possibilities are the following. 1) Normalization to a Reference Handset: This is usually also done for a reference use case—most often free space. This normalization provides an easy way to compare overall capacity performance between handsets. The mean power from all Tx/Rx antenna combinations for the reference scenario is computed. The complex channel coefficients of all handsets are then normalized to the square root of this mean value. This way of normalizing preserves the fading, correlation and branch power as well as handset efficiency differences and user influence information. Similar procedure is described in [38] as first normalization option. The disadvantage of this method is however, that since all capacity influencing parameters are preserved, it is hard to determine, which variable exactly causes the capacity to change in the case when there is indeed some difference between measurements or handsets. The different efficiencies of the different handsets lead to lower or higher effective SNR when computing (7) and the capacity changes accordingly. The problem is even further deepened when users are introduced as a variable, although on the other hand, this can be an indicator on the capacity degradation relative to some mean body loss factor for example. 2) Normalization to Each Individual Measurement With Averaged Antenna Powers: In this case, for each measurement, the power collected by both antennas and all transmitters is averaged and then the channel coefficients are normalized to the square root of that value. The branch power ratio, correlation and fading information is preserved. However handset efficiency information and the relative body loss effect due to the users, are lost in the normalization. This corresponds to the second method for normalization from [38]. 3) Normalization to Each Individual Receiving Antenna: In this case the normalization is done separate for each antenna within a single measurement. Branch power ratio information is thus lost, leaving only correlation as a free capacity influencing parameter. The following normalization is used

(8)

(10)

where are the instantaneous complex channel coefficients for a 2 2 MIMO system, which is the one used in this paper. denotes Hermitian transpose, is the antenna index and is the transmitter index. This way, (7) is used to compute the instantaneous channel capacity and then the mean is taken for the whole measurement. The resulting ergodic capacity values are collected for all relevant cases (for example all measurements with users). The upper bound capacity of such system is given in [37] by letting , and is the signal to noise ratio of the normalized channel.

where each instantaneous channel coefficient is divided by the square root of the mean power received by antenna , from the corresponding transmitter , , 2 and , 2. This is somewhat artificial way of looking at capacity and the goal is to isolate correlation as the only capacity determining factor. It must be noted that the correlation for both receive but also transmit antennas is present after this normalization method. The transmit correlation is here computed by correlating the received power on one antenna from two different transmitters, with the same procedure given in Section IV-A. Since in this case, the 2 2 MIMO scenario includes only transmitters from the near base, the propagation path to the measurement room is nearly the same, contributing to a higher, but overall constant transmitter correlation. Few exceptions near the room opening are observed. 4) Normalization to Each Individual Receiving Antenna With Slow Fading Cleared: Note that the denominator in (10) is the mean power including the slow fading. This preserves the local

C. Channel Capacity Formulation To compute the open loop channel capacity (channel state information (CSI) known only at the receiver) the common formula found in [37] is used (7)

(9) D. Power Normalization Normalization of the H matrix, gives the freedom to select arbitrary SNR. There are however various ways to normalize,

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means within the measurement leading temporarily to lower of higher effective SNR, different from that given in (7). This can lead to the slow fading pattern contributing to the average capacity as well as the correlation. While correlation computed with the slow fading present, makes little sense, the presence of slow fading when computing capacity, can be interpreted as temporary channel variations that a user can experience. This effect can be significant since the logarithm function in (7) is not linear. To remove the effect, the same moving average filter, is used as for the correlation

(11) Fig. 5. Low band envelope correlation with slow fading removed for H1.

This paper uses the third and fourth methods for the computed capacity results. E. Statistical Analyses Details The means, standard deviations and percentiles of all results presented in the later sections are based on statistical samples from the measurement data population, for the relevant cases. For example the measured free space correlation for H1 is based on 16 measurements, along the four sides of the room (Fig. 4). The antenna correlation is computed for the two low and high band transmitters on the near base leading to a statistical sample size of 32 values for each band. These same transmitters have later been used for MIMO channel capacity computation. In the case with users, since the two grips are combined, the total statistical sample size is over 100. Same is done for the other handsets. Fig. 5 shows a plot of the received envelope correlation values for the low band of H1 with slow fading removed. In the figure BS1:Tx1/Tx2 stand for Base station 1, transmit antenna 1/2 as listed in Table III. The numbers under the X-axis are the users and the sides of the square are given above the X-axis for each user. The multiple points for each user/side combination are due to repeated measurements and the combination of the two grips. This particular sample has a mean value of and standard deviation of . The probability distribution of the sample is shown in Fig. 6 and is similar to Gaussian. For relatively small sample sizes, for example free space only, the cumulative density function (CDF) has been observed and the normality assumption has been confirmed. All data samples statistically analyzed in this paper are considered normally distributed. To be able to differentiate between means, which are nearly the same, statistical significance testing is used. The sample variances are tested for equality with the robust Levene’s test. In case the null hypothesis of equal variances is confirmed, the sample means are compared in an ANOVA procedure. In case the variances are not equal, a modified two sample T-test procedure for not equal variances is used. In all cases significance level is used unless otherwise noted. All procedures described above are given in detail in [35].

Fig. 6. Probability Density Function (PDF) of the data in Fig. 5. Percentiles are also shown.

V. DESIGN STAGE RESULTS The antenna correlation at the design stage is computed from simulated radiation patterns using the (1)–(4) for the three selected handsets and power models. For the computations given in Table IV all handsets are defined in spherical coordinates, aligned with the standard x,y,z coordinate system as defined in [39] and then the radiation patterns are rotated around the y axis under . Since the AAU model is directive in azimuth, in Table IV the low/mean/high values of the correlation coefficient are given, as the handset is rotated around azimuth. Similar is done to estimate the mean effective gain (MEG) sensitivity to the pattern rotation in various power distribution models in [11]. As an example, only rotation around the z axis (azimuth) of H1, results in correlation variation about for low band in the AAU power model. This is primarily due to the ideal modeling in the simulation tool and the perfectly symmetric antenna placement on top and bottom of the handset. For high band on H4 since the antennas are asymmetrical. Further

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TABLE IV DESIGN STAGE ENVELOPE CORRELATION. AAU MODEL GIVEN WITH LOW/MEAN/HIGH VALUES

rotation in 3D including elevation can lead to even larger differences (also for the Gaussian model) but is not of interest here since all measurements are done at about the simulated . As can be seen from Table IV the correlation can vary significantly with the introduction of errors by the measurements cables and RF chokes. Although the RF chokes help prevent the cables from radiating, they are still a significant scatterer and the cable position cannot be controlled accurately, especially during field measurements with moving users. Furthermore, in the simulations, the cable positions have been optimized for least influence, leading them out in the middle of the handset along the width, where the electric field is weakest. This is also a practical way to measure in an anechoic chamber afterwards. Even with this, the cable introduces significant errors and the benefit of optical link measurements is again highlighted. The different channel power models also provide different results. The reason for selecting these particular handsets for further analysis are the correlation values in free space—one high (H1) and one low (H2). At this stage of the design process one might conclude that H2 would perform significantly better as it has much lower correlation. However, already here, one can observe the beneficial effect of the user in the simulation with the CTIA hand or SAM-head phantoms, leading to a much lower H1 correlation. This is also seen in the results published in [12]. Note also that the high band correlation is not significant in either case even for very closely spaced high band antennas as in H4. It is important however to consider that the variation in the high band can be significant. VI. MEASUREMENT RESULTS Correlation computed from the channel sounding data is presented in Table V. In all cases the statistics include all four sides

TABLE V 50%/95% PERCENTILE CORRELATION VALUES IN VARIOUS CASES

of the room and in the case of users all 12 of them with both grip types. It can be seen that the low frequency 95% percentile is at for H1 in the case with slow fading not removed. Also, the high band has a 95% percentile at . It is curious to note that, while the low band seems to be comparable to the design stage values the high band is underestimated. One possible reason is the presence of a slow fading pattern in the high band. Indeed, for the given dimensions of H1 the low band antennas utilize the whole handset body as a radiator [40], resulting in a rather omni-directional radiation pattern, while the high band antennas are more space confined and also more directive. Thus the high band antennas are more selective and have higher probability of experiencing large variations in received power. This becomes clearer when the slow fading effect is removed and the two correlation numbers are adjusted. Based on these adjusted numbers one can conclude that only the AAU power distribution model gives somewhat realistic estimate at the design stage. Looking at the rotation in azimuth variation, this is generally true for the high band and cases with users as well. This is expected result since the model has been developed specifically for mobile reception in a room with openings. The 50% percentile is given in Table V to show the estimated median of the samples for comparison with the values given in Table IV. The higher overall high band correlation observed in measurements is most probably due to the non ideal de-meaning procedure. Indeed some 2 dB local mean variation can be observed after the de-meaning. Limited port isolation at the optical unit can also be a contributing factor for errors at the low correlation range. The users’ orientation on the different sides of the square can be seen as the measurement equivalence of the azimuth rotation done in Table IV for the AAU model. Analysis of the per side statistical samples shows that indeed the different sides are statistically different. Table VI lists the results for H1 and the same is confirmed for all other cases. The variations observed can only be explained by a directive power model. It is however true that changing sides, changes the location in the room as well and it is not possible to separate the two variables with the measurements performed. Therefore this investigation is taken no further. It is also very significant to note that in the case with users, the correlation is always significantly different from the free space one, thus making the free space estimate inadequate for such different use case. For the low band, slow fading removed case,

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TABLE VI 50%/95% PERCENTILES FOR H1 ALONG DIFFERENT SIDES

note that the user influence can be both advantageous as in the case of H1, also seen at the design stage but also disadvantageous as in the case of H2. For H1 this can be interpreted as the user actively changing the radiation patterns by interacting with the near fields and thus asymmetrically changing the antennas’ reception of the incoming power leading to de-correlation. In the case of H2, since the handset is a clamshell and features an RF choke at the hinge (implemented with a coil and capacitor), the user mainly interacts with the bottom antenna. Assuming the top antenna remains undisturbed and keeping in mind that the correlation is already rather low in free space, the user influence can be interpreted as in [5] where the absorption from the body in some directions is seen as limiting factor for the utilization of all differences in the radiation patterns. In other words, if the radiation patters are different enough in free space, leading to low correlation when weighted with the power distribution, the addition of the user can only block certain incoming power directions, due to absorption in the tissue, resulting in more correlated signals. Alternatively, if the patterns are very correlated in free space, meaning that the whole phone radiates, the addition of the user disturbs the near fields of both antennas in an asymmetric way, leading to lower correlation. Both effects are observed at the low band, while at the high band neither is obvious from the correlation numbers in Table V. Statistical analysis on the high band showed that the increased correlation effect is true for H1 and the mean correlation, indeed becomes significantly higher with the addition of the user. In the H2 and H4 cases the correlation means are confirmed equal, most probably due to the very asymmetric antenna location on H4 and the large distance on H2. The de-correlation effect could not be observed at the high band, since all high band antennas were with low correlation. Finally form Table V one can conclude that correlation at the high band is rather low in all situations. The correlation numbers for the center, upper and lower regions of the bands are within . Other factors such as antenna coupling have also been shown to influence the correlation [41]. The addition of the user can certainly change those too. [41] also suggests that for coupling has limited effect on correlation, which is also shown in [42]. Since dynamic tracking of the coupling during measurements was not possible, this could not be studied. The coupling values of the handsets however, are close to the 10 dB rule of thumb number and it should not be a major issue.

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TABLE VII MEAN CHANNEL CAPACITY FOR CONFIGURATION

OF A

2

2 MIMO

VII. DISCUSSION Looking at Table V it is not easy to predict the impact these correlation values would have on the end metric—channel capacity. In free space case, it looks obvious that H1 will perform much worse than H2 ( ). In the case with users however this is not so clear— for H1 vs. for H2. It is therefore necessary to quantify the gain of low correlated antennas compared to high correlated ones, especially from a design effort point of view. A. Capacity Results Using the normalizations described in Section IV-D-3 and Section IV-D-4, the channel capacity is given in Table VII. Again removing the slow fading has some effect but not as significant as for the correlation. Overall the results relative to each other are the same in both cases. It is important to emphasize that these capacity numbers cannot be in any way seen as expected for such handsets/environments as they are produced by a very artificial normalization method with a lot of idealizations implied. Furthermore the normalization is not ideal and other capacity influencing effects could have contributed to the results. The main goal is to compare them relative to one another for the purposes of evaluating envelope correlation influence and not to take them as absolutes. In all cases the capacity is generally linked to Table V—higher correlation leads to lower capacity and vice versa. The most significant result is that with the addition of the user on the low band, two otherwise separable in free space performance handsets, become nearly indistinguishable—H1 and H2 with users. Statistical comparison of the two samples shows that they are significantly different at significance level, while being the same for with p-value of for the case with slow fading present. Same conclusion is valid when the slow fading is removed. Similarly, at the high band H1 and H4 are statistically equal, while H2 has significantly higher capacity for slow fading present, which disappears when the slow fading is removed indicating that the local mean power is what causes the statistical difference. This is most probably due to the few extreme measurements near the windows. When comparing the capacity in the free space case with the capacity in the case with users for each handset, H2 low band is the only one where the MIMO capacity is observed to be equal. In all other cases the addition of the user leads to lower capacity when the free space correlation is low, or higher capacity when

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the free space correlation is high. Again some deviations due to imperfect demeaning, normalization or not accounted for coupling can be expected. A very important note here is that whenever two values are said to be significantly different, the statistical meaning of the phrase is used. For example, H2 has lower correlation than H1 in all cases, thus reaching higher low band capacity with users of 6.7 [bits/s/Hz], however H1 is very close with 6.6 [bits/s/Hz]. Statistically significant difference in the mean achieved capacity of –0.2 [bits/s/Hz], is certainly not something significant from a design effort point of view. Another interesting thing to note is that, the maximum capacity difference when using MIMO, observed between H1 low band and H2 high band in free space, is only for the two extreme correlation cases with slow fading removed. Comparing the more realistic case of low band only where the problem is expected in the first place, it is seen that the maximum difference is and that is only in free space. The SISO capacity at the low band for H4 is also computed. As expected, since correlation is not relevant in that case and the power is normalized, there is no difference between the free space and the case with users. Same is observed for all other handsets when used in SISO mode. It also shows that even for the high correlation low band case, some 30–40% improvement can be achieved with the use of MIMO schemes. Of course there is even further improvement when going to the very low correlated high band. VIII. CONCLUSIONS The paper analyses the adequacy of correlation estimation at the design stage, comparing it to the actual performance of the MIMO capable mobile in the real environment with the presence of diverse users and in free space. The main conclusions are that free space correlation computed for the isotropic environment yields inadequate results, both when compared to free space measurements and especially when directly used to predict the overall performance in the presence of the user. Realistic power distribution models have to be chosen, when computing correlation and the user influence must be included as well. With the results presented, regarding the user influence on the antennas and correlation, it is doubtful that it is worth investing much design effort in optimizing for low correlation antennas—certainly not for free space and with isotropic environment. The richness of the user interaction brings the correlation numbers of two handsets—one with low and one with high correlations—very close to each other. Evaluating the capacity as an end metric confirms that little can be gained by making low correlation antennas without accounting for the user’s presence. Large variations can be found in diverse MIMO figures of merit when the user’s presence is accounted for. It is thus concluded that other factors such as branch power ratio, power absorbed and overall mean effective gain will have much more significant effect on the perceived channel capacity and system diversity than just antenna correlation. REFERENCES [1] D. Tse and P. Viswanath, Fundamentals of Wireless Communication. New York: Cambridge Univ. Press, 2005.

[2] G. Pedersen, “Antennas for Small Mobile Terminals,” Ph.D. dissertation, Aalborg University, Aalborg, Denmark, 2003. [3] T. Taga, “Analysis for mean effective gain of mobile antennas in land mobile radio environments,” IEEE Trans. Veh. Technol., vol. 39, no. 2, pp. 117–131, May 1990. [4] R. Vaughan and J. Andersen, “Antenna diversity in mobile communications,” IEEE Trans. Veh. Technol., vol. 36, no. 4, pp. 149–172, Nov. 1987. [5] G. F. Pedersen and J. B. Andersen, “Handset antennas for mobile communications: Integration diversity, and performance,” Rev. Radio Sci. 1996–1999, pp. 119–137, 1999, Oxford Univ. Press. [6] G. Pedersen, J. Nielsen, K. Olesen, and I. Kovacs, “Measured variation in performance of handheld antennas for a large number of test persons,” in Proc. 48th IEEE Veh. Technol. Conf., May 1998, vol. 1, pp. 505–509. [7] G. Pedersen and S. Skjaerris, “Influence on antenna diversity for a handheld phone by the presence of a person,” in Proc. 47th IEEE Veh. Technol. Conf., May 1997, vol. 3, pp. 1768–1772. [8] G. Pedersen, J. Nielsen, K. Olesen, and I. Kovacs, “Antenna diversity on a UMTS handheld phone,” presented at the 10th IEEE Int. Symp. Personal, Indoor and Mobile Radio Commun., Osaka, Japan, Sep. 1999. [9] K. Ogawa and T. Matsuyoshi, “An analysis of the performance of a handset diversity antenna influenced by head, hand, and shoulder effects at 900 MHz .I. Effective gain characteristics,” IEEE Trans. Veh. Technol., vol. 50, no. 3, pp. 830–844, May 2001. [10] K. Ogawa, T. Matsuyoshi, and K. Monma, “An analysis of the performance of a handset diversity antenna influenced by head, hand, and shoulder effects at 900 MHz .II. Correlation characteristics,” IEEE Trans. Veh. Technol., vol. 50, no. 3, pp. 845–853, May 2001. [11] J. O. Nielsen and G. Pedersen, “Mobile handset performance evaluation using radiation pattern measurements,” IEEE Trans. Antennas Propag., vol. 54, no. 7, pp. 2154–2165, Jul. 2006. [12] V. Plicanic, B. K. Lau, A. Derneryd, and Z. Ying, “Actual diversity performance of a multiband diversity antenna with hand and head effects,” IEEE Trans. Antennas Propag., vol. 57, no. 5, pp. 1547–1556, May 2009. [13] S. Blanch, J. Romeu, and I. Corbella, “Exact representation of antenna system diversity performance from input parameter description,” Electron. Lett., vol. 39, no. 9, pp. 705–707, May 2003. [14] P. Hallbjorner, “Accuracy in reverberation chamber antenna correlation measurements,” in Proc. IWAT, Mar. 2007, pp. 170–173. [15] J. Welinder, L. Fast, T. Bolin, and L. Manholm, “The multi path simulator for over the air testing,” in Proc. EuCAP, Apr. 2010, pp. 1–4. [16] A. Yamamoto, T. Sakata, T. Hayashi, K. Ogawa, J. O. Nielsen, G. F. Pedersen, J. Takada, and K. Sakaguchi, “Effectiveness of a fading emulator in evaluating the performance of MIMO systems by comparison with a propagation test,” in Proc. EuCAP, Apr. 2010, pp. 1–5. [17] T. Sakata, A. Yamamoto, K. Ogawa, and J.-I. Takada, “MIMO channel capacity measurement in the presence of spatial clusters using a fading emulator,” in Proc. IEEE 20th Int. Symp. Personal, Indoor Mobile Radio Commun., Sep. 2009, pp. 97–101. [18] J. Valenzuela-Valdes, A. Martinez-Gonzalez, and D. Sanchez-Hernandez, “Emulation of MIMO nonisotropic fading environments with reverberation chambers,” IEEE Antennas Wireless Propag. Lett., vol. 7, pp. 325–328, 2008. [19] R. Vaughan and J. B. Andersen, “Channels, propagation and antennas for mobile communications,” IEE Electromagnetic Waves Series, vol. 50, 2003. [20] B. K. Lau, J. Andersen, G. Kristensson, and A. Molisch, “Impact of matching network on bandwidth of compact antenna arrays,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3225–3238, Nov. 2006. [21] A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. Norwood, MA: Artech House, 2005. [22] W. A. T. Kotterman, G. F. Pedersen, and P. Eggers, “Cable-less measurement set-up for wireless handheld terminals,” in Proc. PIMRC, Sep. 2001, pp. B112–B116. [23] C. Icheln, J. Krogerus, and P. Vainikainen, “Use of balun chokes in small-antenna radiation measurements,” IEEE Trans. Instrum. Meas., vol. 53, no. 2, pp. 498–506, Apr. 2004. [24] C. Icheln, J. Ollikainen, and P. Vainikainen, “Reducing the influence of feed cables on small antenna measurements,” Electron. Lett., vol. 35, no. 15, pp. 1212–1214, Jul. 1999. [25] B. Yanakiev, P. Eggers, G. Pedersen, and T. Larsen, “Assessment of the physical interface of UHF passive tags for localization,” in Proc. 1st Int. EURASIP Workshop on RFID Technol., Vienna, Austria, Sep. 2007, pp. 25–28.

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[26] B. Yanakiev, J. O. Nielsen, and G. F. Pedersen, “On small antenna measurements in a realistic MIMO scenario,” in Proc. EuCAP, Apr. 2010, pp. 1–5. [27] “Method of Measurement for Radiated rf Power and Receiver Performance,” CTIA, Oct/ 2009 [Online]. Available: http://www.ctia.org/, CTIA, Tech. Rep., CTIA Certification Test Plan for Mobile Station Over The Air Performance. rev. 3.0 [28] M. Knudsen and G. Pedersen, “Spherical outdoor to indoor power spectrum model at the mobile terminal,” IEEE J. Sel. Topics Quantum Electron., vol. 20, no. 6, pp. 1156–1169, Aug. 2002. [29] J. Pierce and S. Stein, “Multiple diversity with nonindependent fading,” Proc. IRE, vol. 48, no. 1, pp. 89–104, Jan. 1960. [30] M. Narandzic, C. Schneider, R. Thoma, T. Jamsa, P. Kyosti, and X. Zhao, “Comparison of SCM, SCME, and WINNER channel models,” in Proc. VTC, Apr. 2007, pp. 413–417. [31] J. Sánchez-Heredia, J. Valenzuela-Valdés, A. Martínez-González, and D. Sánchez-Hernández, “Emulation of MIMO Rician-fading environments with mode-stirred reverberation chambers,” IEEE Trans. Antennas Propag., vol. 59, no. 2, pp. 654–660, Feb. 2011. [32] J. Andersen and K. Pedersen, “Angle-of-arrival statistics for low resolution antennas,” IEEE Trans. Antennas Propag., vol. 50, no. 3, pp. 391–395, Mar. 2002. [33] K. Kalliola, K. Sulonen, H. Laitinen, O. Kivekas, J. Krogerus, and P. Vainikainen, “Angular power distribution and mean effective gain of mobile antenna in different propagation environments,” IEEE Trans. Veh. Technol., vol. 51, no. 5, pp. 823–838, Sep. 2002. [34] Mathworks May 2010, Matlab [Online]. Available: http://www.mathworks.com/help/toolbox/stats/corr.html [35] D. Montgomery, Design and Analysis of Experiments: 7th International Student Edition. New York: Wiley, 2009. [36] I. Kashiwagi, T. Taga, and T. Imai, “Time-varying path-shadowing model for indoor populated environments,” IEEE Trans. Veh. Technol., vol. 59, no. 1, pp. 16–28, Jan. 2010. [37] E. Telatar, “Capacity of multi-antenna Gaussian channels,” Eur. Trans. Telecommun. vol. 10, no. 6, pp. 585–595, 1999 [Online]. Available: http://dx.doi.org/10.1002/ett.4460100604 [38] H. Ozcelik, M. Herdin, R. Prestros, and E. Bonek, “How MIMO capacity is linked with single element fading statistics,” in Proc. Int. Conf. Electromagn. Adv. Appl., Sep. 2003, pp. 775–778. [39] C. A. Balanis, Antenna Theory: Analysis and Design, 2nd ed. New York: Wiley, 1997. [40] O. Kivekäs, J. Ollikainen, T. Lehtiniemi, and P. Vainikainen, “Effect of the chassis length on the bandwidth, SAR, and efficiency of internal mobile phone antennas,” Microw. Opt. Technol. Lett. vol. 36, no. 6, pp. 457–462, 2003 [Online]. Available: http://dx.doi.org/10.1002/mop. 10789 [41] J. Thaysen and K. B. Jakobsen, “Design considerations for low antenna correlation and mutual coupling reduction in multi antenna terminals,” Eur. Trans. Telecommun. vol. 18, no. 3, pp. 319–326, 2007 [Online]. Available: http://dx.doi.org/10.1002/ett.1111 [42] I. Salonen, C. Icheln, and P. Vainikainen, “Pattern correlation and mismatch in two-element antenna arrays,” Microw. Opt. Technol. Lett. vol. 48, no. 1, pp. 41–43, 2006 [Online]. Available: http://dx.doi.org/10. 1002/mop.21254 Boyan Yanakiev received the B.S. degree in physics from Sofia University, Bulgaria, in 2006, and the M.S. degree in wireless communication from Aalborg University, Denmark, in 2008, where he is currently pursuing the Ph.D. degree. His current position is as an industrial Ph.D. student in cooperation with Molex Antenna Business Unit. His primary interests are in the area of small integrated mobile antennas, optical antenna measurement techniques and radio channel measurements. He has been involved in the design and development of multiple RF-to-optical convertors, for onboard handset measurements.

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Jesper Ødum Nielsen received the M.S. degree in electronics engineering in 1994 and the Ph.D. degree in 1997, both from Aalborg University, Denmark. He is currently employed at Department of Electronic Systems, Aalborg University, where his main areas of interests are experimental investigation of the mobile radio channel and the influence on the channel by mobile device users. He has been involved in channel sounding and modeling, as well as measurements using the live GSM network. In addition he has been working with handset performance evaluation based on spherical measurements of handset radiation patterns and power distribution in the mobile environment.

Morten Christensen was born in 1973. He received the M.Sc. degree in electrical engineering from Aalborg University, Denmark in 1998. In 1998, he joined Bosch Telecom A/S, Pandrup, Denmark (acquired by Siemens Mobile Phones in 2000), where he designed integrated antennas for mobile terminals. In 2006, he joined Motorola A/S, Mobile Devices Aalborg where he was heading the EMC and Antenna department. He is now with Molex Antenna Business Unit responsible for the RF Research activities. His areas of interests includes handset antenna design, performance evaluation methods and radio propagation models.

Gert Frølund Pedersen was born in 1965. He received the B.Sc.E.E. degree (hons), in electrical engineering from College of Technology, Dublin, Ireland, and the M.Sc.E.E. and Ph.D. degrees from Aalborg University, Aalborg, Denmark, in 1993 and 2003. He has been employed by Aalborg University since 1993 where he is now a Full Professor heading the Antenna, Propagation and Networking Group and is also the Head of the Doctoral School on Wireless which has enrolled approximately 100 Ph.D. students. His research has focused on radio communication for mobile terminals especially small antennas, diversity systems, propagation and biological effects and he has published more than 75 peer reviewed papers and holds 20 patents. He has also worked as consultant for developments of more than 100 antennas for mobile terminals including the first internal antenna for mobile phones in 1994 with lowest SAR, first internal triple-band antenna in 1998 with low SAR and high TRP and TIS, and lately various multi antenna systems rated as the most efficient on the market. He has been one of the pioneers in establishing over-the-air measurement systems. The measurement technique is now well established for mobile terminals with single antennas and he was chairing the COST2100 SWG2.2 group with liaison to 3GPP for over-the-air test of MIMO terminals.

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Compensating for Non-Linear Amplifiers in MIMO Communications Systems Seyed Alireza Banani, Student Member, IEEE, and Rodney G. Vaughan, Fellow, IEEE

Abstract—MIMO systems, including those for mobile channels, are well studied as combinations of antennas, other microwave components, and sophisticated digital signal processing. The communications performance is based on many assumptions, including that of linear channels. But in practice, key components such as microwave amplifiers are non-linear. This paper addresses MIMO compensation of non-linear amplifiers at both the transmitter and the receiver. The in-band distortion is modeled using Busgang’s theorem. Based on this model, a decision algorithm obtains an optimized initial estimate of the transmitted symbols which are used for subsequent channel estimation. The final channel matrix estimate is obtained through two alternative methods: statistical linearization; or analytical linearization. The approach is blind in the sense that no pilots are used for sounding the channel. Performance is evaluated by simulation, allowing comparison with the benchmark of coherent detection with perfect channel knowledge. We establish the maximum SNR value for which the nonlinearities are essentially compensated. The performances of the two methods converge as the MIMO system becomes linear. The linear case allows fair comparison with known results of the conventional decision-directed Kalman filtering, and two pilot-aided systems. Finally we compare the performance with a look-up table technique for compensating the non-linearity. Index Terms—Blind channel estimation, MIMO communications, mobile channels, non-linear amplifier, non-linear modeling for MIMO, unscented transformation.

I. INTRODUCTION

T

HE use of multiple antennas at both the transmitter and receiver in wireless communications provides increased spectral efficiency compared to single antenna systems [1]. Nevertheless, there is not a significant commercial presence for fullMIMO systems that use large numbers of elements, which is where the potential increase of spectral efficiency becomes dramatic. One reason for this lack of commercial uptake is that the extra hardware for many-element systems is too expensive for commercial viability. Being able to use low cost amplifiers is particularly important. The performance of MIMO systems has been studied extensively, and simulation is the basic tool for estimating the communications performance. Most studies assume that both the Manuscript received June 13, 2010; revised June 21, 2011; accepted July 02, 2011. Date of publication October 25, 2011; date of current version February 03, 2012. This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. The authors are with the School of Engineering Science, Simon Fraser University Canada (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2011.2173441

transmitter and receiver amplifiers are operated in the linear region and so that the MIMO channel matrix is linear. A microwave amplifier can indeed operate as a quasi-linear device under small signal conditions, and low signal distortion is possible with low power efficiency and higher cost (because they are higher power) amplifiers. It follows that there is a tradeoff between power efficiency and the resulting signal distortion. In communications systems, this tradeoff is governed by the need to limit the out-of-band interference in the radio spectrum. Nonlinear distortion at the transmitter causes interference both inside and outside the signal bandwidth. The in-band component determines a degradation of the communications performance, often expressed as bit-error rate (BER) [2], [3], whereas the out-of-band component affects users in adjacent frequency bands. For more powerful MIMO systems (i.e., those with more antenna elements) to emerge as economically viable, there is a need for highly efficient power amplifiers, especially for battery-powered terminals. In other communications systems, such as satellite, the payload weight, including the on-board high power amplifiers (HPAs) is critical, and the amplifiers must run at high efficiency. In these applications, distortion compensation is also possible using signal processing. At the receiver, the low noise amplifiers (LNAs) are key components because their gain and noise tend to dominate the sensitivity. In fact, the LNA design involves many tradeoffs. These are between noise figure, gain, linearity, impedance matching, power dissipation and cost. With large-dimensioned MIMO systems where the capacity efficiency, with sufficient assumptions, becomes proportional to the number of antennas, a large number of high performance LNAs are required. This can make the cost prohibitive, and lower cost (with greater distortion) LNAs are always a pragmatic solution. However, the impact of their non-linearities will need to be compensated. The cost for the compensation using signal-processing is relatively low in the sense that the digital processors are in place anyway and the extra processing is relatively modest. Nonlinear LNAs and their problems appear in many applications. For example, designers strive to minimize the intermodulation distortion at the receiver by a minimum of nonlinear LNA cascades [4], [5]. Also, to enable consumer products (e.g., GPS, etc.), an integrated receiver should minimize the number of off-chip components, particularly the number of passive filters which are relatively expensive. These considerations motivate research into highly integrated CMOS solutions which typically feature nonlinearity in the LNAs [6], [7]. Another example is satellite diversity (a form of MIMO, using many PAs), used for fading channels in low earth orbit systems [8]. These

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ALIREZA BANANI AND VAUGHAN: COMPENSATING FOR NON-LINEAR AMPLIFIERS IN MIMO COMMUNICATIONS SYSTEMS

issues motivate research into the impact of nonlinear amplifiers in MIMO systems. A related problem in communications is estimating the channel in order to deploy signal processing for reliable communications. The time-varying MIMO channel has to be estimated and this is undertaken either by using pilot symbols or in a blind manner. Many channel estimation techniques for linear MIMO systems have been reported. Examples of pilot-aided systems are [9]–[11]. The cost of using training-based approaches includes: a reduced payload bandwidth because the pilots bite into the communications bandwidth; and the added complexity of the implementation. Also, the training symbols can produce inaccurate channel estimates owing to the limited duration and number of training intervals available for time-varying channels [12]. Blind techniques have become topical in research, because of the unique advantage they offer, viz., the channel is effectively sounded without biting into the communications bandwidth. In blind and semi-blind techniques, the channel estimation is developed based on second or higher-order statistics of the fading process, see, for example, [13]–[32], and other references too numerous to list. However, most blind methods that employ higher order statistics typically require a large number of data symbols, and a shortfall of symbols causes poor convergence which means poor channel estimates and decreased channel efficiency. The convergence problems associated with blind techniques can be avoided by using a semiblind technique [20]–[25], i.e., employing a reduced number of training symbols together with blind statistical information. One semi-blind approach for identification of the main eigenmode, without estimating the channel matrix itself, is presented in [23]. Two whitening-rotation-based algorithms for semi-blind estimation of the flat MIMO channel are presented in [24] and [25]. Such estimation procedures arise naturally in the ICA-based source separation [26]. The use of higher-order statistics based ICA is widespread in multiuser detection, e.g., [27], [28]. The main advantage of ICA techniques is that, under mild mathematical conditions (independence of the sources), signal recovery is guaranteed regardless of the source constellation and spectral characteristics [29]. But this guarantee is for static or slow-changing channels only. Channel estimation/tracking based on Kalman/particle filtering is also well established, e.g., [30], [31]. These are based on the tenet that the recursive least squares (RLS) algorithm and the Kalman filtering algorithm are both better than the LMS algorithm, in convergence rate and tracking capability. Kalman filtering has long been used to extend forms of the recursive least-squares (RLS) algorithm which tracks better than the standard RLS and LMS forms [32]. In this paper, a novel approach for joint blind channel estimation and data recovery for MIMO systems with nonlinearity in both transmitter and receiver amplifiers, is presented. The mobile MIMO channel considered is time-selective and has Rayleigh flat fading, i.e., it is narrowband—which is where the power of MIMO dominates other communications techniques for gaining spectral efficiency. Bussgang’s theorem [33], [34] is used to model the amplifier-induced nonlinearity in the received signal. The model has time-varying coefficients which depend

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on both the data and channel. Using this model, a primary data vector estimate of the transmitted signal is obtained based on the constrained linear minimum mean square error (LMMSE) criterion. Then, the channel matrix is estimated/tracked using two alternative, recursive methods: statistical linearization via unscented transformation; or analytical linearization which results in a nested iterative scheme for updating the channel matrix estimate. Finally, the transmitted data vector is recovered using the channel matrix estimates. This extends the work in [35] where the nonlinearity is introduced only at the receiver amplifier. The main thrust of this paper is to introduce and describe two new blind channel estimation techniques and evaluate the performance of the systems with nonlinear amplifiers at both the transmitter and the receiver. For a nonlinear system, we must use the simulations to compare the results with the benchmark performance of coherent detection with perfect channel state information (CSI) at the receiver. We also compare the results of the two linearization techniques with a look-up table (LUT) approach to the nonlinear problem. The statistical/analytical linearization approaches are marginally better for low SNR (the usual region for wireless) but the LUT is better for high SNR. In addition, for the linear system, the performance comparison is made with the result of the conventional decision-directed Kalman filtering and two pilot-aided systems already known in the signal-processing community. Here, improved performance is observed over the known techniques. The robustness of the proposed blind technique to time variations of the channel is also quantified and compared with that of conventional channel estimation techniques. Finally, the impact of assumptions in the channel modeling is quantified using simulation, offering a feel for the performance with time-correlation coefficient mismatch between the channel model and the assumed model at the receiver. The rest of the paper is organized as follows. Section II describes the system model, and this, and the other sections, are couched in terms of communications signal processing notation for MIMO. The new blind estimation technique is formulated in Section III and the simulation results are presented in Section IV. Section V concludes the paper. The notation is conventional, as follows. Symbols for matrices (in capital letters) and vectors are in boldface. The notations and stand for conjugate transpose, transpose, and complex conjugate, respectively. is the identity matrix and denotes expectation. Also, in order to distinguish the amplifiers at the transmitter and the receiver, the sub-(super-) script “T” refers to the amplifiers at the transmitter side and the sub-(super-) script “R” refers to the amplifiers at the receiver. II. NONLINEAR MIMO SYSTEM MODEL The baseband equivalent representation of a non-linear MIMO system with transmit and receive antennas employing a spatial multiplexing scheme is displayed in Fig. 1. At the transmitter, data is picked up from a constellation set with set size and the uncoded data stream is demultiplexed to branches at each symbol time with symbol time duration . Then data symbols are passed through transmit amplifiers (each with nonlinear function ) before launching from transmit

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Fig. 1. Baseband representative of nonlinear MIMO system.

antennas. Assuming a Rayleigh flat fading MIMO channel, the received signal from the th antenna is modeled as

Gaussianity of the inputs of the receive amplifiers is guaranteed. (We note, therefore, that the formulation presented here is not applicable to 16-QAM, etc.) Under such a condition, and the receive amplifier output can be represented by [33] (3)

(1) where

and is the nonlinear function introduced by the receiver amplifier. The vector is the transmit signal vector with i.i.d. data symbol entries each with variance , and is the zero mean additive white Gaussian noise with variance . (In practice, for a terrestrial system, this noise is dominated by interference from other users, and other systems, i.e., the interference is assumed here to be Gaussian.) is the th row of channel matrix , comprising i.i.d. complex Gaussian entries, , each with variance 1; index is the time index showing that at each iteration (symbol time) the channel matrix is changing. For both amplifiers’ nonlinearity ( and ), we consider the general memoryless AM/AM and AM/PM characteristics [36], [37]. In particular, denoting a transmitter/receiver amplifier complex input as , the signal at the output of a nonlinear block becomes

is an arbitrary deterministic complex coefficient (exwhere pressed as a function, below), and is suitably introduced additive noise term. It is desirable to have zero-mean noise, uncorrelated to the input process . This can be achieved by setting as [3] (4) Denoting in (4) are formulated as

, the derivatives appearing

(5) (2) where and are the real functions for AM-to-AM and AM-to-PM conversions respectively. The super-script T/R in and means that (2) is written in the general format and holds for any amplifier at the transmitter or receiver with AM/AM and AM/PM characteristics. Based on Bussgang’s theorem [33], [34], the output of a nonlinear memoryless amplifier excited by a Gaussian distributed signal can be represented by the scaled version of the original signal plus an additive noise term. Here, we make use of Bussgang’s theorem to approximate the nonlinearity introduced at the receiver side, i.e., , with a linearized model having time-varying coefficients. By using the constant amplitude signaling with , e.g., -PSK, however, the

and as a result, we obtain (6) Also, the variance of the noise term in (3) can be obtained as

(7) Applying Bussgang’s theorem to (1), we get

(8)

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statistics, i.e., the correlation function values, relative to the a priori information assumed by the receiver. On reception of the th data symbol, the receiver first employs a new decision algorithm to obtain a primary data vector estimate of the transmitted signal. The detail is described below.

where we have substituted with its instantaneous value

A. Decision Algorithm (9) since calculating the expectation in (6) may be difficult. In order to recover the transmitted data vector from , the channel matrix has to be estimated. The idea is to estimate the channel matrix in a blind manner at each symbol time without making use of pilot symbols or training sequences. III. BLIND CHANNEL ESTIMATION Many authors have tried to approximate the time variation of the fading channel by different dynamic models depending on the application. However, the results in [38] have shown that the first-order autoregressive model provides a sufficiently accurate model for time-selective fading channels. Therefore, the relation between and can be approximated by (10) is the value of the channel coefficients’ autowhere correlation function, , evaluated at and is a matrix with zero-mean, independent, white Gaussian noise entries each with variance 1. When the fading statistics are unknown, can be usually estimated from the data in a training-assisted mode or decision-directed mode [39]. However, we are not trying to estimate this statistic here, and for simulation, it is taken as where is the zeroorder Bessel function of the first kind and is the maximum Doppler frequency. This form encompasses a commonly used, but major, assumption—a 2D-omnidirectional incident uncorrelated power distribution and 2D-omnidirectional antennas. The exact form of the correlation function is not important here in the sense that the algorithm below uses only one sample value of it. In practice, if this correlation sample value changes with time, it will do so slowly, and this allows time to track its estimate for its application in this algorithm. A sensitivity analysis (shown below) indicates that the proposed blind technique is robust for a moderate mismatch of the channel’s second-order

Having the unbiased MMSE estimate of the channel matrix coefficients, , and the corresponding error variances associated with the estimation process, , obtained from the previous symbol interval (this is a standard type of assumption in deriving iterative algorithms), the channel matrix estimation process at the th symbol time can be expressed by (11) and is a matrix with where zero-mean independent white Gaussian noise entries having the corresponding variances , and also (12), shown at the bottom of the page. Moreover, the optimal channel coefficients’ linear predictions, given that the channel follows the AR(1) model of (10), but ignoring the addition of received data measurements , are (13) with the corresponding prediction error variances (14) From (10)(13) and the set of (8) in matrix form, the received is approximated as vector

(15) where

(16)

(12) .. .

.. .

..

.

.. .

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in which

(17)

(23)

(18)

substituted by its instantaneous value since calculating the expectation in (7) is difficult. It is worth noting is a function of which, in turn, depends on that . Consideration of these in the above equations makes the new decision algorithm . yield a more accurate primary symbol data vector estimate

In calculating

In the

the noise

above

expressions, the notation is used to emphasize that vector and matrix depend on , and . The equation of (15) can be

re-written as

, the noise variance

is

B. Channel Estimation

(19) . In the arrangement of (19), the key idea where of introducing is to treat it as an unknown deterministic variable and we try to estimate it. The receiver searches over the -dimensional transmit data vector constellation set to see which candidate of yields the MMSE estimate of according to the observations constrained by . The primary data vector estimate is

at hand, the Having the primary data vector estimate channel matrix estimate can now be refined in the form of two, alternative methods: using statistical linearization via unscented transformation; or using analytical linearization which results in a locally (nested) iterative scheme for updating the channel matrix estimate. Both of these methods are presented below. 1) Statistical Linearization: Here, the knowledge gained from observing the measurements are used to refine the predicted channel vector . At first, the new set of observations is generated as

(20) (24) where

is the unbiased LMMSE of obtained by (21)

with

(22) is the noise covariance matrix and calculated at . According to (12) and since the elements in are independent, matrix is a diagonal matrix with th diagonal element as

The Unscented Transformation (UT) [40], [41] is to handle the nonlinearities in (24). However, the standard UT is characterized with real-valued random variables. As a result, to fit the UT principles to our problem involved with complex random variables, a summary of UT is described below. Consider propagating a -dimensional real-valued random vector with mean and covariance , through an arbitrary nonlinear function , to produce a random variable . A set of points, called sigma points, are generated by the following algorithm whose sample mean and sample covariance are and , respectively:

(25) where , and root of

is a scaling parameter such that is the th column of the matrix square , and is the weight that is associated with

ALIREZA BANANI AND VAUGHAN: COMPENSATING FOR NON-LINEAR AMPLIFIERS IN MIMO COMMUNICATIONS SYSTEMS

the th point. The weights are normalized; that is, they satisfy . The set of samples chosen by (25) are guaranteed to have the same sample mean, covariance, and all higher, odd-ordered central moments, as the distribution of the random vector . The matrix square root and affect the fourth and higher order sample moments of the sigma points [41]. Now each sigma point is propagated through the nonlinear function ,

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sigma points are passed through the nonlinear function to yield the prediction measurement (34) with variance

(26) and the first two moments of

are computed as follows (35)

(27) (28) To fit the UT principle to our problem, we stack all the real and imaginary parts of into vector as (29), shown at the bottom of the page. Considering the above arrangement along with (13)–(14), would be a random vector with mean and diagonal covariance matrix as (30) and (31), shown at the bottom of the page. With the assumption of wide sense stationary uncorrelated scattering (WSSUS), and are uncorrelated random variables with nearly equal variances. (Asymptotically they are equal). As a result, for a complex channel coefficient, , we get

The problem of refining the channel vector estimate , is finalized with a new estimation problem as follows. We wish to linearly estimate the random vector as in (29) with mean and covariance matrix measurement square sense ( mator is [42]

, from in the minimum mean is the innovation term). The LMMSE esti-

(36) where

(32) in (31) by (33), shown at the Thus, we approximate bottom of the page. Now, in (24) is taken as the nonlinear function with the corresponding output, and sigma points, are generated according to (25). These

The associated estimation error covariance matrix is (37)

(29)

(30) (31)

(33)

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Finally, obtained as

which is the

th element of vector

is

with

and (43)

(38) with approximated estimation variance

and the associated measurement noise variance. The strategy of finding a minimum is to use Newton-Raphson iteration starting from . At the beginning of the th iteration step, we have already an estimate obtained from previous step. Now the set of equations (8) is better approximated by

Note that each of the channel vectors is obtained individually from the algorithm described above. 2) Analytical Linearization: Here, the set of equations (8) are rewritten as

(44) with noise variance

(39) is the value of

where

evaluated at (45)

. For brevity, let

and denote the set of all sampled received signal from th antenna up to th symbol time. Using Bayes’ theorem on the conditional density for memoryless sensor systems yields

(40) with

a normalization constant

At this point, we expand Taylor series approximation:

around

to a second order

(46) where and denote the Gradient and Hessian matrix of with respect to complex vector , respectively. The estimate is the minimum of the approximation of (46). It is found by equating the gradient of the approximation to zero. Differentiation of (46) with respect to complex vector gives (47)

(41) The approximation is made such that both the predicted channel matrix elements in (13) and the noise term in (39) are considered normally distributed. Thus, the posterior probability density , which is the product of two Gaussians, is also a Gaussian. Therefore, the MMSE estimate coincides with the MAP estimate and the task is now to find the maximum of . Equivalently, we can maximize its logarithm. After the elimination of the irrelevant constants and factors, it boils down to minimization the following function

(42)

which results in (48) The Gradient and Hessian of tained from (42) as

, in explicit form, are ob-

(49)

ALIREZA BANANI AND VAUGHAN: COMPENSATING FOR NON-LINEAR AMPLIFIERS IN MIMO COMMUNICATIONS SYSTEMS

(50) Substitution of (49)–(50) into (48) yields the following iteration scheme:

(51) converges very fast and it is possible to fix We note that, the number of iterations to some small number , e.g., . (The effect of on system error performance is analyzed through simulation below). The final result is set to the last iteration, i.e., . The factor in (51) can be regarded as the error covariance matrix associated with , i.e.,

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timate, and the corresponding variances associated with the estimation processes, , also help the decision algorithm in the subsequent th symbol interval to obtain the subsequent primary data vector estimate . We note that for initialization, it is sufficient for the proposed algorithm to use any of the training approaches developed in [43] only once at the beginning of whole data sequence transmission. To obtain a meaningful estimate of at the beginning, we need at least as many training measurements as unknowns, which implies that at the first th iteration, any kind of training-based scheme, e.g., LS or MMSE pilot-aided channel estimation, is used for an initial estimate of the channel, . From the th iteration, the algorithm switches to the presented iterative algorithm and uses the channel estimate that is at hand. This means that the algorithm switches to the blind approach (in the sense that no further pilots are required) after at least the th iteration. The initial channel estimates obtained this way are accurate enough for the algorithm to have fast convergence for the typical application of systems with fade rates of 0.005. IV. SIMULATION RESULTS

(52) This insight gives another connection to the last term in (51) because, in comparison with the standard Kalman filter recurcan be regarded sion formulas, the term as the Kalman gain matrix during the th iteration. has Note that each of the channel vectors to be obtained individually from the locally iterative algorithm described above. C. Data Vector Recovery Here, the receiver recovers the transmitted data vector using the channel matrix estimate and the primary data vector estimate . The minimum distance receiver [44] chooses the vector that solves (53) denotes the Frobenius norm and the equation where shown at the bottom of the page. In (53) the search is performed over all the candidate vector symbols, , and the decoding complexity of the receiver is exponential in . Note that in fact, (53) is the optimum ML decoder when the MIMO system is linear. Finally, the estimated symbols are fed to the hard decision block to yield the detected transmitted symbols by setting the optimal thresholds in the constellation regions of the transmitted signal. The channel matrix es-

The optimal receiver performance sets a lower bound on the error rate probability of sub-optimal receivers. However, no exact optimal analytical solution is available for error probability, even for linear MIMO systems. (For linear systems several upper bounds on error probability for the ML as well as other sub-optimal receivers have been derived.) Thus, we simulate the SER performance results of coherent detection with perfect CSI as benchmark, and evaluate and compare the results of the presented blind system with the associated perfect CSI reference ones. We take i.i.d. QPSK data symbols with zero mean and variance 1, and for convenience of interpretation, the data symbol duration is ms (i.e., 10 k symbols/sec) and the channel fade rate is . Also, throughout the simulations, the signal-to-noise ratio is dB

(54)

It is worth noting that the proposed algorithm is formulated in a general form and it can be applied to any linear and nonlinear MIMO systems with nonlinearities introduced by and in (1). The last sub-section below, IV.B, is dedicated to linear MIMO systems since with this choice, more direct assessment of the proposed blind channel estimation technique on system error performance is possible. Also, this allows fair performance comparison with known results of the conventional decision-directed Kalman filtering [30] and two pilot-aided systems (least-squares (LS), and an MMSE pilot-aided system [11]).

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of solid state power amplifier (SSPA) nonlinearity which is defined as [36], [37]

(55)

Fig. 2. SER performance of a 2 2 nonlinear MIMO system with different nonlinearity configurations for transmit and receive amplifiers, when the statistical linearization technique is used, and with fade rate 0.001.

where defines the smoothness of the transition from linear operation to saturation, and is the saturation output amplitude where for simulation it is set as . is a standard parameter which the designer must assign to the SSPA amplifier. This may require a calibration measurement. Designers would be able to decrease the cost of the amplifiers if a larger non-linearity could be tolerated. For large values of , the SSPA model approaches the soft limiter model that is commonly used to represent the clipping operation [45] to reduce the dynamic range of the OFDM signal. The soft limiter model is specified as

(56)

Fig. 3. The effect of nonlinear parameter (representing the nonlinearity at . the transmitter) on the system SER performance with fixed

Here, the value of is assumed to be known, i.e., we are not including estimation of these statistics as part of the algorithm. Including this estimate is a relatively straightforward extension, but the goal here is to quantify the behavior of the blind estimation with known channel statistics. The impact of any mismatch in the time-correlation coefficient mismatch (perhaps caused by an incorrect estimate of , or simply because the model is incorrect) on the proposed system’s error performance is analyzed by simulation below. We show that the proposed blind technique is robust for a mild mismatch of the channel’s second-order statistics, i.e., the correlation function values which relate to , relative to the a priori information assumed by the receiver. However, a large degradation in performance is demonstrated as the mismatch increases, as expected, and this is demonstrated below. A. Nonlinear MIMO Systems Despite nonlinearities being usually small, they are known to be very difficult to deal with [44]. Here, for both transmit and receive amplifiers, we provide some examples from the family

We note that the model used in (55) is just an example of amplifier nonlinearity provided here for simulation purposes. Any kind of memoryless AM/AM and AM/PM characteristics can be used instead. Furthermore, throughout the simulations, and are used as the corresponding transmit and receive amplifier smoothness parameter, respectively. Fig. 2 illustrates the SER performance of a 2 2 nonlinear MIMO system with different nonlinearity configurations for transmit and receive amplifiers when the statistical linearization technique is used. In general, as either of the parameters or increases, less degradation in performance is observed since the nonlinearity becomes smoother. A useful result is that, for a given receiver nonlinearity represented by parameter, the ensuing system performance curves are essentially shifted versions of the curves obtained with the ideal linear transmit amplifier . This is seen in Fig. 3 where the effect of nonlinear parameter (representing the nonlinearity at the transmitter) on the system SER performance with fixed is illustrated. As an example, there is a shift of 1.1 dB in SNR, except near the error floor region. As a result, in order to assess the impact of the receiver nonlinearity (represented by ) on system error performance more directly, in the rest of the simulations, we evaluate the SER performance of nonlinear MIMO systems with ideal linear amplifiers at the transmitter by setting . Here we can also benchmark the two statistical/analytical linearization techniques with a look-up table (LUT) approach to the nonlinear problem. 1) Statistical/Analytical Linearization Approaches: : The impact of nonlinearity parameter on the SER performance of a 2 2 nonlinear MIMO system using the statistical linearization technique is shown in Fig. 4. Comparison is also made with the linear system error curve which corresponds to large values of (soft limiter model). The nonlinearity is nearly compensated for values of dB for

ALIREZA BANANI AND VAUGHAN: COMPENSATING FOR NON-LINEAR AMPLIFIERS IN MIMO COMMUNICATIONS SYSTEMS

Fig. 4. Impact of nonlinearity parameter on SER performance of a 2 2 nonlinear MIMO system employing the statistical linearization technique while .

. The performance curves with analytical linearization also follow the same trend as the curves with statistical linearization. The SNR value of 13 dB would change with different fading rates. At large values of SNR, the difference between the curves of the statistical/analytical linearization approaches and that for a linear system increases with SNR. The performance degradation associated with the statistical/analytical approaches can be explained via (8): it is found via simulations (not shown here) that the noise variance (7) increases with SNR. As a result, the Bussgangs’ approximation in (8) becomes less accurate for larger values of SNR. In turn, this causes inaccuracies in the decision algorithm which is built up from (8). Fig. 5 shows the SER performance of a nonlinear SISO and a 2 2 nonlinear MIMO system with the nonlinearity parameter and perfect CSI at the receiver. The corresponding curves of the presented blind system employing statistical and analytical linearization techniques are also illustrated. The analytical linearization technique finishes the locally iterative (nested) scheme in steps. The effect of on system performance is studied below. The degradation in performance of a 2 2 nonlinear system is more than that in the nonlinear SISO system. This trend is expected since more nonlinear amplifiers contribute more nonlinearity as the number of receive antennas increases. Fig. 5 reveals the details. Finally, the impact of the analytical linearization parameter on SER performance is shown in Fig. 6. Typically, the performance gets better as the total number of iterations in the proposed local iterative scheme increases from 1 to 3. For , the local iterative scheme nearly converges to a steady state which is the locally optimum value, and as a result no further improvement in performance is observed. So far, we assumed that the normalized time-correlation function of the channel coefficients is known beforehand. In the channel estimation process we make use of one value of the channel normalized correlation coefficient function, i.e., . However, a real-world, local autocorrelation is seldom exactly (or some other model),

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Fig. 5. SER performance of a nonlinear SISO and a 2 2 nonlinear MIMO and . Dashed and system with the nonlinearity parameter solid lines correspond to coherent detection with perfect CSI, and the proposed . blind systems, respectively. The analytical linearization parameter is

Fig. 6. Impact of the analytical linearization parameter . of a 2 2 nonlinear MIMO system, for

on SER performance

Fig. 7. Effect of mismatch parameter (57) on the relative SER performance of system employing the presented blind channel estimation with statistical lindB. earization at

even in the main lobe region, and almost never (or another model) away from the main lobe. Furthermore, estimating a

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Fig. 8. Receiver nonlinearity compensation by means of LUT, here for the th antenna branch and . The outputs of all branches, to the multiple antenna decoder block for channel estimation and data recovery, designed for linear MIMO systems.

, are fed

correlation coefficient from finite samples introduces uncertainty depending on the number of samples used. In order to get a reliable estimate where the function becomes small, a very large number of samples is required [46]. In order to test the performance sensitivity to the secondorder statistics, we define a simple percentage correlation function sample mismatch as

(57) where the normalized time-correlation function used at the re. ceiver takes on different values from Fig. 7 illustrates the effect of the mismatch parameter on SER performance, given as the relative SER change, , at dB using the statistical linearization. The system remains moderately insensitive to the mismatch of (57)—up to 20% for fate rate 0.005, but for higher mismatch, there will be a larger degradation in the SER performance. Also, there is more sensitivity to the mismatch for higher fade rates. The reason is that, for a given mismatch, the higher fade rate results in the addition of an error term to (19) which in turn causes more signal estimation inaccuracies in the decision algorithm. Thus, for the typical applications with fade rates 0.005, the proposed blind technique is robust to mild mismatches of the channel’s second-order statistics. The figure helps to quantify the sensitivity of the proposed receiver to the modeling of the temporal second order statistics of the channel. 2) Look-Up Table Approach Followed by Linear Blind Channel Estimation: : We may also attempt to directly compensate the nonlinearity at the receiver before proceeding to channel estimation and data recovery by means of an LUT approach. First, by processing as shown are in Fig. 8, the estimation values of obtained. The estimation process at this step, can be modeled as (58) is a vector with i.i.d. complex Gaussian entries each where with variance 1 and is the associated estimation error variance reflecting the inaccuracies in estimating . Next, these estimates are fed to the multiple antenna decoder block, designed for linear MIMO systems where blind channel

Fig. 9. SER performance curves of a 2 2 system with nonlinearity compenand . The effect of gridding size on sation using LUT, for the error performance is also illustrated and comparison is made with the presented statistical/analytical linearization approaches of Section III.

estimation and data recovery is carried out. From the SNR point of view, we have (59) Equation (59) states that the proposed blind channel estimation/data recovery designed for the linear system is going to operate on the signal (i.e., ) that has the reduced SNR value of in comparison to . Simulations show that depends mainly on the gridding size (quantization for LUT) and does not change with SNR. As a result, for a fixed gridding size, the curves of LUT-based system are essentially shifted versions of the curve for a linear system. We note that the inversion operation shown in Fig. 8 is performed by means of LUT. The SER performance curves of system based on LUT compensation are shown in Fig. 9 for the nonlinearity parameters . The effect of different values of gridding sizes (quantization for the LUT) is also illustrated. Here, the input signal full scale amplitude is taken as 0 to 4, so a grid size of 0.005 means there are 800 LUT entries. The curves are essentially shifted versions of the curve for a linear system which confirm (59). However, as the gridding size increases (less LUT entries), a larger shift is observed. The comparison can also be made with the SER results of the techniques proposed in Section III using statistical/analytical linearization and Bussgang’s theorem. The proposed statistical/analytical linearization approaches outperform the

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ALIREZA BANANI AND VAUGHAN: COMPENSATING FOR NON-LINEAR AMPLIFIERS IN MIMO COMMUNICATIONS SYSTEMS

Fig. 10. Comparison of SER performance of the presented algorithm with that of LUT-based approach in a 2 2 system with nonlinear transmit and receive and various values of ). amplifiers (

system based on LUT for SNR values smaller than about 13.5 dB. Since the error performance of statistical/analytical linearization approaches coincide with the curves of linear system for low values of SNR (where the nonlinearity is completely compensated), it is concluded that the main reason that the performance of LUT-based approach falls behind the statistical/analytical approaches, is the gridding size. In particular, for very small values of gridding sizes, , the resultant LUT-based curve coincides with the corresponding curve for the linear system (refer to (59)) and the LUT-based approach and the statistical/analytical approaches yield the same performance for small values of SNR ( dB for the example provided). On the other hand, at large values of SNR, the difference between the curves of the statistical/analytical approaches, and that for a linear system, increases with SNR while the LUT-based curves experience a constant degradation in all SNRs. As a result, for large values of SNR the LUT-based approach outperforms the presented statistical/analytical linearization approaches. Comparison is also made between the performance of the presented algorithm and that of LUT-based approach in a 2 2 system with nonlinear amplifiers at both transmitter and receiver (both and are small). The results are illustrated in Fig. 10 for and various values of the transmit nonlinearity parameter, . The LUT has a grid size of 0.005. For small values of , the presented algorithm outperforms the LUT-based approach in SER performance for all values of SNR. In particular, the difference between SER performances becomes larger as decreases. This is simply because the presented LUT-based approach is not designed to compensate the transmit nonlinearity. The result in Fig. 10 lays out that the presented algorithm is more effective than the LUT-based approach in MIMO systems with nonlinearities at both transmit and receiver amplifiers. We note that all presented techniques require knowledge of the nonlinearity characteristics, and . However, the systems based on LUT require the extra memory of the table. The size of the extra memory increases, as the gridding size decreases.

Fig. 11. SER performance of a linear 2 2 MIMO system employing ML, MMSE, ZF, and MMSE-OSUC receivers. Dashed and solid lines correspond to coherent detection with perfect CSI and proposed blind system, respectively; .

In order to assess the impact of the proposed blind channel estimation technique on system error performance more directly, the next section considers linear MIMO systems. This also allows fair performance comparison with a known blind system employing Kalman filtering to track the channel [30] and two pilot-aided systems (least-squares (LS), and an MMSE pilotaided system [11]). B. Linear MIMO System: For the linear MIMO systems ( signal model (1) simplifies to

, and

), the

(60) The proposed blind channel estimation can be joined with any decoding structure (e.g., ML, MMSE, ZF and MMSE-OSUC) at the receiver. Each decoding structure provides a specific order of diversity. The zero forcing (ZF) receiver provides order diversity [47] (the same as MMSE and successive cancellation (SUC) receivers but with different SNR loss). As an alternative, one may take advantage of an ordered successive cancellation (OSUC) receiver [48] which may have more than order diversity because of the ordering (selection) process [47], or use the optimal ML receiver which extracts order diversity with the expense of high decoding complexity (exponential in ). For different decoding structures, we compare the SER performance of the system employing the proposed blind channel estimation with the associated coherent detection curve with perfect CSI. The results are illustrated in Fig. 11 for a 2 2 system. Each pair of curves bearing the same color (also labeled) corresponds to a specific decoding structure (the “dotted line” is associated with the “coherent detection with perfect CSI” and the “solid line with marker” is the performance when the effect of blind channel estimation is added to that system). The statistical and analytical linearization techniques yield the same performance in this case since no nonlinearity exists. With each receiver type (decoding structure), the presented

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Fig. 12. Comparison of SER performances of linear 2 2 MMSE-OSUC receivers employing different channel estimation techniques using SM-HE, . QPSK signaling and fade rate

system exploits the same diversity order as the coherent detection with perfect CSI but experiences an SNR loss. However, the SNR loss depends on the system parameters and the type of decoding structure. In particular, it is within 3 dB (specifically, 2.5 dB) of the perfect CSI curves in an ML (in MMSE-OSUC) receiver at fade rate and SER of . We may also compare the results of a system employing the presented blind channel estimation with that of a system using other channel estimation techniques for a given decoding structure. Here, a fair comparison is possible with a known blind channel estimation based on Kalman filtering (conventional decision-directed Kalman filtering [30]), and two known pilotaided channel estimations: Least Squares (LS) and an MMSE pilot-aided system [11]. The results are shown in Fig. 12 using the MMSE-OSUC receiver. The presented system outperforms both pilot-aided channel estimation techniques but with just a slight improvement in performance over the decision-directed Kalman-based estimation at moderate-high values of SNR. Recall that the technique of [30] is a decision-directed algorithm which uses channel predictions to obtain the coarse symbol estimate for formulating the measurement equations in the Kalman filtering. However, obtaining the coarse symbol estimate is undertaken without considering the associated channel estimation error variances, , whereas these have been taken into consideration in the proposed decision algorithm ((15)–(22)). Compared to pilot-aided systems, the proposed blind system has superior performance for all SNRs, at least for the fade rate used here. This is expected, because in pilot-aided systems, the channel is estimated only after at least consecutive symbols, whereas in the presented blind technique, the channel is estimated at each symbol time which results in more accurate channel estimates in the time-varying environment. The robustness of the proposed blind system to the time-variations of the channel can also be quantified by simulation and compared with that of other conventional channel estimation techniques. The MMSE-OSUC decoding structure is used for all the systems. The effect of fade rate (maximum Doppler shift) on error performance is shown in Fig. 13 for

Fig. 13. Effect of maximum Doppler shift on blind/pilot-aided system error dB. performance employing MMSE-OSUC receiver at

Hz at dB. For the proposed blind system, there is a maximum performance degradation of 15% in the SER (compared to 60% in pilot-aided systems) for a fading rate 0.01 or 100 Hz, relative to the case of block fading in a quasi-static channel (the Kalman-based estimation has the same trend as with the proposed blind channel estimation). The pilot-aided systems are more sensitive to time-variations of the channel. However, in general, the system performances depend on many factors such as channel fade rate, SNR and pilot scheme used. For example, the LS pilot-aided system is always worse than the MMSE pilot-aided system on this measure, and at very low fade rates (static fading), all the algorithms (two-pilot aided systems, the Kalman-based estimation, and the proposed blind channel estimation technique) yield nearly the same performance at all values of SNR. However, as the fade rate increases, the deference between the SER curves increases. It is worth noting that techniques that are based on the three conventional channel estimators under comparison (the two LS/MMSE pilot-aided channel estimator and decision-directed Kalman filtering) and/or detectors such as ZF, MMSE and OSUC, become ineffective in nonlinear MIMO systems. This is because these channel estimators and detectors are designed based on the linearity in a system. As an example, it is well known that the Kalman filter is the optimum linear state estimator when the set of state and observation equations are linear [42], [30]. The performance of a Kalman filter degrades significantly even when a mild nonlinearity exists in the system. More severely, in most nonlinear cases the Kalman filter does not converge at all if an inappropriate initial state value is set within the algorithm [42]. As a result, a blind Kalman-based channel estimator is not capable of tracking the time-variation in the channel when the system in nonlinear, and the system remains running without appropriate channel estimates, and the receiver fails to detect the transmitted symbols correctly. This is not the case with the presented algorithm. As shown earlier, the presented algorithm is also effective for nonlinear MIMO systems. As a result, this can be considered as one of the advantages of the presented algorithm over the other conventional techniques (including detection and channel estimation) designed exclusively for linear systems.

ALIREZA BANANI AND VAUGHAN: COMPENSATING FOR NON-LINEAR AMPLIFIERS IN MIMO COMMUNICATIONS SYSTEMS

V. SUMMARY AND CONCLUSIONS The amplifiers in a practical MIMO system can be performance-limiting. Amplifier non-linearity is modeled here with a memoryless, AM/PM amplifier characterization. The theory and signal-processing is presented for compensating the link degradation caused by the non-linearity. This includes a new blind approach in the form of two alternative channel estimation/tracking methods (statistical and analytical linearization) for nonlinear MIMO systems. The MIMO performance is estimated by simulation. For a fixed nonlinearity in each receiver amplifier, the resultant system error curves are essentially shifted versions of the curves obtained with ideal linear transmit amplifiers. Furthermore, for the examples provided, the proposed approach is capable of nearly compensating the nonlinearity induced at the receiver side for values of SNR less than about 13 dB. That is, in this range of SNR, the error curves coincide with those of the linear MIMO system when the amplifiers are linear. The two channel estimation methods, statistical linearization and analytical linearization, have similar performance, being within a fraction of a dB in SNR. They both follow the same trend as coherent systems with perfect CSI for small- to midsized SNR, and develop an error floor for large SNR. The look-up table (LUT) approach also offers good performance, being more effective than the presented algorithm in compensating the receiver nonlinearity at high SNR when the transmit amplifier is linear. This is at the expense of extra memory. For smaller values of the SNR which are typical of wireless at extended ranges, the performance is similar, with the linearization outperforming the LUT approach by about a half dB. However, with nonlinearities at both transmit and receiver amplifiers, the presented algorithm is more effective than the LUT-based approach in MIMO systems at all values of SNR. As the MIMO system becomes linear, typically possible by using expensive amplifiers, the performances of the statistical and analytical linearization approaches converge. The blind schemes presented here compare favorably against known blind schemes such as conventional decision-directed Kalman filtering, and two established, pilot-aided systems. The proposed blind channel estimation is also more robust to the time-variations of the channel compared to LS/MMSE pilot-aided systems. The comparison of simulation results with benchmark and other known results puts a focus on the importance of checking the channel modeling. We show that the proposed blind technique is robust for a moderate mismatch of the channel’s second-order statistics, i.e., the correlation function values, relative to the a priori information assumed by the receiver. However, a large degradation in performance is demonstrated as the mismatch increases, as expected. REFERENCES [1] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Personal Commun., vol. 6, no. 3, pp. 311–335, Mar. 1998. [2] R. O’Neil and L. B. Lopes, “Performance of amplitude limited multitone signals,” in Proc. IEEE Veh. Technol. Conf., Jun. 1994, pp. 1675–1679.

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Seyed Alireza Banani (S’07) received the B.Sc. and M.Sc. degrees in electrical communication engineering from Shiraz University, Shiraz, Iran, in 2004 and 2007, respectively. He is currently working toward the Ph.D. degree with the School of Engineering Science, Simon Fraser University, Burnaby, BC, Canada. His research interests include target tracking, independent components analysis, nonlinear state estimation, blind channel estimation, multiple-input-multiple-output (MIMO) capacity, and signal processing for MIMO wireless communications systems. Mr. Alireza Banani has been a recipient of a Canada graduate scholarship from the Natural Science and Engineering Research Council of Canada since 2009.

Rodney G. Vaughan (M’84–SM’89–F’07) received the B.E. and M.E. degrees in electrical engineering from the University of Canterbury, New Zealand, and the Ph.D. degree from Aalborg University, Denmark. He was with the New Zealand Post Office (now Telecom NZ), the New Zealand Department of Scientific and Industrial Research, and Industrial Research Limited (IRL). During this time, he undertook mechanical and electrical projects from heating and ventilation designs to network analysis and traffic forecasting, as well as microprocessor applications from abattoir automation to communications networks. In 1992, when he was with IRL, he developed research programs and personnel in communications technology. Here, his industrial projects included antennas for personal, cellular, and satellite communications; sonar array processing; large-N multiple-input multiple-output (MIMO) communications systems design and capacity theory; and statistical field theory. Since 2003, he has been a Professor of electrical engineering and the Sierra Wireless Chair in Communications with the School of Engineering Science, Simon Fraser University, Burnaby, BC, Canada. His recent projects include mobile communications; bio-implantable antennas; wideband elements, compact multielement antenna design and evaluation; optimal circular polarization purity antennas, multifaceted arrays; MIMO capacity realization, blind techniques and interference mitigation for orthogonal frequency division multiplexing; channel modeling and estimation; and on body propagation analysis. Prof. Vaughan was an International Union of Radio Science (URSI) Young Scientist in Fields and Waves and in Electromagnetic Theory and a 2003 Fellow of the BC Advanced System Institute. He is an URSI Correspondent and continues as New Zealand’s URSI Commission B Representative.

Digital Object Identifier 10.1109/TAP.2012.2186031

Digital Object Identifier 10.1109/TAP.2012.2186033

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION Editorial Board Brenn Ellsworth, Editorial Assistant Michael A. Jensen, Editor-in-Chief e-mail: [email protected] Department of Electrical and Computer Engineering (801) 422-3903 (voice) 459 Clyde Building Brigham Young University Provo, UT 84602 e-mail: [email protected] (801) 422-5736 (voice) Senior Associate Editor Karl F. Warnick Dimitris Anagnostou Hiroyuki Arai Ozlem Aydin Civi Zhi Ning Chen Jorge R. Costa George Eleftheriades Magda El-Shenawee Lal C. Godara Yang Hao

Associate Editors Derek McNamara Stuart G. Hay Andrea Neto Sean V. Hum Claude Oestges Ramakrishna Janaswamy George W. Pan Buon Kiong Lau Athanasios Panagopoulos Jin-Fa Lee Patrik Persson Kwok Wa Leung K.V. S. Rao Duixian Liu Shanker Balasubramaniam Andrea Massa

Satish Sharma Jamesina Simpson Mei Song Tong Jon W. Wallace Fan Yang Ali Yilmaz Zhengqing Yun Zhijun Zhang Yue Ping Zhang

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For additional information about the electronic submission process and creating files for electronic submission, visit the AP TRANSACTIONS website at: http://ieeeaps.org/aps_trans/ COPYRIGHT: It is the policy of the IEEE to own the copyright to the technical contributions it publishes on behalf of the interests of the IEEE, its authors, and their employers, and to facilitate the appropriate reuse of this material by others. To comply with the U.S. Copyright Law, authors are required to sign and submit an IEEE Copyright Form before publication. This form returns to authors and their employers the full rights to reuse their material for their own purposes. Authors must submit a signed copy of this form before their manuscript can be published. The copyright form can now be completed electronically in Manuscript Central, and downloaded from the AP TRANSACTIONS website as a PDF file. 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If the author will not agree to pay mandatory charges, the author will be required to reduce the manuscript to eight printed pages or less (four printed pages for Communications) prior to final acceptance and scheduling for publication. This reduction will occur after technical review of the manuscript. The above policy has no relationship to requests by the Editor to reduce very long manuscripts prior to technical review. PAPERS may be any length from one to about 25 typewritten double-spaced pages and are subjected to review by the Editor, Associate Editors, and their staff of reviewers. Each paper must have an abstract of about 150 words. Authors should allow approximately 12 weeks for the initial review cycle. Authors are encouraged to make their initial submission as short as possible. 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As a result, the review of past work is expected to be limited to the key material. The manuscript length is normally up to four journal pages (two-column template) and should not exceed six journal pages. Page charges apply after four pages. COMMUNICATIONS are subjected to the same rigorous review as used for PAPERS. COMMENTS are brief notes containing remarks (and Authors’ replies) as well as corrections on previously published manuscripts. Usually, they are reviewed only by the Editor, and are published at his discretion. REVIEWS AND TUTORIALS are full length papers which need not contain original work. They primarily review the state of the art and developments leading thereto. Please contact the Editor prior to undertaking preparation of a review or tutorial. ILLUSTRATIONS should be kept to a minimum. Figures and photos should be original proofs and not photocopies. Photos must be glossy prints with no screens. 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Digital Object Identifier 10.1109/TAP.2012.2186029

INSTITUTIONAL LISTINGS The IEEE Antennas and Propagation Society is grateful for the support given by the organizations listed below and invites applications for Institutional Listings from other firms interested in the field of Antennas and Propagation.

The charge for an Institutional Listing is $75 per issue, $375 for six consecutive issues, and $725 for 12 issues. Agency fee is not granted on Institutional Listings. Applications for Institutional Listings, should be sent to the Editor-in-Chief or Susan Schneiderman, IEEE Media, 445 Hoes Lane, Piscataway, NJ 08854, [email protected]. Please include name of company, company contact information, billing address, name of publication, dates of issue, artwork in the form of a pdf should be sent to Felicia Spagnoli, [email protected], +1 732-562-6334.

Digital Object Identifier 10.1109/TAP.2012.2186411