Integration of Unmanned Aerial Vehicles in Wireless Communication and Networks: UAVs and 5G 3031038797, 9783031038792

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Unmanned System Technologies

Dushantha Nalin K Jayakody P. Muthuchidambaranathan Rui Dinis Stefan Panic   Editors

Integration of Unmanned Aerial Vehicles in Wireless Communication and Networks UAVs and 5G

Unmanned System Technologies

Springer’s Unmanned System Technologies (UST) book series publishes the latest developments in unmanned vehicles and platforms in a timely manner, with the highest of quality, and written and edited by leaders in the field. The aim is to provide an effective platform to global researchers in the field to exchange their research findings and ideas. The series covers all the main branches of unmanned systems and technologies, both theoretical and applied, including but not limited to: • Unmanned aerial vehicles, unmanned ground vehicles and unmanned ships, and all unmanned systems related research in: • Robotics Design • Artificial Intelligence • Guidance, Navigation and Control • Signal Processing • Circuit and Systems • Mechatronics • Big Data • Intelligent Computing and Communication • Advanced Materials and Engineering The publication types of the series are monographs, professional books, graduate textbooks, and edited volumes.

Dushantha Nalin K Jayakody • P. Muthuchidambaranathan • Rui Dinis • Stefan Panic Editors

Integration of Unmanned Aerial Vehicles in Wireless Communication and Networks UAVs and 5G

Editors Prof. Dushantha Nalin K Jayakody COPELABS Lusófona University Lisbon, Portugal

Rui Dinis Instituto de Telecomunicações FCT-Nova University of Lisbon Lisbon, Portugal

P. Muthuchidambaranathan Department of Electronics and Communication Engineering National Institute of Technology Tiruchirappalli, Tamilnadu, India Stefan Panic Faculty of Natural Science University of Pristina Kosovska Mitrovica, Serbia

ISSN 2523-3734 ISSN 2523-3742 (electronic) Unmanned System Technologies ISBN 978-3-031-03879-2 ISBN 978-3-031-03880-8 (eBook) https://doi.org/10.1007/978-3-031-03880-8 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To the families of all authors...

Foreword

Unmanned aerial vehicle (UAV) or “drones” is identified as an effective mechanism to collect data from SNs in IoT applications, especially when there is no feasible connection towards the data processing centers. UAVs were mainly utilized in military-related works and deployed for remote surveillance to reduce pilot losses. Recently, enthusiasm for using UAVs in civilian and commercial applications has emerged, due to the advancement of UAVs’ manufacturing technologies and reduction in cost, making them more appealing for civil applications. Unlike the traditional static data collection methods, UAV utilizes the favorable line-of-sight (Los) dominant air-to-ground channels increasing coverage area and sum-throughput of the IoT network. However, there is a trade-off between sum-throughput and energy efficiency of the system, thus, UAV should be power aware during the data collection process. Furthermore, UAV’s trajectory needs to be optimized to maximize the number of serving IoT devices in the network while considering the performance metrics. This first-of-its-kind book from the experts on this subject presents a comprehensive framework for the design and analysis and integration of UAV in wireless communication systems. This book focuses on the recent advances in UAVs and 5G communications and networks. This book aims to provide a unique research perspective to various industry and academic researchers. The role of UAVs with current advances in wireless communication helps to improve the quality of services, such as disaster resilient systems, Internet of things (IoT), power sensor networks, age of information (AoI), wireless networks, and so on. There are a wide variety of applications using UAV and wireless communication, and some of these standards and applications are addressed in this book. The channel tracking and equalization schemes to address ISI are presented in detail, which help in improving the system performance by reducing latency and channel estimation overheads in fast varying channels. Different transmission techniques in air-toair (A2A) and air-to-ground (A2G) communications for uplink and downlink are highlighted. The outage probability and average throughput analysis is presented for dual hop self-energized full duplex UAV-assisted wireless networks. UAV assisted wireless power network is presented here and the UAV collects data from sensor vii

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Foreword

network, where each sensor harvests energy from the data-collecting UAV for its own information transmission. The suitability of UAVs communication for providing reliable communications using 5G cellular networks New Radio (NR) is analyzed in this book. The extensive discussion about how the emerging wireless communication use cases paved the path for several UAV-related applications and integration of UAVs into wireless communication to provide various services in disaster resilient systems is also presented. The AoI performance metric for UAVassisted communication networks is described in detail in this book. Arthur C. Clarke Institute for Modern Technologies

Prof. K. K. Y. W. Perera

Preface

The book Integration of UAVs in 5G Communication and Networks focuses on the recent advances in the UAVs and 5G communications and networks. This book aims to provide a unique research perspective to various industry and academic researchers. The role of UAVs with current advances in wireless communication helps to improve the quality of services, such as disaster resilient systems, Internet of things (IoT), power sensor networks, age of information (AoI), wireless networks, and so on. There are a wide variety of applications using UAV and wireless communication, and some of these standards and applications are addressed in this book. Chapter 1 presents a suitable solution for UAVs with reference to channel tracking and equalization to address the inter-symbol interference (ISI) stemming from multi-path propagation and the time-varying nature of the radio channel due to Doppler shifts. UAVs are considered to be working as a base station and the uplink communication is considered from mobile terminal to base station. The doubly selective UAV channel demands single-carrier modulations combined with frequency-domain equalization (SC-FDE). A detailed interpretation of SCFDE is presented in this chapter. A low-complexity iterative frequency-domain equalizer based on the iterative block decision-feedback equalization (IB-DFE) and the tracking procedure is conducted by an extended Kalman filter (EKF) to attain equalization. An efficient frame structure is designed in this chapter, which is suitable for UAV communications that help in reducing channel estimation overheads. Decision-directed approach helps in further reducing channel estimation overheads. These proposed systems are very efficient for fast varying channels due to the very low density of training symbols. Only two consecutive training symbols overheads are needed to initialize the tracking procedure. These schemes help in reducing overall latency and channel estimation overheads. The employment of these approaches helps in tracking the channel variation along with limiting the number transmitted blocks. The presence of EKF in the equalization for decisionmaking produces new channel estimates recursively. The wide application area of UAVs includes military applications for reconnaissance and attacks, as well as civilian applications, which range from film ix

x

Preface

making to agriculture. Almost all of these applications require energy-efficient and reliable wireless communications, but air-to-air (A2A) and air-to-ground (A2G) UAV communications pose various challenges regarding the design of the underlying transmission technique. An overview of broadband, block-based transmission techniques is presented in Chap. 2, which also pointed to the suitability of these communication schemes to overcome most of the UAV communication challenges. The data rate and latency can vary scenario to scenario, hence highly flexible waveforms are needed at the transmitter. Block transmission techniques such as OFDM are excellent candidates for the high multipath and Doppler spread present in UAV channels. OFDM offers various advantages, but also presents severe amplification issues due to large envelope fluctuations of the resulting signals, hence it is not recommended for uplink scenarios. The single carrier with frequencydomain equalization (SC-FDE) technique can be an excellent alternative for the uplink communication and is more adequate to UAV communications than OFDM. As OFDM, SC-FDE is a block-based transmission technique which offers FDE equalization features. However, its single-carrier nature leads to signals with lower envelope fluctuations than OFDM, which enables a more efficient amplification and, consequently, larger flight times. Therefore, OFDM and SC-FDE can be used together regarding the downlink and the uplink, respectively. Single-carrier SC-FDE receivers are less complex compared to OFDM and present a great flexibility to adapt the transmission to the channel conditions. The single-carrier signals enforce a much lower peak-to-average power ratio (PAPR) than OFDM, which in fact provides significantly higher energy efficiency at the transmitter. Cooperative wireless communication is one of the promising techniques, which is used in 5G wireless cellular technology to improve system performance and provide better communication range. The investigation of half and full duplex system performance for cooperative UAV networks using SWIPT technique and TS protocol is presented in Chap. 3. A mathematical expression is derived for an outage probability and average throughput for a dual-hop decode and forward UAV system, where a direct link is present between source and desired user. The system analysis is done by using generalized Weibull fading channel, which has never been studied before in the UAV-aided systems. The Weibull distribution was identified as the probability distributions for modelling amplitude fading in a varying environment and was also recognized as an effective measurement method for empirical channel models. It may be used to demonstrate UAV fading channels with severe fading characteristics that are suitable for higher altitude and open space usages. It provides a lot of flexibility when it comes to characterizing UAV fading channels in various conditions, and less practical research on the Weibull distribution has been reported. The UAV-aided full duplex system performs better based on numerical results when self-interference at the UAV is less. In high SNR regime, selection combining technique at receiver helps to mitigate high SNR regime. Unmanned aerial vehicles (UAVs) platforms and terrestrial base stations (BSs) are jointly used for data collection in UAV-assisted Internet of Things (IoT) networks. UAV platforms also have potential to enhance the 3D positioning accuracy of IoT networks, serving as aerial anchor nodes. In particular, UAV-

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assisted relaying is able to serve existing networks by enabling communication between two nodes suffering from blockages and by recovering the network in inaccessible disaster affected areas. In Chap. 4, a scenario of UAV data collection from a sensor network, where each sensor harvests energy from the data-collecting UAV for its own information transmission, has been observed. In the first instant, the wireless energy transfer (WET) to sensor nodes is performed, while in the second instant, UAV collects data from sensor nodes. In order to take into account the possibility of occurrence of obstacles that could block the line-of-sight (LOS) link in-between sensor nodes and UAV, and in order to observe fluctuations of the LOS signal that are brought by shadowing effect, we have used the assumption of Rician Shadowed fading channels and analyzed the outage probability (OP) properties of such network. Closed-form expressions are derived for OP, and OP features are observed and discussed in the function of system parameters such as shadowing severity, targeted information rate, UAV location, and the time ratio of WET. Further, communication in the Hoyt fading environment has been observed, since it represents generalization of Rayleigh fading environment, the most widely used non-LOS case scenario model. Closed-form expression for OP of the wireless sensor network (WSN) in Hoyt fading environment has been delivered, and also the time allocation of down-link and up-link to minimize end-to-end OP subjected to UAV’s power profile. The impact of the target information rate and outage OP acceptable for required quality-of-service (QoS) and UAV’s hovering location is investigated. UAV support has been enhanced in the fifth generation (5G) networks. Besides acting as terminals, 5G introduced the slicing concept, which enables serviceoriented configuration of wireless networks in a flexible and agile manner supported by the core. The flexible resource allocation introduced makes the 5G new radio (NR) interface a promising choice for the radio interface. The height of the UAV connected to a terrestrial BS allows a broader coverage range but also produces more interference in neighbor BS. In order to evaluate the level of reliability achievable in the air-to-ground (A2G) link, for uplink transmissions, a reliable channel model is required. The suitability of UAVs communication for providing reliable communications using 5G cellular networks New Radio (NR) is analyzed in Chap. 5. The air-to-ground channel model on a rural scenario is considered using MIMO 2 × 8 and the maximum transmission power specified for a 5G terminal. The capacity, coverage range, and UAV positioning that allow providing reliable communications with a guaranteed block error rate below 1% and a 99% guaranteed throughput are calculated, and are compared to the scenario where reliability is not required. It is shown that the coverage and UAV possible horizontal distances and heights are reduced because a minimum SNR is required for reliable operation, compared to a pure throughput maximization approach. A significant influence of the UAV height on the provided service and more channel bandwidth used to increase the throughput reduce coverage range. Unmanned aerial vehicles (UAVs) are commonly referred to as drones and have a wide range of applications in the modern era. Applications of the UAVs are exponentially increasing with the continuous development of various features

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of it. The extensive discussion about how the emerging wireless communication use cases paved the path for several UAV-related applications and integration of UAVs into wireless communication to provide various services in disaster resilient systems is presented in Chap. 6. The low implementation cost, ease of deployment, and ability to deploy in any geographical area make UAVs a better candidate in disaster-resilient applications. But all these advantages come with several challenges to overcome, which were not there in classical or typical systems, such as real time placement, crucial energy constraints, and moving cells. Most common challenges with the nature of the problem and a sample scenario to methodologically realize the problems related to the above application is discussed in this chapter. The problem studies the placement and the user association of UAV aerial base stations to temporarily enable the coverage in a region where the terrestrial communication infrastructure is destroyed due to a disaster. The objective of the problem is identified as maximizing the achievable rate while increasing the fairness among the users. The main problem is analyzed by dividing into three sub problems. Those are the user association and clustering sub problem, intra-cluster positioning sub problem, and the altitude selection sub problem. User association and clustering problem is addressed through k-means clustering and Gale-Shapley algorithm. Intra-cluster placement sub problem is addressed via modified pattern search algorithm. Altitude selection sub problem is solved by understanding the impact on the achievable rate with the elevation angle between the user and the UAV. The proposed algorithm is compared through numerical simulations with the benchmark approach provided in the literature for performance evaluation. The exponential growth of Internet-of-Things (IoT) applications in nextgeneration communications has led to increasingly connected devices in the communication infrastructures. This will lead to a huge amount of information generated under different applications. Therefore, it is essential to maintain freshness of the information received since outdated information can jeopardize reliability of the system output giving rise to safety risks. Age of Information (AoI) is the performance metric used to quantify the freshness of information received with respect to its generated time. AoI in wireless communication has emerged as an end-to-end performance metric to measure the timeliness of received status updates at the destination. The concept of age is common that age-based optimizations can be found almost in all network layers. The introduction of AoI has led the scientific world into the development of new analytical models for status update freshness and tools for age analysis. It is also noteworthy that the AoI metric is now beginning to be applied in UAV-assisted communication networks, IoT applications, etc. However, it is clear that there are still lots of unanswered questions, open problems, and unexplored potential applications related to AoI performance metric. Chapter 7 describes AoI performance metric in detail, giving examples and mathematical foundation. Further, evolution of AoI along with the other performance metrics emerged from AoI, that is, peak AoI, cost of update delay, and value of information update were explained along with their mathematical formulations. Then, a SWIPTPS enabled two-way relay network was used to formulate the AoI performance metric in EH-enabled wireless setup following the mathematical formulations

Preface

xiii

described earlier. After obtaining a closed-form expression for time average AoI, an optimization problem was formulated to identify the optimal power-splitting factor that minimizes the AoI performance. Further, the relationship between AoI and the traditional performance metric of outage probability is established for better understanding. Finally, potential applications and recommendations were provided for future investigation of AoI performance metric in different research domains. We hope the reader will enjoy this book that presents high-level research conducted in the area of UAVs and 5G wireless communication networks. Lisbon, Portugal Tiruchirappalli, Tamilnadu, India Lisbon, Portugal Kosovska Mitrovica, Serbia

Dushantha Nalin K Jayakody P. Muthuchidambaranathan Rui Dinis Stefan Panic

Acknowledgment

I would like to express my sincere gratitude to all the colleagues who contributed to the work and projects that led to this book. I would also like to particularly thank our editor as well as the editorial staff at Springer for producing this book. This work is supported by the Scheme for Promotion of Academic and Research Collaboration (SPARC) grant No. SPARC/2018-2019/P145/SL of the Ministry of Human Resource Development, Government of India.

Dushantha Nalin K Jayakody

xv

Contents

1

Channel Tracking and Equalization for UAV Communications . . . . . . . . Pedro Pedrosa, Rui Dinis, Daniel Castanheira, Adão Silva, and Atílio Gameiro

1

2

Transmission Techniques for UAVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . João Guerreiro and Rui Dinis

27

3

Self-energising of Full-Duplex UAV-Assisted Wireless Networks . . . . . . . Anandpushparaj Jeganathan, Gupta Mitali, Dushantha Nalin K Jayakody, and P. Muthuchidambaranathan

39

4

UAV-Assisted Wireless Power Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . Stefan Panic and Caslav Stefanovic

61

5

Reliable Capacity of A2G Drone Communications Using 5G NR . . . . . . Marco Corrente, Ricardo Sacoto-Martins, Luis Bernardo, Rui Dinis, Rodolfo Oliveira, Paulo Pinto, and Luis Campos

79

6

Application of UAV for a Disaster-Resilient System. . . . . . . . . . . . . . . . . . . . . . 105 Hassaan Hydher and Dushantha Nalin K Jayakody

7

Analysis of Age of Information in Wireless Communication Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Tharindu D. Ponnimbaduge Perera and Dushantha Nalin K Jayakody

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

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Chapter 1

Channel Tracking and Equalization for UAV Communications Pedro Pedrosa, Rui Dinis, Daniel Castanheira, Adão Silva, and Atílio Gameiro

1.1 Introduction Unmanned aerial vehicles (UAVs) have recently found many applications, including the support of wireless communication systems [1, 2]. In fact, UAVs may serve as base stations (BSs), for capacity enhancement or data offloading [3–6], or relays, to extend coverage or aggregate data [7–9]. In this chapter we consider the UAV to be working as a BS and the communication link to be from the mobile terminal (MT) to the BS, i.e., the uplink (see Fig. 1.1). Accordingly, to cope with the inter-symbolic interference (ISI) originating from the multi-path propagation and time-varying nature of the radio channel we propose using single-carrier modulations combined with frequency-domain equalization (SC-FDE) [10–12]. More specifically, we use an iterative block-decision feedback equalizer (IB-DFE) [13], which in practice is a turbo equalizer operating in the frequency domain [14]. With regard to the time-varying nature of the channel, we propose using an extended Kalman filter (EKF) exploiting a purposefully designed frame structure.

P. Pedrosa () · D. Castanheira Instituto de Telecomunicações and Universidade de Aveiro, Aveiro, Portugal e-mail: [email protected]; [email protected] R. Dinis Instituto de Telecomunicações and DEE, FCT, Universidade Nova de Lisboa, Monte de Caparica, Portugal e-mail: [email protected] A. Silva · A. Gameiro Instituto de Telecomunicações and DETI, Universidade de Aveiro, Aveiro, Portugal e-mail: [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 D. N. K. Jayakody et al. (eds.), Integration of Unmanned Aerial Vehicles in Wireless Communication and Networks, Unmanned System Technologies, https://doi.org/10.1007/978-3-031-03880-8_1

1

2

P. Pedrosa et al. UAV (BS)

LOS

MT Multipath

Fig. 1.1 Considered scenario for UAV communications

With the approach proposed in this chapter, the variations of the channel can be efficiently tracked while keeping the number of transmitted training blocks to a minimum. Actually, the use of the EKF allows us to update the state-mean vector and the state-covariance matrix of the state-model governing the channel variations resorting to training sequences and predict the channel behavior during data transmission, thus ensuring reliable symbol detection. Alternatively, we can also employ a decision-directed approach. In this case, the state-model is updated during data transmission and no training sequences are used. Kalman filters are one of the most effective and robust tracking solutions present in the signal processing literature [15–20]. Particularly, the problem of delay estimation in the presence of multipath is addressed by Iltis in [15], while Haykin et al. exploit the one-to-one correspondence between the recursive least-squares (RLS) and the Kalman variables to formulate extended forms of the RLS algorithm in [16]. Also notable is the approach developed by Komniakis et al. in [17] to address the problem of channel tracking and equalization in multi-input multi-output (MIMO) channels. Finally, Simon et al. proposes a state-space approach to jointly estimate the multipath Rayleigh channel gains and the carrier frequency offset (CFO) in [18], and a soft-Kalman filter in [19]. Similar approaches based on iterative detection and decoding can be found also in [20–22]. Particularly important to our approach is the definition of the state-model governing the transitions of the time-varying radio channel. More specifically, the complex channel gains are assumed to have constant amplitude and time-varying phase. Actually, when the radio channels is characterized by a small number of rays, each of them arriving more or less from the same direction, it is reasonable to consider that the amplitude varies at a much lower rate than the phase. This motivates defining the state-space vector as being built upon the phases of the channel gains and their associated Doppler terms and results in a very simple and elegant state-transition model that has a clear and evident relation with the physics of the problem.

1 Channel Tracking and Equalization for UAV Communications

3

Also present in this chapter is the derivation of the Bayesian Cramér–Rao bound for the state-vector estimate. Notably, with the definition of the Bayesian Cramér– Rao bound we are able to compare the performance of the proposed algorithm with respect to the limits as defined by the estimation theory. To conclude this chapter, the convergence rate of the proposed algorithms is also investigated. Particularly, we consider different simulation scenarios each with different positioning of the training symbols. Different lengths for the initial training stage are also considered. In this way multiple frame design possibilities are evaluated and a deeper understanding of the proposed solution provided. Concluding the chapter and to assess the robustness of the channel tracking algorithm, several additional simulation scenarios with particularly demanding regimes (e.g., large values for the Doppler terms) are included. This chapter is organized as follows. Section 1.2 presents the model of the system; Sect. 1.3 formulates the problem of tracking the channel as a stateestimation problem and derives the EKF; Sect. 1.4 discusses the performance results of the proposed system, and Sect. 1.5 draws the final conclusions. In this chapter we use the following notation. Small-case bold types (e.g., a) denote column vectors; upper-case bold types (e.g., A) denote matrices. Particularly, I denotes the identity matrix, while 0 denotes a matrix where all the matrix elements are zero. Depending on the context, 0 can also denote a column vector. Operations (·) and (·)∗ denote matrix and/or vector transpose and conjugate, respectively. Scalar functions with matrix and/or vector arguments are assumed to happen element-wise (e.g., if v = [v1 v2 ] , then sin(v) = [sin(v1 ) sin(v2 )] ). Operator Var(·) returns the variance of its argument. DFT{·} and IDFT{·} denote the discrete Fourier transform and its inverse, respectively. Operator sign(·) is defined as  1, a≥0 sign(a) = −1, a < 0 with a ∈ R. Operators R(·) and I(·) are, respectively, the real and imaginary parts of a given complex number. HD{·} denotes hard decisions and is defined as HD{·} ≡ √ sign[R(·)] + j sign[I(·)] with j = −1. Finally, in Algorithm 1.1, and Algorithm 1.2 operators a = b and a = b test integers a and b for equality and inequality, respectively. Finally, mod(·, ·) is the modulo operation.

1.2 System Model Consider Fig. 1.2, where we depict the frame structure. Notably, M consecutive training symbols are placed in the beginning of the frame for synchronization purposes. Then, data symbols follow and these are further interspersed with additional training symbols. These additional training symbols have a gap of p − 1

4

P. Pedrosa et al. Initial training p − 1 data symbols symbols

k = 0; 1; : : : ; N − 1

Frequency

Fig. 1.2 Frame structure

:::

:::

Training symbol

:::

d = 0; 1; : : : Time

data symbols between them. Notice that each data symbol has duration TB and corresponds to a size-N DFT block. Training symbols have a duration of TTS seconds and sample size equal to or smaller than TB . An NG -sized cyclic prefix with duration TCP proceeds both training and data symbols. Cyclic prefix duration, TCP , is assumed larger than the overall channel impulse response duration. At the transmitter side, we have  sd (t − dTB ). (1.1) s(t) = d

where s(t) is the overall time-domain signal associated with a single frame and sd (t) is the time-domain signal associated with the dth DFT-block. Clearly, sd (t) =

N −1 

sn,d g(t − nTs ),

(1.2)

n=−NG

where Ts denotes the duration of the DFT-block samples, and g(t) the adopted pulse shaping filter. Clearly, Ts = TB /N, and NG = TCP /Ts .

1.2.1 Channel Model Regarding the channel model, we consider a broadband multipath radio channel, where each ray has a small number of contributions all arriving approximately from the same direction. Significantly, if each ray has a small number of contributions all arriving approximately from the same direction, then it is a reasonable assumption to consider that the variation of the amplitude of each channel ray occurs at a much lower rate than the variation of the phase. Particularly, consider the multipath channel has L rays and that each ray is given by the complex exponential αl,d ∈ C, l = 1, . . . , L, with a relative delay τl . Also,

1 Channel Tracking and Equalization for UAV Communications

5

define ϕl,d  arg{αl,d }, particularly ϕl,0  arg{αl,0 }; assume the presence of a Doppler frequency shift term νl = fD TB cos(θl ), where fD , TB , and θl are the Doppler frequency, the symbol duration, and the angle of arrival, respectively, then ϕl,d = ϕl,0 + 2π dνl and the model for the continuous channel impulse response (CIR) results h(t, dTB ) =

L 

αl,0 exp(j 2π dνl )δ(t − τl )

l=1

=

L 

|αl,0 | exp(j ϕl,d )δ(t − τl )

l=1

=

L 

αl,d δ(t − τl ).

(1.3)

l=1

Consequently, the continuous channel frequency response (CFR) is given by: Hd (f ) =

L 

αl,d exp (−j 2πf τl ).

(1.4)

l=1

Whereas the discrete CFR is in turn Hk,d = Hd (f )|

k f=T

, with k = 0, 1, . . . , N −1.

B

Considering further that {hn,d ; n = 0, 1, . . . , N − 1} = IDFT{Hk,d ; k = 0, 1, . . . , N − 1}, the sampling occurs at instants {τl ; l = 0, 1, . . . , L − 1}, and that the number of rays is L = NCP , with most of the rays being equal to zero then {αl,d ; l = 0, 1, . . . , L − 1} = {hn,d ; n = 0, 1, . . . , NCP − 1}, and since the channel gains αl,d have constant amplitude with respect to d, particularly, |αl,d | = |αl,0 |, then αl,d /|αl,0 | is the phasor of the time-varying the multipath channel associated with the dth DFT-block.

1.2.2 Channel Equalization The use of a cyclic prefix (CP) does not solve the problem of ISI in SC-FDE-based transmissions, unlike to what happens using OFDM. Actually, with SC-FDE, the use of a CP solves the interference between transmitted symbols but does not solve the interference between DFT-blocks. So, and provided that the duration of the CP is longer than the overall channel impulse response, the received signal is given in the frequency-domain by: Yk,d = Sk,d Hk,d + Nk,d ,

k = 0, 1, . . . , N − 1, d = 0, 1, . . .

(1.5)

6

P. Pedrosa et al.

Fig. 1.3 A general overview of the IB-DFE scheme

(i−1) Sˆk

(i)

Bk

(i−1)

DFT

sˆn

Delay

(i)

Fk Yk

+

− ˜(i) Sk

(i)

IDFT

s˜n

(i)

HD

sˆn

where DFT-samples {Sk,d ; k = 0, 1, . . . , N − 1} result from applying the discrete Fourier transform (DFT) to the time-domain signal {sn,d ; n = 0, 1, . . . , N − 1}, i.e., {Sk,d ; k = 0, 1, . . . , N − 1} = DFT{sn,d ; n = 0, 1, . . . , N − 1}. Similarly, {Nk,d ; k = 0, 1, . . . , N − 1} is the DFT of the channel noise process. Finally, channel fading during one DFT-block is also assumed to be constant. In fact, if the phase noise and/or the carrier frequency offset (CFO) is known at the receiver through some estimation process, then the phase variations occurring inside the block be compensated and time-invariant property of the block ensured [23]. From (1.5), it is clear that the time-dispersive channel scales each subcarrier. Typically, a linear FDE is employed to cope with the residual effects of the channel; however, significantly better performances can be attained if the linear FDE is replaced by an IB-DFE [13]. A schematic representation of the IB-DFE is depicted in Fig. 1.3. After completing its ith iteration, the IB-DFE output (i.e., the equalized signal in the frequency domain) can be expressed as (i) (i) (i) ˆ (i−1) k = 0, 1, . . . , N − 1, S˜k,d = Fk,d Yk,d − Bk,d Sk,d , d = 0, 1, . . .

(1.6)

(i) (i) where {Fk,d ; k = 0, 1, . . . , N − 1}, and {Bk,d ; k = 0, 1, . . . , N − 1}, are the feedforward and feedback coefficients, respectively. The DFT of the time-domain (i−1) decisions obtained in the previous iteration are denoted {Sˆk,d ; k = 0, 1, . . . , N − (i−1) (i−1) 1} (i.e., {Sˆ ; k = 0, 1, . . . , N − 1} = DFT{ˆs ; n = 0, 1, . . . , N − 1} k,d

n,d

(i−1) (i−1) with {ˆsn,d ; n = 0, 1, . . . , N − 1} = HD{˜sn,d ; n = 0, 1, . . . , N − 1}, where (i) (i) ˜ {˜sn,d ; n = 0, 1, . . . , N − 1} = IDFT{Sk,d ; k = 0, 1, . . . , N − 1}). The filtering coefficients can be found in, e.g., [24], and their optimal values are reproduced here for convenience. Specifically for QPSK constellations, the expressions for the feedback and feedforward coefficients are, respectively, (i)

(i)

Bk,d = Fk,d Hk,d − 1, and

k = 0, 1, . . . , N − 1, d = 0, 1, . . .

(1.7)

1 Channel Tracking and Equalization for UAV Communications

(i) Fk,d

(i) F˘k,d

=

(i) γd

,

k = 0, 1, . . . , N − 1, d = 0, 1, . . .

7

(1.8)

where (i) = F˘k,d

∗ Hk,d

SNRd−1

(i−1) 2 + (1 − (ρd ) )|Hk,d |2

,

k = 0, 1, . . . , N − 1, d = 0, 1, . . .

(1.9)

and SNRd−1 = E[|Nk,d |2 ]/E[|Sk,d |2 ] is the reciprocal of the signal-to-noise ratio (SNR). The denominator in (1.8) is given by: (i)

γd =

N −1 1  ˘ (i) Fk,d Hk,d , N

d = 0, 1, . . .

(1.10)

d = 0, 1, . . .

(1.11)

k=0

(i−1)

and the feedback reliability ρd (i−1)

ρd

=

by:

(i−1) ∗ E[ˆsn,d sn,d ]

E[|sn,d |2 ]

,

Notice that, in this work, the SNR is considered known. Notably, SNR estimation techniques like those in [25, 26] allow to infer the SNR from the feedback reliability term (1.11) and can be easily implemented at the receiver.

1.2.3 Channel Estimation The values of the feedback and feedforward coefficients, respectively, (1.7) and (1.8), depend on the CFR. Noticing (1.5), a least-squares (LS) estimate of the CFR is readily available doing Yk,d , H˜ k,d = Sk,d

k = 0, 1, . . . , N − 1, d = 0, 1, . . .

(1.12)

Obviously, {Sk,d ; k = 0, 1, . . . , N − 1} is only available at the receiver if it is a known training sequence {SkTS ; k = 0, 1, . . . , N − 1}. Alternatively, decisions on the transmitted symbols {Sˆk,d ; k = 0, 1, . . . , N − 1} can also be used. The former approach is dubbed training symbol (TS) channel estimation and the last decisiondirected (DD) channel estimation. An alternative to the LS estimator is the minimum mean-squared error (MMSE) estimator [27]:

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P. Pedrosa et al.

H˜ k,d =

∗ Yk,d Sk,d

|Sk,d

|2

+ SNRd−1

k = 0, 1, . . . , N − 1, . d = 0, 1, . . .

,

(1.13)

Since training symbols can be designed to have constant amplitude, the use of the MMSE seems to be unjustified; however, if decision symbols are employed, then this use is reasonable due to the fact that {|Sk,d |; k = 0, 1, . . . , N − 1} are approximately Gaussian.

1.3 Channel Tracking A state-space formulation for problem of tracking a time-varying multipath channel is presented in this section. Since, in its basic form, the Kalman filter is limited to linear models and the model for the observations of the time-varying channel is nonlinear, we are considering the EKF.

1.3.1 The EKF for Channel Tracking 1.3.1.1

Process Model

The rules governing the state dynamics are captured by the process (or state transition) model. Particularly, assuming that the state vector is x d = [ν  ϕ  d] ,   where ν = [ν1 · · · νL ] , and ϕ d = [ϕ1,d · · · ϕL,d ] , then the state-transition equation is x d+p = H (p) x d ,

(1.14)

where the p-step state-transition matrix, H (p) , is given by:  I L 0L . = 2πpI L I L 

H

1.3.1.2

(p)

(1.15)

Observation Model

Defining the nonlinear vector function:   f (ϕ d ) = [f1 (ϕ d )] [f2 (ϕ d )] ,

(1.16)

1 Channel Tracking and Equalization for UAV Communications

9

with f1 (ϕ d ) = cos(ϕ d ), and f2 (ϕ d ) = sin(ϕ d ), results in the observation vector zd = [z1,d · · · zL,d ] , zd = f (ϕ d ) + v d ,

(1.17)

with v d = [v1,d · · · vL,d ] being the observation noise vector. The observation noise covariance matrix is R = σv2 I , and σv2 is the variance of the real (or imaginary) part of the complex circularly distributed white Gaussian noise process {vl,d ; l = 0, 1, . . . , L − 1; d = 0, 1, 2, . . .}. The elements of the noise vector v d are independent and identically distributed. Since the variance of the observation noise depends on the approach used (i.e., if it uses training or decisions), we distinguish each case with a superscript. Namely, R TS and R DD are the covariance matrices for the channel observation noise obtained using the training-based approach and the decision-based approach, respectively.

1.3.1.3

Prediction Stage (At the Training Symbols)

Assuming that the training symbols occur for d = 0, p, 2p, . . ., then the prediction stage corresponds to the computation of the pth-order a priori state-mean x d|d−p , and state-covariance P d|d−p , using the pth-order a posteriori state-mean and statecovariance obtained during the previous training symbol, x d−p|d−p and P d−p|d−p , respectively. Accordingly,

1.3.1.4

x d|d−p = H (p) x d−p|d−p ,

(1.18a)

P d|d−p = H (p) P d−p|d−p H (p) .

(1.18b)

Update Stage (At the Training Symbols)

The a priori state-mean x d|d−p is combined with the so-called measurement residual ed during the update stage, occurring for each training instance and resulting in a refined state estimate. Accordingly, the a posteriori state-mean x d|d and statecovariance matrix P d|d are given by: x d|d = x d|d−p + K d ed ,

(1.19a)

P d|d = (I − K d J d|d−p )P d|d−p ,

(1.19b)

where K d is the Kalman gain and J d|d−p the Jacobian of (1.16) evaluated with respect to the state-prediction mean x d|d−p , i.e., J d|d−p = J (x d )|x d =x d|d−p .

(1.20)

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P. Pedrosa et al.

The Jacobian itself is derived in Sect. 1.3.1.7.

1.3.1.5

Measurement Residual

The measurement residual corresponds to: ed = zTS d − f (ϕ d|d−1 ) 

TS    cos(ϕ d|d−1 ) R αˆ TS /|αˆ d | d

TS − = , sin(ϕ d|d−1 ) ˆd | I αˆ TS d /|α

(1.21)

where αˆTS d is the vector  of the channel estimates obtained through training symbols, TS · · · α TS . αˆ TS ˆ 1,d ˆ L,d d = α

1.3.1.6

Kalman Gain

In (1.19a), K d is the Kalman gain K d = P d|d−p J d|d−p S −1 d ,

(1.22)

where S d is the residual covariance matrix, S d = R TS + J d|d−p P d|d−p J  d|d−p . 1.3.1.7

(1.23)

Jacobian Derivation

To solve the EKF, we approximate the nonlinear observation function (1.16) by its first-order Taylor series and evaluate the estimated state vector. This first-order Taylor series is the Jacobian J (x d ) =

∂f (ϕ d ) ∂x d  ∂f (ϕ )

∂f1 (ϕ d ) ∂ν ∂ϕ d ∂f2 (ϕ d ) ∂f2 (ϕ d ) ∂ν ∂ϕ d 1

=

d



  0L [f1 (ϕ d )] I L , = 0L [f2 (ϕ d )] I L where f1 (ϕ d ) = − sin(ϕ d ), and f2 (ϕ d ) = cos(ϕ d ).

(1.24)

1 Channel Tracking and Equalization for UAV Communications

1.3.1.8

11

Prediction Stage (At the Data Symbols)

Assuming that the data symbols occur in instance d = q +h, with q = 0, p, 2p, . . ., and h = 1, 2, . . . , p − 1, we can use the a posteriori state-mean x d−h|d−h to obtain the state-prediction mean x d|d−h . Accordingly, x d|d−h = H (h) x d−h|d−h ,

(1.25)

where  I L 0L . 2π hI L I L

 H (h) =

(1.26)

To obtain an estimate of the CFR, we use the state-estimate xˆ d , which in turn results from the state-prediction mean x d|d−h , i.e., xˆ d = x d|d−h . An algorithmic description of the proposed channel tracking EKF is offered in Table 1.1. Notice that in Table 1.1 we consider only training symbols to observe the channel. This means that there is no update stage during data transmission. In order to circumvent this limitation we propose an approach based on the decisions performed at the equalizer output over the data symbols. This alternative approach allows us to obtain state-observations even during the transmission of data.

1.3.2 The EKF with Decision-Directed Channel Estimation As we already mentioned, employing the decisions-based approach allows us to conduct the state-prediction and state-update stages during both the transmission of training and data symbols. Clearly, under such conditions the state-prediction and state-update equations have unit-steps.

1.3.2.1

Prediction Stage (At the Training Symbols)

Accordingly, the state-prediction mean and state-prediction covariance are, respectively, x d|d−1 = H x d−1|d−1 ,

(1.27a)

P d|d−1 = H P d−1|d−1 H  ,

(1.27b)

where 

 I L 0L H = . 2π I L I L

(1.28)

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Table 1.1 The EKF for channel tracking Require: R TS for all d = 0, 1, . . . do if mod(d, p) = 0 then {the dth symbol is a training symbol; d = 0, p, 2p, . . .} if d = 0 then {Initialize the filter} x 0|0 ← x init P 0|0 ← P init end if x d|d−p ← H (p) x d−p|d−p P d|d−p ← H (p) P d−p|d−p H (p) J d|d−p ← J (x d )|x d =x d|d−p S d ← R TS + J d|d−p P d|d−p J  d|d−p K d ← P d|d−p J d|d−p S −1 d TS · · · α TS ] αˆ TS ˆ 1,d ˆ L,d d ← [α    cos(ϕ ) ˆ TS R{αˆ TS d }/|α d | ed ← − sin(ϕ d|d−p) TS TS I{αˆ d }/|αˆ d |

d|d−p

x d|d ← x d|d−p + K d ed P d|d ← (I − K d J d|d−p )P d|d−p xˆ d ← x d|d else if mod(d, p) = 0 then {the dth symbol is a data symbol; d = p + h; h = 1, 2, . . . , p − 1} h ← mod(d, p) x d|d−h ← H (h) x d−h|d−h xˆ d ← x d|d−h end if end for

1.3.2.2

Update Stage (At the Training Symbols)

Similarly, the state-updated mean and state-update covariance are, respectively, x d|d = x d|d−1 + K d ed ,

(1.29a)

P d|d = (I − K d J d|d−1 )P d|d−1 ,

(1.29b)

where we evaluate the Jacobian with respect to the posterior state-mean (1.27a), i.e., J d|d−1 = J (x d )|x d =x d|d−1 . In its turn, the Kalman gain is K d = P d|d−1 J d|d−1 S −1 d ,

(1.30)

and the innovation covariance matrix S d = R TS + J d|d−1 P d|d−1 J  d|d−1 .

(1.31)

1 Channel Tracking and Equalization for UAV Communications

1.3.2.3

13

Prediction and Update Stages (At the Data Symbols)

Notice that we use the same equations while using either the training or the decisions-based approach (i.e., (1.27a)–(1.29b)) except that for the decisions-based approach the state-observations are obtained using the decisions on the transmitted data. Accordingly, to compute the innovations covariance matrix (1.31) we now use R DD , which corresponds to the state-observation noise covariance matrix associated to the decisions-based approach. An algorithmic description of the proposed channel tracking EKF based on decisions is offered in Table 1.2.

Table 1.2 The decisions-based EKF Require: R TS , R DD for all d = 0, 1, . . . do if mod(d, p) = 0 then {the dth symbol is a training symbol; d = 0, p, 2p, . . .} if d = 0 then {Initialize the filter} x 0|0 ← x init P 0|0 ← P init end if x d|d−1 ← H x d−1|d−1 P d|d−1 ← H P d−1|d−1 H  J d|d−1 ← J (x d )|x d =x d|d−1 S d ← R TS + J d|d−1 P d|d−1 J  d|d−1 K d ← P d|d−1 J d|d−1 S −1 d TS · · · α TS ] αˆ TS ˆ 1,d ˆ L,d d ← [α    cos(ϕ ) ˆ TS R{αˆ TS d }/|α d | − sin(ϕ d|d−1) ed ← TS TS I{αˆ d }/|αˆ d |

d|d−1

x d|d ← x d|d−1 + K d ed P d|d ← (I − K d J d|d−1 )P d|d−1 xˆ d ← x d|d else if mod(d, p) = 0 then {the dth symbol is a data symbol; d = p + h; h = 1, 2, . . . , p − 1} x d|d−1 ← H x d−1|d−1 P d|d−1 ← H P d−1|d−1 H  xˆ d ← x d|d−1 J d|d−1 ← J (x d )|x d =x d|d−1 S d ← R DD + J d|d−1 P d|d−1 J  d|d−1 K d ← P d|d−1 J d|d−1 S −1 d DD ] αˆ DD [αˆ DD · · · αˆ L,d d ←  1,d    cos(ϕ ) ˆ DD R{αˆ DD d }/|α d | ed ← − sin(ϕ d|d−1) DD DD I{αˆ d }/|αˆ d |

d|d−1

x d|d ← x d|d−1 + K d ed P d|d ← (I − K d J d|d−1 )P d|d−1 end if end for

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P. Pedrosa et al.

Notice that the state-estimate xˆ d obtained at the pilot symbols results from the posterior state-mean, x d|d , while at the data symbols it results from the prediction state-mean x d|d−1 . The state-estimate is used to produce an estimate Hˆ d (f ) of the  ˆ CFR (1.4). In fact, using the state-estimate vector xˆ d = [ˆν  d ϕ d ] , particularly  ϕˆ d = [ϕˆ1,d · · · ϕˆL,d ] , we produce the estimate Hˆ d (f ) =

L 

|αl,0 | exp [j (ϕˆ l,d − 2πf τl )].

(1.32)

l=1

As for the EKF initialization, it is ensured assigning x 0|0 = x init

(1.33)

P 0|0 = P

(1.34)

init

and using at the state-prediction stage the state-transition matrix  I L 0L . 2π I L I L

 H init =

(1.35)

Finally, starting the radio frame with Ntrain consecutive training symbols allows us to obtain an initial estimate for state-variables and to ensure a shorter convergence time for the EKF.

1.3.3 Recursive Bayesian Cramér–Rao Bound To determine the performance limits of the proposed EKF, we resort to the recursive Bayesian Cramér–Rao bound proposed by Tichavský et al. in [28]. Accordingly, Fisher information matrix can be obtained recursively:

−1 T J d+1 = H d J −1 H d d   . + Ex d+1 D Td+1 R −1 D d+1 d+1

(1.36)

Defining  Jd =

νϕ  Jdνν Jd νϕ ϕϕ , Jd Jd

we have that the first term on the right-hand side of (1.36) is

(1.37)

1 Channel Tracking and Equalization for UAV Communications

15



−1 T H d J −1 d Hd  ϕϕ νϕ ϕϕ νϕ  (2π )2 Jd − 4π Jd + Jdνν −2π Jd + Jd = ϕϕ νϕ ϕϕ −2π Jd + Jd Jd

(1.38)

and by noting that matrix D d+1 is the Jacobian of the observation function (1.16) results that the 2nd term on the right-hand side of (1.36) is     2 00 −1 T Ex d+1 D d+1 R d+1 D d+1 = 2 . σv 0 1

(1.39)

Finally, adding (1.38) and (1.39) results in J d+1



ϕϕ

νϕ

ϕϕ

νϕ

(2π )2 Jd − 4π Jd + Jdνν −2π Jd + Jd = ϕϕ νϕ ϕϕ −2π Jd + Jd Jd + σ22



(1.40) .

v

Notice that the elements of the Fisher information matrix are associated with a single element of the state-estimate xˆ d , i.e., for the phase and Doppler of a single ray. Accordingly, −1  , Var(ˆνl,d ) > Jdνν  ϕϕ −1 . Var(ϕˆl,d ) > Jd

(1.41) (1.42)

The Bayesian Cramér–Rao bound is plotted together with the variance of the estimate of the Doppler shift and phase, respectively, in Figs. 1.4 and 1.5. In these plots we consider only a single path, i.e., L = 1. Also, we consider that the variance of the observation noise is σv2 = 0.1, the Doppler shift ν = 0.01, and that the initial phase has a uniform distribution, ϕl,0 ∼ U [−π, π ]. The Bayesian Cramér–Rao bound together with the variance of the Doppler shift estimate is plotted in Fig. 1.6 for different values of the Doppler shift and observation noise variance. Namely, ν ∈ [0.01, 1] for the Doppler shift and σv2 = {0.1, 0.15, 0.25} for the observation noise variance. From inspecting the figure, we can clearly see that when the Doppler shift is small (e.g., ν ∈ [0.01, 0.1]), and the observation noise variance is also small (e.g., σv2 ≤ 0.1), the EKF performance is very well aligned with the derived lower bound. However, for larger values of ν and nnnn the EKF‘ performance degrades rapidly 54and this alignment is lost. Similar results were obtained for the estimate of the phase.

16

P. Pedrosa et al. 10 0 BCRB EKF

10 -2

10 -9

2 1.5

10 -4

1

10 -6

200

250

300

10 -8

10 -10

10 -12

0

200

400

600

800

1000

Fig. 1.4 Bayesian Cramér–Rao bound and variance of the Doppler shift estimate 10 -1 BCRB EKF 10 -4 10

10

-2

9 8 7 200

250

300

10 -3

10 -4

0

200

400

600

800

Fig. 1.5 Bayesian Cramér–Rao bound and variance of the phase term estimate

1000

1 Channel Tracking and Equalization for UAV Communications

17

10 0

10 -2

10 -4

10 -6

10 -8

10 -10 10 -2

10 -1

10 0

Fig. 1.6 Bayesian Cramér–Rao bound and variance of the Doppler shift estimate with recursion index d = 200, and observation noise variance σv2 = {0.1, 0.15, 0.25}

1.4 Performance Results Table 1.3 lists the parameter values considered in our simulations. Additionally, in Table 1.4 we list the vehicle velocities and associated Doppler shifts. As for the channel gains {αl ; l = 0, 1, . . . , L − 1}, they were sampled from the circularly symmetric Gaussian distribution CN(0, σα2 ), with σα2 = 1. We used no channel coding. The BER performance curve corresponding to the normalized Doppler shift ν = 0.01 is plotted in Fig. 1.7 for three different scenarios: (1) when a perfect channel estimator is used (i.e., the true CFR is used to obtain the optimal filtering coefficients for IB-DFE); (2) when the EKF is used to estimate the CFR (CFR, in turn, that will be used to derive the filtering coefficients of the IB-DFE) but the decisions-based approach not (EKF w/o DD); (3) when the EKF is used together with the decisionsbased approach to estimate the CFR (EKF w/ DD). Notice that for each scenario we consider three iterations of the IB-DFE (the linear MMSE corresponds to a single iteration). The plots clearly show that the EKF tracks the variations of the channel effectively even if a (small) Doppler shift (e.g., ν = 0.01) is present. The BER performance curve corresponding to the normalized Doppler shift ν = 0.1 is plotted in Fig. 1.8. Compared to the previous scenario, the normalized Doppler shift is considerably larger now. By inspecting the plots, we see that even

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P. Pedrosa et al.

Table 1.3 Simulation parameters

Parameter Modulation DFT-size Frame size Number of rays Size of training stage Training symbol period

Table 1.4 Velocity

v = f fc c

Value QPSK N = 256 modulation symbols Nsym = 300 symbols L = 16 rays Ntrain = 30 symbols p = 10 symbols

Doppler shift ν = f TB Velocitya [km/h] a

0.01 0.03 0.05 0.1 25 76 126 252

fc = 6 GHz; TB = 1/14 ms

10 0

10 -1

10 -2

10 -3

10 -4

0

5

10

15

Fig. 1.7 BER vs. the Eb /N0 for ν = 0.01

though we have considerably increased the value of the Doppler term, the EKF used together with the decisions-based approach shows almost no loss in performance when compared to the ideal case. As for the EKF without the use of the decisionsbased approach, we can see a small performance loss. In order to obtain a graphical reference on the system-supported Doppler shift range we trace the BER vs. the normalized Doppler shift values ν when the EKF does not use the decisions-based approach in Fig. 1.9. By inspecting the figure, it is evident that, for Doppler shift values up to ν = 0.06, the BER remains practically constant. This corresponds to an UE velocity of more than 120 km/h for a carrier

1 Channel Tracking and Equalization for UAV Communications

19

10 0

10 -1

10 -2

10 -3

10 -4 0

5

10

15

Fig. 1.8 BER vs. the Eb /N0 for ν = 0.1

10 0

10 -1

10 -2

10 -3

10 -4

10 -5

10 -6 10 -3

10 -2

10 -1

Fig. 1.9 BER vs. the normalized Doppler shift, ν, for the EKF without the decisions-based approach

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P. Pedrosa et al.

10 0

10 -2

10 -4

10 -6

10 -3

10 -2

10 -1

Fig. 1.10 BER vs. the normalized Doppler shift, ν, for the EKF using the decisions-based approach

frequency fc = 6 GHz and block duration TB = 1/14 ms. Next we will see that this range can be increased using the decisions-based approach. Similarly to what happens in Fig. 1.9, we plot in Fig. 1.10 the BER vs. the normalized Doppler shift ν but this time for the EKF combined with the decisionsbased approach. By inspecting Fig. 1.10, we can see that now the BER remains practically constant for Doppler values up to ν = 0.1. This value corresponds to a very large Doppler shift. In fact, if we look up in Table 1.4 we see that this value for the normalized Doppler shift corresponds to an UE velocity of approximately 250 km/h for a carrier frequency of fc = 6 GHz and block duration of TB = 1/14 ms. In order to assess the frequency of transmission of training symbols required to ensure a successful data detection, we trace the curves for the evolution of the BER with respect to the period of transmission for training symbols, p, in Fig. 1.11 when the EKF is used without decisions-based approach. By inspecting the figure, it is visible that the BER does not vary significantly if the Doppler shift has a small value (e.g., ν = 0.01). On the contrary, if the Doppler shift has a large value (e.g., ν = 0.1), then significant losses in performance may occur and a transmission period of up to p = 10 would be required to prevent such losses. Similarly to Figs. 1.11 and 1.12 depicts curves for the evolution of the BER with respect to the transmission period of the training symbols, p, but this time the EKF uses the decisions-based approach. Comparing both figures, we see significant

1 Channel Tracking and Equalization for UAV Communications

21

10 -1

10 -2

10 -3

10 -4

10 -5 5

10

15

20

25

30

Fig. 1.11 BER vs. the transmission period of the training symbols, p, for the EKF without the decisions-based approach 10 -1

10 -2

10 -3

10 -4

50

100

150

200

250

300

Fig. 1.12 BER vs. the transmission period of the training symbols, p, for the EKF using the decisions-based approach

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P. Pedrosa et al. 10 -1

10 -2

10 -3

10 -4

2

3

4

5

6

7

8

9

10

Fig. 1.13 BER vs. the transmission period of the training symbols, p, for the linear piece-wise channel tracking

differences. In fact, in Fig. 1.12 we can see that the BER is practically constant. This means that, when employing the decisions-based approach, the EKF can track the time-varying channel effectively regardless of how large the transmission period for training symbols is. In fact, after the initial training stage no other training symbol is required. We can see exactly this if we notice that a transmission period p = 301 symbols is larger than Nframe = 300 symbols, the size of the frame, and still no meaningful performance loss is visible. In Fig. 1.13, we also plot the BER with respect to the transmission period for the training symbols, p, but in addition to the EKF with and without the decisions-based approach we also consider a linear piece-wise solution. By inspecting the figure, we see that the linear piece-wise channel tracking is very sensitive to the Doppler shifts. In fact, for a normalized Doppler ν = 0.01, and Eb /N0 = 12 dB, the BER obtained using the linear-piecewise approach is only comparable to the BER obtained using the EKF when one in every other transmitted symbol is a training symbol, which is manifestly unaffordable in terms of overheads. These results clearly justify the need for appropriate channel tracking (e.g., through the use of the EKF) even when the Doppler shifts are small.

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The MSE of the CFR estimate E[|Hˆ k,d − Hk,d |2 ] is plotted in Fig. 1.14 for different transmission periods of the training symbol p, Eb /N0 = 12 dB, and ν = {0.01, 0.1}. The initial training stage has Ntrain = 20 symbols and the EKF uses the decisions-based approach. By inspecting the figure, we can clearly see that, under such conditions, the EKF has the same MSE performance regardless of the transmission period of the training symbols. The MSE of the CFR estimate E[|Hˆ k,d − Hk,d |2 ] is plotted in Fig. 1.15 for different sizes of the initial training stage, Ntrain . Particularly, Ntrain = {2, 5, 20, 50}. Clearly, the size of the initial training stage has a significant impact on system performance. By inspecting the figure, we can see that the larger the initial training stage the faster the EKF will converge. Finally, the MSE of the CFR estimate E[|Hˆ k,d − Hk,d |2 ] is plotted in Fig. 1.16 for different values of Eb /N0 . Particularly, Eb /N0 = {8, 12, 16, 20} dB. Clearly, the impact of Eb /N0 on the MSE is less evident if the Doppler shift is large (e.g., ν = 0.1). When the Doppler shift is small enough (e.g., ν = 0.01), increasing the Eb /N0 reduces the MSE, as expected.

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1.5 Conclusions A channel equalization and tracking scheme were proposed to deal with cellular radio communications over time-varying multipath channels. A scenario that is likely to occur in UAV supported communications. Specifically, under the proposed method, the IB-DFE deals with ISI and the EKF by tracking the CFR. Simulation results show that communication systems employing the proposed method are able to successfully decode the transmitted data even if small to moderate Doppler shifts are present. This is particularly true if state-observations are obtained not only from the training symbols but also from data, through a decisions-based approach. In fact, this approach based on data-decisions provides a double advantage since not only its use ensures increased reliability for the CFR estimates but also allows to reduce the weight of the overheads associated with the channel estimation process. Actually, when using the decisions-based approach, the only training symbols required are those used in the initial training stage of the EKF.

References 1. Y. Zeng, R. Zhang, T.J. Lim, Wireless communications with unmanned aerial vehicles: opportunities and challenges. IEEE Commun. Mag. 54(5), 36–42 (2016) 2. S. Hayat, E. Yanmaz, R. Muzaffar, Survey on unmanned aerial vehicle networks for civil applications: a communications viewpoint. IEEE Commun. Surv. Tutor. 18(4), 2624–2661 (2016) 3. Z. Hu, Z. Zheng, L. Song, T. Wang, X. Li, UAV offloading: Spectrum trading contract design for UAV-assisted cellular networks. IEEE Trans. Wirel. Commun. 17(9), 6093–6107 (2018) 4. S. Yin, Y. Zhao, L. Li, F.R. Yu, Resource allocation and base station placement in cellular networks with wireless powered UAVs, in IEEE International Conference on Communications (ICC) (2019), pp. 1–6 5. B. Gao, L. Lu, K. Xiong, J. Park, Y. Yang, Y. Wang, Spectrum sharing among rapidly deployable small cells: a hybrid multi-agent approach. IEEE Trans. Wirel. Commun. 19(1), 395–409 (2020) 6. H. Wu, Z. Wei, Y. Hou, N. Zhang, X. Tao, Cell-edge user offloading via flying UAV in nonuniform heterogeneous cellular networks. IEEE Trans. Wirel. Commun. 19(4), 2411–2426 (2020) 7. S. Zhang, H. Zhang, Q. He, K. Bian, L. Song, Joint trajectory and power optimization for UAV relay networks. IEEE Commun. Lett. 22(1), 161–164 (2018) 8. Y. Takahashi, Y. Kawamoto, H. Nishiyama, N. Kato, F. Ono, R. Miura, A novel radio resource optimization method for relay-based unmanned aerial vehicles. IEEE Trans. Wirel. Commun. 17(11), 7352–7363 (2018) 9. M. Mozaffari, W. Saad, M. Bennis, M. Debbah, Efficient deployment of multiple unmanned aerial vehicles for optimal wireless coverage. IEEE Commun. Lett. 20(8), 1647–1650 (2016) 10. H. Sari, G. Karam, I. Jeanclaude, An analysis of orthogonal frequency-division multiplexing for mobile radio applications, in Proceedings of IEEE Vehicular Technology Conference, Stockholm, Sweden (1994), pp. 1635–1639 11. A. GusmÃˇco, R. Dinis, J. ConceiÃ˘gÃˇco, N. Esteves, Comparison of two modulation choices for broadband wireless communications, in Proceedings of IEEE Vehicular Technology Conference, vol. 2, Tokyo (2000), pp. 1300–1305

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12. D. Falconer, S. Ariyavisitakul, A. Benyamin-Seeyar, B. Eidson, Frequency domain equalization for single-carrier broadband wireless systems. IEEE Commun. Mag. 40(4), 58–66 (2002) 13. N. Benvenuto, R. Dinis, D. Falconer, S. Tomasin, Single carrier modulation with nonlinear frequency domain equalization: an idea whose time has come – again. Proc. IEEE 98(1), 69– 96 (2010) 14. M. TÃchler, R. Koetter, A. Singer, Turbo equalization: principles and new results. IEEE Trans. Commun. 50(5), 754–767 (2002) 15. R.A. Iltis, Joint estimation of PN code delay and multipath using the extended Kalman filter. IEEE Trans. Commun. 38(10), 1677–1685 (1990) 16. S. Haykin, A.H. Sayed, J.R. Zeidler, P. Yee, P.C. Wei, Adaptive tracking of linear time-variant systems by extended RLS algorithms. IEEE Trans. Signal Process. 45(5), 1118–1128 (1997) 17. C. Komninakis, C. Fragouli, A.H. Sayed, R.D. Wesel, Multi-input multi-output fading channel tracking and equalization using Kalman estimation. IEEE Trans. Signal Process. 50(5), 1065– 1076 (2002) 18. E.P. Simon, L. Ros, H. Hijazi, J. Fang, D.P. Gaillot, M. Berbineau, Joint carrier frequency offset and fast time-varying channel estimation for MIMO-OFDM systems. IEEE Trans. Vehic. Tech. 60(3), 955–965 (2011) 19. E.P. Simon, M.A. Khalighi, Iterative soft-Kalman channel estimation for fast time-varying MIMO-OFDM channels. IEEE Wireless Commun. Lett. 2(6), 599–602 (2013) 20. Y. Liao et al., EKF-based joint channel estimation and decoding design for non-stationary OFDM channel, in Proceedings of the IEEE Global Communications Conference, Singapore (2017), pp. 1–6 21. H. Kim, J.K. Tugnait, Turbo equalization for doubly-selective fading channels using nonlinear Kalman filtering and basis expansion models. IEEE Trans. Wirel. Commun. 9(6), 2076–2087 (2010) 22. Q. Shi, N. Wu, X. Ma, H. Wang, Frequency-domain joint channel estimation and decoding for faster-than-Nyquist signaling. IEEE Trans. Commun. 66(2), 781–795 (2018) 23. P. Pedrosa, R. Dinis, F. Nunes, A. Rodrigues, Joint frequency domain equalisation and phase noise estimation for single-carrier modulations in doubly-selective channels. IET Commun. 9(8), 1138–1146 (2015) 24. R. Dinis, A. GusmÃˇco, N. Esteves, On broadband block transmission over strongly frequencyselective fading channels, in Proceedings of the International Conference on Wireless Communications, Calgary (2003), pp. 261–269. 25. P. Montezuma, F. Silva, R. Dinis, Frequency-Domain Receiver Design for Doubly Selective Channels (CRC Press, Boca Raton, 2019) 26. F. Silva, R. Dinis, P. Montezuma, Estimation of the feedback reliability for IB-DFE receivers. ISRN Commun. Netw. 2011, 980830 (2011) 27. S.M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Upper Saddle River, 1993) 28. P. Tichavsky, C.H. Muravchik, A. Nehorai, Posterior Cramer-Rao bounds for discrete-time nonlinear filtering. IEEE Trans. Signal Process. 46(5), 1386–1396 (1998)

Chapter 2

Transmission Techniques for UAVs João Guerreiro and Rui Dinis

2.1 Introduction Unmanned aerial vehicles (UAVs) are gaining a tremendous importance for both military and civilian applications. Therefore, the design of energy-efficient and reliable wireless links for air-to-air (A2A) and air-to-ground (A2G) UAV communications is of extreme importance. That design should take into account the particularities of these channels, which depend on the flying altitude, type of UAV, type of environment, etc. [1]. Depending on the specific scenario, the required data rate and latency can vary substantially, which means that the underlying waveform should offer high flexibility. Regardless of the use case, most UAV communication channels present high multipath and a large Doppler spread [2]. In that context, block-transmission techniques such as orthogonal frequency-division multiplexing (OFDM) [3] arise as excellent candidates for unmanned aerial systems (UASs), since they offer several degrees of freedom regarding the design of the communication link and high robustness to multipath propagation and inter-symbol interference (ISI). This can be explained by the combination of large symbol times and a cyclic prefix (CP), which enable a simple frequency-domain equalization (FDE) that can be done efficiently in the digital domain. Besides these wellknown advantages, OFDM schemes present severe amplification issues due to the large envelope fluctuations of the resulting signals [4]. In the last years, several techniques for reducing the peak-to-average power ratio (PAPR) of OFDM have been proposed [5, 6]. However, these techniques often bring other drawbacks such as higher complexity, lower spectral efficiency, or nonlinear distortion. Therefore,

J. Guerreiro () · R. Dinis Faculdade de Ciências e Tecnologias da Universidade Nova de Lisboa, Monte da Caparica, Portugal e-mail: [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 D. N. K. Jayakody et al. (eds.), Integration of Unmanned Aerial Vehicles in Wireless Communication and Networks, Unmanned System Technologies, https://doi.org/10.1007/978-3-031-03880-8_2

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they do not constitute efficient solutions reducing the PAPR, i.e., the amplification issues of OFDM are still an open (and hot) topic among the research community. In fact, although energy efficiency is a very important aspect in modern wireless communications in general, it becomes particularly important for UAV communications. Clearly, UAV wireless links should offer a high energy efficiency, so that the battery lifetimes and the corresponding flight times can be maximized. Therefore, although OFDM is adequate for the downlink (i.e., for communication between the ground stations and the UAVs), it is not recommendable for the uplink, where the UAV acts as the transmitter and the energy efficiency should be as high as possible. In that sense, the single-carrier with frequency-domain equalization (SC-FDE) [7] can be an excellent alternative for the uplink. As OFDM, SC-FDE is a block-based transmission technique, which offers FDE equalization features [8]. However, its single-carrier nature leads to signals with lower envelope fluctuations than OFDM, which enables a more efficient amplification and, consequently, larger flight times. Therefore, OFDM and SC-FDE can be used together regarding the downlink and the uplink, respectively. In both techniques, the FDE can be done digitally by means of fast Fourier transform (FFT) algorithms, which constitutes a great advantage over complex, time-domain equalizers (TDEs) [9], enabling broadband transmissions in severely time-dispersive channels. In fact, OFDM and SC-FDE are widely used in broadband wireless communications such as long-term evolution (LTE) [10], 5G [11], and WiFi [12]. The organization of this chapter is as follows: Sect. 2.2 is concerned with OFDM techniques. While in Sect. 2.2.1 the nature and generation of OFDM signals are discussed, and in Sect. 2.2.2 the amplification issues of OFDM are analyzed. Section 2.3 is dedicated to SC-FDE techniques. Under this section, the nature and signal generation of SC-FDE signals are described in Sect. 2.3.1 and IB-DFE techniques are described in Sect. 2.3.2. Finally, Sect. 2.4 finalizes this chapter.

2.2 OFDM 2.2.1 Main Idea and Signal Generation Let us consider the A2A and A2G links represented in Fig. 2.1. In many use cases, these links require large data rates. However, it is well known that the adoption of large data rates leads to an increased ISI, which arises naturally due to the time-dispersive nature of the wireless propagation channels. In order to obtain reliable communications with high data rates in these environments, block-based transmission techniques such as OFDM can be employed. OFDM is a block-based, multicarrier transmission technique [3]. In contrast with single-carrier modulations where a high-rate data stream is transmitted directly in one carrier, an OFDM signal is composed by a set of N orthogonal carriers modulated by N low-rate data streams. These streams are transmitted in parallel

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UAV

UAV Ground Staon

Fig. 2.1 Representation of A2A and A2G links in a multipath propagation scenario

Fig. 2.2 General scheme of an OFDM transmitter and receiver

during the symbol time, which is N times larger than that of an equivalent singlecarrier transmission with the same data rate. The OFDM signal is also extended with the so-called cyclic prefix (CP). The CP consists in guard interval composed by the repetition of the last part of the signal that is appended to its beginning. It is well recognized that the CP is a very important feature of OFDM, since it allows to simplify the equalization process. Essentially, after removing the CP, the receiver transforms the frequency-selective channel as a set of N flat-fading channels without inter-carrier interference (ICI). These channels can be easily equalized with a digital, one-tap FDE. A general OFDM transceiver is represented in Fig. 2.2. As can be observed, OFDM signals are generated and decoded digitally with fast Fourier transform (FFT) algorithms, namely by means of an inverse discrete Fourier transform (IDFT) and a discrete Fourier transform (DFT), respectively. The IDFT’s input is a set of

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complex symbols selected from a given constellation that can be represented as {Sk ; k = 0, 1, · · · , N}. The IDFT output represents the time-domain samples of the underlying baseband OFDM signal {sn = IDFT(Sk ); n = 0, 1, · · · , N}. After the IDFT, the CP is appended to the block and a parallel-to-serial (P/S) converts the samples into a discrete stream. This stream is submitted to a digital-to-analog converter (DAC) and modulated by a carrier before being amplified and sent to the antenna. At the reception, an analog-to-digital converter (ADC) is used to recover the time-domain samples of the baseband OFDM signal. Then, the samples associated to the CP are discarded and serial-to-parallel (S/P) generates a block with the remaining samples, which are converted to frequency domain through a DFT so that the FDE can be performed. The received signal at the kth subcarrier is Yk = Sk Hk + Nk ,

(2.1)

where Hk and Nk denote the channel and the additive white Gaussian noise (AWGN) components for the kth subcarrier, respectively. The FDE consists in a multiplication of the signal represented in (2.1) by the equalization coefficients Fk , which are computed according to a given equalization criterion (e.g., minimum mean squared error (MMSE), zero forcing (ZF), etc.). The equalized signal is hence S˜k = Fk Yk .

(2.2)

After equalization, the samples are sent to the decision device that outputs the estimated symbols {Sˆk ; k = 0, 1, · · · , N}. Figure 2.3 shows the BER of an OFDM system with N = 256 subcarriers, QPSK constellations, and a ZF equalization.

2.2.2 Amplification Issues It is widely known that amplification is the most significant issue of OFDM. This is explained by the fact that OFDM signals are composed by the sum of several independent carriers, which means that they exhibit a large PAPR. In fact, the envelope of an OFDM signal is approximately Rayleigh distributed, provided that the number of subcarriers is large [13]. This characteristic of OFDM signals can be observed in Fig. 2.4, which shows the envelope of an OFDM signal with N = 256 subcarriers modulated by quadrature phase shift keying (QPSK) constellations. From the figure, one can note that the peak amplitude is much larger than the average amplitude. Therefore, OFDM signals present a large PAPR, which is defined for a given OFDM signal as PAPR =

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Fig. 2.5 Nonlinear PA characteristic operating with an IBO

where Pmax and Pavg represent the maximum and the average power of the signal, respectively. This issue can be even noticeable if larger constellations such as highorder quadrature amplitude modulation (QAM) are employed. A signal with such a level of envelope fluctuations cannot drive an efficient power amplifier (PA) that works close to the saturation, since that would lead to frequent excursions to the nonlinear region of the PA characteristic and yield intolerable nonlinear (NL) distortion effects at the PA output. This behavior is illustrated in Fig. 2.5, which shows the nonlinear characteristic of a conventional PA. The IBO is defined as IBO =

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where Pin,sat represents the input power that leads to the saturation and Pin,avg represents the average input power. Clearly, if a large IBO is not employed, there will be severe NL effects that would introduce both in-band radiation, which can severely degrade the performance (i.e., the bit error rate (BER)), as well as outof-band radiation that can compromise the underlying spectral mask. To avoid a nonlinear transmission, the PA should work significantly below the saturation, i.e., a large back-off should be adopted. However, the use of large back-offs leads to a strong reduction in the energy efficiency of the amplification process, not to mention a significant reduction of the coverage [14]. For this reason, OFDM transmissions are less suitable for battery-powered devices such as UAVs, where the energy efficiency is important to guarantee a large autonomy. This explains why OFDM is commonly adopted for downlink transmissions, where the access point

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(AP) or the base station (BS) can manage a lower energy efficiency, and not for uplink transmissions, where the mobile terminals need larger energy efficiencies to preserve their autonomy.

2.3 SC-FDE 2.3.1 Main Idea and Signal Generation SC-FDE is a single-carrier transmission technique that constitutes an alternative to OFDM [7, 15]. Due to their single-carrier nature, SC-FDE signals present much lower PAPR than multicarrier signals, which make them suitable for uplink transmissions [16]. Moreover, and besides having less amplification issues, the performance of SC-FDE is comparable to that of OFDM, although SC-FDE presents less flexibility regarding the matching of the transmissions characteristics (i.e., energy, constellation size) to the channel response. SC-FDE can be employed with iterative block decision feedback equalization (IB-DFE) schemes [17]. In fact, IBDFE are powerful nonlinear FDE schemes that can eliminate most of the residual ISI at the output of linear FDEs and achieve performances close to the matched filter bound (MFB) with controllable complexity [18]. As with OFDM, SC-FDE can be combined with MIMO schemes, namely to obtain diversity gains [19, 20]. A general SC-FDE transceiver is represented in Fig. 2.6. As it happens in OFDM, SC-FDE schemes operate on a block basis and consider a CP to reduce the ISI and ease the equalization process. Regarding the transmitter, an S/P gathers N data symbols to form the block of data. After that, a CP is inserted and a P/S block rebuilds the serial stream that will form the analog baseband signal at the DAC output. After the amplification, the signal is modulated by a carrier and sent to the transmit antenna.

Fig. 2.6 General scheme of an SC-FDE transmitter and receiver

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At the reception, the CP is removed and there is an S/P converter that rebuilds the block. Then, a DFT brings the samples to the frequency domain so that the FDE can be performed. The received signal on the kth subcarrier is given by: Yk = Sk Hk + Nk .

(2.5)

After the FDE process, the equalized samples should be converted to the time domain so that the decision device can estimate the transmitted symbols {ˆsn ; n = 0, 1, · · · , N}. In comparison with OFDM, it can be noted that although both techniques have a DFT in the receiver to perform the FDE, OFDM has the IDFT in the transmitter (since it transmits the data symbols in the frequency domain), while in SC-FDE, the IDFT is placed at the receiver, since the detection is made in the time domain. For this reason, although the overall complexity of both techniques is comparable, SC-FDE presents a less complicated transmitter and a more complicated receiver, and this explains why it fits well in uplink transmissions where autonomy is a concern and why it can be a good choice for UAV communications.

2.3.2 IB-DFE Like OFDM, the linear FDE can be carried out with different algorithms (e.g., MMSE, ZF, etc.). However, it has been shown that the performance of SC-FDE schemes can be substantially improved by using nonlinear FDE schemes [8, 17]. In IB-DFE, the equalization is performed in an iterative fashion (i.e., it can be repeated up to L times) so that the residual ISI that exists after the linear FDE (e.g., after the first iteration) can be removed and the performance can be enhanced. Figure 2.7 shows a block diagram of an IB-DFE receiver.

Fig. 2.7 Block diagram of an IB-DFE receiver

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The IB-DFE is characterized by the feedforward coefficients Fk and by the feedback coefficients Bk . Commonly, IB-DFE is used with MMSE and the coefficients Fk are computed as Hk∗ (l) Fk =  2 1 − ρ (l)  |Hk |2 +

1 SNR

(2.6)

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where ρ (l) denotes the reliability of the data block estimated at the lth iteration (the reader is referred to [18] for details on the computation of ρ (l) ) and SNR is the channel’s signal-to-noise ratio (SNR). This reliability improves as more equalization iterations are made. The feedback equalization coefficients Bk associated to a given iteration can be calculated as (l)

(l)

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(2.7)

Under these conditions, the equalized signal associated to the kth subcarrier at the lth iteration is computed as (l) (l) (l) (l−1) Sk = Fk Yk − Bk Sˆk .

(2.8)

Figure 2.8 shows the BER of an SC-FDE with IB-DFE considering different values of L and blocks with N = 256 subcarriers and QPSK constellations. From the 100

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figure, it can be noted that using a nonlinear FDE receiver leads to substantial performance improvements relatively to the linear FDE (which is the performance associated to L = 1). When L = 4, the BER is very close to the matched filter bound (MFB), which is the theoretical best performance that can be achievable. The SC-FDE with IB-DFE can be employed with multiple antenna systems, namely diversity techniques at the reception. Let us consider a receiver with P antennas. Figure 2.9 shows the BER of an IB-DFE scheme considering L = 4 iterations (only the 4th iteration is shown) and different diversity orders P . From the figure, it can be observed that by considering a receiver with P antennas, the performance can be substantially improved. In fact, when P > 1, the performance associated with L = 4 iteration is almost equal to the MFB.

2.4 Conclusions The particularities of UAV communications, especially the ones related to the energy efficiency requirements for the cases where the UAV is the transmitter, impose considerable restrictions on the transmission technique that should be employed. For this reason, besides OFDM presents a great flexibility to adapt the transmission to the channel conditions and less complex receivers, SC-FDE schemes

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are more adequate to UAV communications. This can be explained by the fact that single-carrier signals present a much lower PAPR than OFDM, which means that the energy efficiency at the transmitter (i.e., at the UAV) can be substantially higher. This promotes a larger autonomy and, consequently, larger flight times.

References 1. C. Yan, L. Fu, J. Zhang, J. Wang, A comprehensive survey on UAV communication channel modeling, in IEEE Access, vol. 7 (2019), pp. 107769–107792 2. Z. Wu, H. Kumar, A. Davari, Performance evaluation of OFDM transmission in UAV wireless communication, in Proceedings of the 37th Southeastern Symposium on System Theory, 2005. (SSST ’05), Tuskegee, AL 3. L. Cimini, Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing. IEEE Trans. Commun. 33(7), 665–675 (1985) 4. H. Ochiai, H. Imai, On the distribution of the peak-to-average power ratio in OFDM signals. IEEE Trans. Commun. 49(2), 282–289 5. T. May, H. Rohling, Reducing the peak-to-average power ratio in OFDM radio transmission systems, in Proceedings of IEEE VTC ’98, Ottawa, 1998 6. Y. Rahmatallah, S. Mohan, Peak-To-average power ratio reduction in OFDM systems: a survey and taxonomy. IEEE Commun. Surv. Tutor. 15(4), 1567–1592 (fourth quarter, 2013) 7. D. Falconer, S.L. Ariyavisitakul, A. Benyamin-Seeyar, B. Eidson, Frequency domain equalization for single-carrier broadband wireless systems. IEEE Commun. Mag. 40(4), 58–66 (2002) 8. N. Benvenuto, R. Dinis, D. Falconer, S. Tomasin, Single carrier modulation with nonlinear frequency domain equalization: an idea whose time has come—again. Proc. IEEE 98(1), 69– 96 (2010) 9. S. Qureshi, Adaptive equalization. Proc. IEEE 73(9), 1349–1387 (1985) 10. 3rd Generation Partnership Project: technical specification group radio access network; physical layers aspects for evolved UTRA. 3GPP TR 25.814, Sept. 2006 11. A.A. Zaidi, R. Baldemair, V. Moles-Cases, N. He, K. Werner, A. Cedergren, OFDM numerology design for 5G new radio to support IoT, eMBB, and MBSFN. IEEE Commun. Stan. Mag. 2(2), 78–83 (2018) 12. 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. In IEEE Std 802.11-2016 13. S. Wei, D.L. Goeckel, P.A. Kelly, Convergence of the complex envelope of bandlimited OFDM signals. IEEE Trans. Inf. Theory 56(10), 893–4904 (2010) 14. J. Joung, C.K. Ho, S. Sun, Spectral efficiency and energy efficiency of OFDM systems: Impact of power amplifiers and countermeasures. IEEE J. Select. Areas Commun. 32(2), 208–220 (2014) 15. F. Pancaldi, G.M. Vitetta, R. Kalbasi, N. Al-Dhahir, M. Uysal, H. Mheidat, Single-carrier frequency domain equalization. IEEE Signal Process. Mag. 25(5), 37–56 (2008) 16. A. Gusmão, R. Dinis, J. Conceição, N. Esteves, Comparison of two modulation choices for broadband wireless communications, in Proceedings of the VTC2000-Spring, Tokyo, Japan, 2000 17. N. Benvenuto, S. Tomasin, Block iterative DFE for single carrier modulation. Electron. Lett. 38(19), 1144–1145 (2002)

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18. F. Silva, R. Dinis, P. Montezuma, Approaching the matched filter bound with coded OFDM and SC-FDE schemes, in 2011 - MILCOM 2011 Military Communications Conference, Baltimore, MD (2011), pp. 595–599 19. N. Al-Dhahir, Single-carrier frequency-domain equalization for space-time block-coded transmissions over frequency-selective fading channels. IEEE Commun. Lett. 5(7), 304–306 (2001) 20. A. Gusmão, R. Dinis, N. Esteves, On frequency-domain equalization and diversity combining for broadband wireless communications. IEEE Commun. Lett. 51(7), 1029–1033 (2003)

Chapter 3

Self-energising of Full-Duplex UAV-Assisted Wireless Networks Anandpushparaj Jeganathan, Gupta Mitali, Dushantha Nalin K Jayakody, and P. Muthuchidambaranathan

3.1 Introduction The cooperative wireless communication is one of the promising techniques used in future wireless cellular technology (5G). It improves the system performance and provides better range of communication. The contemporary cellular relays have certain limitations, like transmit power, limited mobility, energy management, capacity and coverage [1]. The finest choice to combat these limitations is to use unmanned aerial vehicles (UAVs) as a portable relay. It was first suggested for military-based applications because of their low cost, great mobility and reliability [2]. UAVs as cooperative relay have numerous applications in the field of disaster management, law enforcements, wildlife monitoring, surveillance and search and rescue operations, etc. [3]. Furthermore, UAVs provide a strong line-of-sight (LoS) environment that allows for higher data rates, improved coverage and capacity [4, 5]. One of the most challenging aspects of using UAVs as mobile relays is the restricted on-board weight and hovering duration. The UAVs to have light weight architecture, it is preferred to power them using rechargeable batteries design. But, it is not always possible to replace and recharge exhausted batteries. As a result, researchers have developed an enabling technique called radio frequency energy harvesting (RF-EH) to extend the life of UAV-operated batteries. This delivers a

A. Jeganathan () · G. Mitali · P. Muthuchidambaranathan Department of Electronics and Communication Engineering, National Institute of Technology, Tiruchirappalli, Tamilnadu, India e-mail: [email protected] D. N. K. Jayakody COPELABS, Lusófona University, Lisbon, Portugal e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 D. N. K. Jayakody et al. (eds.), Integration of Unmanned Aerial Vehicles in Wireless Communication and Networks, Unmanned System Technologies, https://doi.org/10.1007/978-3-031-03880-8_3

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huge benefit to the user at the destination, which is positioned far away [6, 7]. In RFEH, the most promising technique is simultaneous wireless information and power transfer (SWIPT), which transfers both energy and information in the same RF band at the same time [8]. In regard to conceptual understanding and practical analysis of SWIPT aspects, major literature and research investigations have been undertaken in [9, 10]. In [11] two SWIPT approaches are investigated, i.e. power splitting (PS) and time switching (TS) architectures and also shown that how PS excels TS on the basis of system performance. In [12] the effect of self-interference on UAV signal power is explored using the SWIPT-based approach. In [13, 14] it was suggested that using UAVs as half-duplex (HD) relays would improve coverage and reliability. In [15], the author established full-duplex (FD) communications, presenting a resource allocation technique for UAV-aided communication using UAV as a source of energy. In order to increase the performance of the system, the authors in [16–20] propose a simple technique, where a user terminal is energised using power signal from base station. According to the author in [21], there is a limited spectral efficiency of half-duplex UAV, because of its time sharing behaviour. As a result of incorporating FD-UAV, performance of the system is enhanced by permitting continuous reception and transmission of the same spectrum, resulting in a spectral efficiency nearly double that of an HD system. Only a few works related to FD-enabled UAV designs for cooperative communication are now available. We proposed a full-duplex UAV communication without energy harvesting and investigated the key metrics of system outage and throughput in [22]. Author in [23] analysed TS-SWIPT and EH technique to energise full-duplex UAV on Rayleigh fading channel model using loop back self-interference. In [24, 25], it is more significant to consider the generalised fading channel model to characterise the wireless system. For better system implementations, most UAV-based studies use classical fading channel distributions such as Nagakami-m, Rayleigh, Rician and others. In this study, we used a generalised fading channel model, which is a Weibull fading channel that has recently attracted the attention of the scientific community. The Weibull distribution was identified as the probability distributions for modelling amplitude fading in a varying environment and was also recognised as an effective measurement method for empirical channel models [26, 27]. It may be used to demonstrate UAV fading channels with severe fading characteristics that are suitable for higher altitude and open space usages. It provides a lot of flexibility when it comes to characterising UAV fading channels in various conditions, and less practical research on the Weibull distribution have been reported [28–30]. The values of the Weibull fading parameter can range from 0 to ∞. When this parameter is set to β = 1, the system acts like Rayleigh distribution, and when it is set to β = 2, the system acts like Nagakami-m fading channel. β < 2 denotes extreme fading, resulting in severe LOS and NLOS scenarios [31, 32]. To the finest knowledge of the authors, this is the initial study to use FD-UAV communication using the Weibull fading channel model.

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41

Our primary contributions of this chapter are summarised as follows: – An unified scheme of TS-SWIPT decode and forward energy harvesting with loop back Self Interference mechanism is presented over Weibull channel for full-duplex UAV-aided co-operative wireless communication. Interference exploitation is carried out, when Self Interference on UAV is used as an energy harvesting source. – We analyse the outage probability and system throughput of an UAV-assisted full-duplex system using performance factors, open space applications and transmit power in various fading scenarios. We also came up with a closed form expression for it. For both HD/FD systems, the sub-optimal values for the TS scheme (α) are also shown. – We also use a direct path between the source and the desired user at destination, as well as a relay link, to obtain diversity gain. We use the selection combining (SC) approach at the receiver for simplicity.

3.2 System Model In urban cities, due to many man-made structures like buildings, towers, bridges etc., the communication is frequently disturbed, the signals are scattered and line-ofsight (LoS) is not achieved. Due to non-line-of-sight (NLoS) state, signal strength at the destination is frequently faded. Thus, to aid to communication, we assume a cooperative wireless communication network, where the source communicates with the desired user at the destination via a cooperative relay provided by a UAV to get better LoS component. In this chapter, we assume such an environment, as depicted in Fig. 3.1. The source and desired user are presumed to be equipped with one antenna each working on the same frequency. On the contrary, for both full and half-duplex operations, the UAV has two antennas, to facilitate simultaneous reception and transmission at the relay. The signal being transmitted from the UAV to the destination offers strong self-interference (SI) to the signal being received from the source at the UAV owing to two antennas operation in FD mode. In this chapter, we shall explore a dual hopping of cooperative communication system with a UAV flying at a distance dsr from source (Base station) to relay (UAV), and drd from relay to destination (desired user), with a height hu from ground surface. The distance between the direct link, i.e. source to desired user is considered as dsd . There are many protocols used for relay transmission like amplify and forward, selective and forward etc. and the fading channel can be modelled using Rayleigh, Rician etc. distributions. But in this chapter, we assume UAV to adhere to the decode and forward protocol and a generalised Weibull fading distribution as the channel model [12], of which the probability density function (PDF) is as follows:

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Fig. 3.1 Illustration of UAV-assisted cooperative communication in urban environments

fi (x) =

 βi  βi βi −1 x , x exp − γi γi

(3.1)

where i indicates the corresponding channel, βi represents fading parameter of the channel, which expresses the degree of fading and γi is the average signal-to-noise ratio (SNR). We also assume that the UAV uses SWIPT technology and follows a time splitting scheme. As shown in Fig. 3.2, the system devotes the entire αT duration for receiving and harvesting energy at the UAV using SWIPT link for subsequent operation. The remaining (1 − α)T duration is then utilised for information transfer in HD, which is further splitted into two parts: first for source to relay transmission, and second for transmission from relay to destination. However, in FD mode, information is transferred and received concurrently in (1 − α)T time, where α is the time splitting factor.

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Fig. 3.2 Timing diagram of the proposed system for HD/FD UAV systems, where αT indicates the time allocated for WPT, (1 − α)T for WIT and T represents the overall UAV operational time

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3.3 Co-operative Communication System in the Absence of Direct Link 3.3.1 Half-Duplex Transmission In the communication and transmission phase, the source first sends a signal x to UAV through the SWIPT link, and corresponding energy is captured at the relay. The obtained signal at the UAV is given by: Yu =

 −m Ps hsr xdsr + nsr ,

(3.2)

where hsr denotes the fading coefficients of Weibull channel, x is the information signal from source, Ps is transmitted power from base station, m represents path loss exponent, dsr is the distance between source and UAV(relay) and nsr is the additive white Gaussian noise (AWGN) with mean as zero and variance as σsr 2 . In αT duration, the maximum harvested energy at relay (UAV) is given as −m . Eh = αT ηPs |hsr |2 dsr

(3.3)

Here, η(0 ≤ η ≤ 1) is the harvesting efficiency and the TS factor is α(0 ≤ α ≤ 1). The energy harvested because of the noise power is insignificant, when compared to the harvested energy using signal power, hence it is ignored. In relay phase duration, the following information signal is received at the UAV: Yu =

 −m Ps hsr xdsr + nsr .

(3.4)

The channel coefficients between the source and the UAV that follow the Weibull distribution are represented by hsr . The SNR at the UAV is calculated as follows: γsr =

Ps |hsr |2 . mσ 2 dsr sr

(3.5)

In the relay phase, the received information is then decoded by the UAV and the decoded information x is sent to the intended user in the subsequent phase. At the destination (User), the signal received is given as: Yd =



−m Pr drd x hrd + nrd ,

(3.6)

where the transmit power without loss from the relay is Pr . The Weibull channel fading co-efficient between the relay and the desired user is hrd , the distance between the relay and the desired user is drd , and the AWGN noise with zero mean 2 is n . and variance σrd rd After energy harvesting, the UAV’s radiated power, Pr , is expressed as

3 Self-energising of Full-Duplex UAV-Assisted Wireless Networks

Pr =

2Eh . (1 − α)T

45

(3.7)

At the destination, the overall corresponding SNR is given by: γrd =

Pr |hrd |2 mσ 2 . drd rd

Substituting from Eq. (3.7), γrd =

2ηαPs |hsr |2 |hrd |2 . m d m (1 − α)σ 2 dsr rd rd

(3.8)

For simplicity, it can be written as γrd = Φ|hsr |2 |hrd |2 , where Φ =

2ηαPs m d m (1−α)σ 2 . dsr rd rd

3.3.2 Overall Outage Performance of Half-Duplex Transmission It is the probability in which the information rate is lower than the needed threshold. The outage probability (OP) analysis for half-duplex mode is realised over Weibull channel with various fading parameters. The OP from source to relay is found as:   γth , Poutsr = P (γsr ≤ γth ) = P x ≤ ρ1

(3.9)

where ρ1 = d mPσs 2 and x denotes |hsr |2 . sr sr The Poutsr is calculated as below taking Weibull fading distribution into consideration:  Poutsr =

  β β−1 xβ dx. x exp − γsr γsr

γth ρ1

0

For ease of integration, we substitute x β = t, thus we have βx β−1 dx = dt, which lead to  Poutsr =

( 0

γth β ρ1 )

  −t 1 exp dt. γsr γsr

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On solving the above equation after integration, we get  Poutsr = P (γsr ≤ γth ) = 1 − exp

−γ th β



β

.

(3.10)

ρ1 γsr

Similarly, OP from relay(UAV) to desired user is obtained as: Poutrd = 1 − P (γrd > γth ),

(3.11)

which can be written as below from Eq. (3.8): P (γrd > γth ) = P (Φ|hsr |2 |hrd |2 > γth ). Further, we can write   γth , P (γrd > γth ) = P x > Φy where x corresponds to |hsr |2 and y to |hrd |2 . The Poutrd is calculated as below taking Weibull fading distribution into consideration:    ∞ β β−1 xβ Poutrd = γ dx. x exp − th γsr γsr Φy For ease of integration, first we solve by keeping y as a constant and considering x β = t thus, its first derivative βx β−1 dx = dt, we get  P (γrd > γth ) =

∞ γ

th )β ( Φy

  1 −t dt. exp γsr γsr

On integration, we get  P (γrd > γth ) = exp

β

γth β Φ γsr y β

 .

Now integrating with respect to y considering Weibull fading distribution for channel modelling, we get  P (γrd > γth ) = 0

∞

    β γth β β−1 yβ exp y exp − dy γrd γrd Φ β γsr y β

3 Self-energising of Full-Duplex UAV-Assisted Wireless Networks

β = γrd





∞

y

β−1

0

β

γ yβ exp − − β th β γrd Φ γsr y

47

 dy.

(3.12)

Using the formula given from the equation 3.478-4 in [33], it is obtained that

P (γrd

⎡  ⎛  ⎞⎤  2ββ β β γth β ⎣ 2 γth γrd ⎠⎦ > γth ) = K1 ⎝ 2 γrd β Φ β γsr γsr γrd φ β ⎛  ⎞ β β γth γth ⎠. =2 K1 ⎝2 γsr γrd φ β γsr γrd φ β 

Thus, we have ⎛  ⎞ β β γth γth ⎠, ≤ γth ) = 1 − 2 K1 ⎝2 γsr γrd φ β γsr γrd φ β 

Poutrd = P (γrd where φ =

2ηαPs m d m (1−α)σ 2 dsr rd rd

(3.13)

and K1 (.) is the modified Bessel function of first kind.

By transmitting information through UAV as relay, the OP for HD system can be determined by taking the minimum of two obtained SNRs as: PoutH D = 1 − (1 − Poutsr )(1 − Poutrd ).

(3.14)

The closed form equation of OP for half-duplex system in the absence of direct path is derived as follows by substituting Eq. (3.10) and (3.13) in (3.14): ⎡ PoutH D = 1 − ⎣exp



−γ th β

β

ρ1 γsr



⎛  ⎞⎤ β β γth γth ⎠⎦ . K1 ⎝2 ×2 γsr γrd φ β γsr γrd φ β 

(3.15)

3.3.3 Full-Duplex Transmission As discussed earlier, due to the presence of two antennas at the relay(UAV), we infer a strong signal interference(SI) from the loop back channel hrr in the FD operation. In recent years, there have been several SI cancellation algorithms that may efficiently cancel out SI; but, due to imperfection, some residual loop interference is generally present in the signal obtained after decoding. Equations (3.2) and (3.3) show the received power signal by the UAV and the energy harvested, respectively. In the second phase, the information signal received

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by the UAV is Yu =

 −m Ps hsr xdsr + q Pr hrr x +nsr . " #$ % " #$ %



Signalf romSource

(3.16)

LoopbackSI

Here q ∈ (0, 1). This variable shows that if q = 0, the system operates in HD mode, i.e. there is absence of loop back self-interference. If q equals 1, the system operates in FD mode. hrr is the loop back interference fading coefficient at the UAV, after energy harvesting Pr is the power radiated from the UAV and x is the transmitted signal from relay after modulation. The UAV’s radiated power after energy harvesting is expressed as Pr =

Eh , (1 − α)T

(3.17)

and the signal-to-noise plus interference ratio (SINR) at the FD-UAV is given by: γsr =

−m Ps |h|2 dSR . 2 Pr |hrr |2 + σsr

(3.18)

In this chapter, we also study the impact of selection combining (SC) technique on our system to promote diversity at the destination. We assume the desired user acquires the information from two directions. The first is a strong direct path between the source and the desired user and the second is via UAV(relay).

3.3.4 Overall Outage Performance of Full-Duplex Transmission We now derive the expressions for overall OP for the FD mode, modelling the channel using Weibull fading distribution. We can write the OP from source to relay as follows: Poutsr = P (γsr ≤ γth ).

(3.19)

Using Eq. (3.18), we can rewrite the above as:    ty + 1 , Poutsr = P x ≤ γth ρ1 ηPs α 2 2 where ρ1 = d mPσs 2 , t = σP2r = (1−α)σ 2 ,x corresponds to |hsr | and y to |hrr | . sr s sr sr Considering both the channel models follow the Weibull fading distribution, we can write

3 Self-energising of Full-Duplex UAV-Assisted Wireless Networks

 Poutsr =

γth (ty+1) ρ1

0

49

  β β−1 xβ dx. x exp − γsr γsr

Here considering x β = a and thus its first derivative as βx β−1 dx = da, we can rewrite the above equation as expressed below:  Poutsr =



γth (ty+1) β ρ1

0

  1 −a da. exp γsr γsr

On solving the above, we get  Poutsr = P (γsr ≤ γth ) = 1 − exp

β

−γ th (ty + 1)β



β

(3.20)

.

ρ1 γsr

The OP from relay to the desired user is obtained same as that in HD mode because the OP of the relayed signal from UAV to destination remains same for the same environmental conditions and is given as:

Poutrd = P (γrd where φ2 =

& ' ' ≤ γth ) = 1 − 2(

β γth

⎛ & ' ' ( ⎝ K 2 β 1

γsr γrd φ2

⎞

β γth β

⎠,

(3.21)

γsr γrd φ2

ηαPs . m d m (1−α)σ 2 dsr d rd

The total OP for the full-duplex system can be determined using cooperative relaying as follows: PoutF D = 1 − (1 − Poutsr )(1 − Poutrd ). The closed form equation of OP for full-duplex system in the absence of direct link is on substituting Eqs. (3.20) and (3.21) in above can be observed as: ⎡ PoutF D = 1 − ⎣exp



β −γ th (ty + 1)β β ρ1 γsr

 & ' ' 2(

β γth

⎛ & ' ' K ⎝2( β 1

γsr γrd φ2

⎞⎤

β γth β

⎠⎦ .

γsr γrd φ2

(3.22) Thus, it is observed that the loop-back SI at UAV has a significant impact on the system performance. As a result, the researchers continue to focus on overcoming the effect of loop-back SI in UAVs and improving system performance by giving diversity gain to the destination node while also taking into account information communicated via the direct path.

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3.4 Co-operative Communication in the Presence of Direct Link There are many combining techniques available these days, like maximal-ratio combining, equal-gain combining etc. For simplicity, we use the selection combining (SC) technique here, which considers one path signal with the highest instantaneous SNR related to the system at the destination, as shown below: γSC = max (min(γsr , γrd ), γsd ) .

(3.23)

The OP employing Weibull channel distribution from source to destination is as follows:   −γ th β . (3.24) Poutsd = P (γsd ≤ γth ) = 1 − exp ρ β γsd where ρ = d mPσs 2 . sd sd As a result, the total OP of the system utilising SC at the destination can be written as: PoutSC = Poutsrd × Poutsd ,

(3.25)

where Poutsrd corresponds to PoutH D or PoutF D for half- and full-duplex mode, respectively.

3.4.1 Half-Duplex Transmission Total HD system OP, utilising SC at the receiver of the destination, is written as: PoutSCH D = PoutH D × Poutsd .

(3.26)

To calculate the outage of the system at the desired user adopting SC in halfduplex mode, we multiply Eq. (3.15) and (3.24) and the obtained result can be written as ⎛ ⎡ ⎛  ⎞⎤⎞    β β β γ γ −γ th th th ⎠⎦⎠ PoutSCH D = ⎝1 − ⎣exp K1 ⎝2 2 β γsr γrd φ β γsr γrd φ β ρ γsr 1

   −γ th β × 1 − exp . ρ β γsd (3.27)

3 Self-energising of Full-Duplex UAV-Assisted Wireless Networks

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3.4.2 Full-Duplex Transmission Total FD system OP, utilising SC at the receiver of the destination, is written as: PoutSCF D = PoutF D × Poutsd .

(3.28)

To calculate the OP of the system at the desired user adopting SC in full-duplex mode, we multiply Eq. (3.22) and (3.24) and the obtained result can be written as ⎛

⎡

PoutSCF D = ⎝1 − ⎣exp



β

−γ th (ty + 1)β β

ρ1 γsr β 

  −γ th × 1 − exp ρ β γsd

 & ' ' 2(

β

γth

⎛ & ' ' K ⎝2( β 1

γsr γrd φ2

⎞⎤⎞

β

γth β

⎠⎦⎠

γsr γrd φ2

. (3.29)

3.4.3 Average Throughput Analysis of Both Half- and Full-Duplex Transmission The system’s throughput is the rate at which information is successfully delivered through a wireless communication channel. For our suggested model, we investigate the influence of the SC approach on a delay limited/delay intolerant system. The following is the HD system’s throughput: T  TpH D = R 1 − Poutx , 2

(3.30)

where T is the total time taken for each transmissions and R is the transmission rate. x = H D/SCH D , with the former indicating cooperative transmission only and the latter indicating cooperative transmission in the presence of direct path between source and desired user. Similarly, throughput of full-duplex system is given as:   TpF D = R 1 − Poutx T ,

(3.31)

where x = F D/SCF D , former denoting the case of cooperative communication in the absence of direct path, whereas latter denoting in the presence of the direct path between source and desired user, respectively.

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3.5 Numerical Results This section demonstrates the efficacy of the above-proposed HD and FD system for UAV-assisted SWIPT-based communication. The simulations are done on the MATLAB platform to present the observations and findings. The values of certain parameters are allotted to generate the numerical results. The distance between source and the desired user, i.e. dsd , which is normalised to 1 so that dsr =0.5 and drd =0.5, the transmission rate R is taken as 1 bit/sec/Hz, the transmission duration T is fixed at 1 sec, the energy harvesting efficiency η=1 and the path loss exponent m is taken as 2. On the other hand, values of other parameters like time splitting factor α, residual SI at relay and fading parameter β are varied to do the analysis. It is also assumed that σsd = σsr = σrd =1. Figure 3.3 plots the OP of HD/FD UAV-aided cooperative systems with respect to SNR with different fading parameters (β). The α value is set to 0.3 and residual loop-back SI is taken as −30 dB to plot this curve. The OP reduces throughout a wide range of transmitting SNR, as can be seen in the plot. Moreover, it is discerned that for β = 1, the system acts like a Rayleigh fading environment characterising the NLoS scenario and for β = 2 displays behaviour as Nakagami-m fading environment portraying LoS-like scenario. In addition, it is observed that as the β value increases, the performance of system improves as better LoS environment and diversity is offered. For both integer and non-integer β values of the generalised Weibull fading channel, the system functions flawlessly. We also notice that while the FD system performs better than the HD system under low SNR conditions, the

100

Outage Probability

10-2

10-4

10-6

HD with FD with HD with FD with HD with FD with HD with FD with

10-8

10-10

10-12

0

5

=1 =1 =1.5 =1.5 =2 =2 =2.5 =2.5 10

15

20

25

30

35

40

45

50

SNR(dB) Fig. 3.3 Overall outage probability at the destination of full- and half-duplex systems with respect to SNR in different β values, β ∈ (1, 1.5, 2, 2.5)

3 Self-energising of Full-Duplex UAV-Assisted Wireless Networks

53

0.7 0.6

Throughput

0.5 0.4

HD with =1 FD with =1 HD with =1.5 FD with =1.5 HD with =2 FD with =2 HD with =2.5 FD with =2.5

0.3 0.2 0.1 0 0

5

10

15

20

25

30

35

40

45

50

SNR(dB) Fig. 3.4 Average throughput at the destination of full- and half-duplex systems with respect to SNR in different β values, β ∈ (1, 1.5, 2, 2.5)

HD system performs better under high SNR conditions due to the loop back SI at the relay. Figure 3.4 shows throughput vs. SNR for various β values. As anticipated, the FD system surpasses the HD system, with nearly double the throughput. Furthermore, as the β value grows, the system saturates quickly at low SNR values, and the FD system saturates earlier than the HD system due to the strong signal power. Figure 3.5 shows the OP system performance vs. time splitting factor (α). With respect to α, it is found that when the SNR grows, OP first falls and subsequently increases. As a result, OP and α are mutually exclusive. We numerically find suboptimum values of α due to mathematical complexity, as shown in Table 3.1. Due to increment in loop-back SI at UAV in asymptotic SNR region, the sub-optimum value of α for HD climbs gradually, whereas the value for FD reduces dramatically as the SNR increases. It signifies that the time necessary for successful information signal transmission is shorter. Similarly, Fig. 3.6 displays throughput vs. time splitting factor (α), revealing that as the SNR rises, better throughput is attained. Furthermore, FD always outperforms HD in terms of throughput. The comparison of full- and half-duplex systems in the presence and absence of SC is shown in Fig. 3.7. The system gets improved outage performance with SC due to the diversity advantage leveraged by the SC, as seen in the figure. Furthermore, it is noticed that the FD system always outperforms the HD system at low SNR, while the HD system outperforms the FD system at high SNR. This is because at high SNR the loop-back SI is very strong at UAV, which degrades the performance of the system.

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Outage Probability

10-2

10-4

HD at SNR=20dB FD at SNR=20dB HD at SNR=30dB FD at SNR=30dB HD at SNR=40dB FD at SNR=40dB

10-6

10-8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time splitting factor ( ) Fig. 3.5 Outage probability at the destination node of full- and half-duplex systems with respect to time splitting parameter (α) at different SNR

Table 3.1 Using Fig. 3.5, sub-optimal values of (α) time splitting factor for both full- and halfduplex systems SNR (dB) 20 30 40

Full-duplex system (via relay) 0.43 0.39 0.25

Half-duplex system (via relay) 0.35 0.36 0.37

Full-duplex system (with SC) 0.43 0.39 0.25

Half-duplex system (with SC) 0.35 0.36 0.37

For various fading parameter values, Fig. 3.8 depicts the OP vs. SNR. As expected, SC offers diversity gain at the destination, which, when combined with higher β values, considerably improves total system performance. The average throughput of full- and half-duplex systems is plotted against SNR and time splitting factor in Figs. 3.9 and 3.10. It has been found that as we use SC at the destination, the system performance improves, allowing us to take advantage of the diversity. The performance of the full-duplex system for varied residual self-interference at UAV after nullifying the loop-back SI is compared in Fig. 3.11, utilising modern SI cancellation approaches. Loop-back SI is recognised as having a significant impact on outage. The system performance enhances as the residual SI at the relay diminishes. As a result, it is advised that stronger SI cancellation methods be used at the relay to reduce the loop back SI.

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0.8 Half duplex at SNR=5dB Full duplex at SNR=5dB Half duplex at SNR=7dB Full duplex at SNR=7dB Half duplex at SNR=10dB Full duplex at SNR=10dB

0.7

Throughput

0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time splitting factor ( ) Fig. 3.6 Average throughput of full- and half-duplex systems at different SNR with respect to time splitting factor (α) 100

10-2

Outage Probability

10-4

10-6

10-8

10-10

10

Half Duplex Via Relay Half Duplex with SC Full Duplex Via Relay Full Duplex with SC

-12

10-14

0

5

10

15

20

25

30

35

40

45

50

SNR(dB) Fig. 3.7 Outage probability with and without SC at the destination node of full- and half-duplex systems with respect to different SNR

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Outage Probability

10-5

10-10

HD Via Relay, HD with SC, FD Via Relay, FD with SC, HD Via Relay, HD with SC, FD Via Relay, FD with SC,

10-15

10-20

10-25

0

5

10

15

=1.5 =1.5 =1.5 =1.5 =2.5 =2.5 =2.5 =2.5 20

25

30

35

40

45

50

SNR(dB) Fig. 3.8 Overall outage probability with and without SC at the destination node of full- and halfduplex systems with respect to SNR in different β values, β ∈ (1, 1.5, 2, 2.5)

0.7 0.6

Throughput

0.5 0.4

HD Via Relay, HD with SC, FD Via Relay, FD with SC, HD Via Relay, HD with SC, FD Via Relay, FD with SC,

0.3 0.2 0.1

=1.5 =1.5 =1.5 =1.5 =2.5 =2.5 =2.5 =2.5

0 0

5

10

15

20

25

30

35

40

45

50

SNR(dB) Fig. 3.9 Average throughput with and without SC at the destination node of full- and half-duplex systems with respect to SNR in different β values, β ∈ (1, 1.5, 2, 2.5)

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1

HD through relay at SNR=10dB HD with SC at SNR=10dB FD through relay at SNR=10dB FD with SC at SNR=10dB

0.9 0.8

Throughput

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time splitting factor ( ) Fig. 3.10 Average throughput of full- and half-duplex systems with varying time splitting factor (α), with and without selection combining with SNR at 10 dB

100

Outage Probability

10-5

10-10

-15

10

10-20 10

FD through relay with residual SI=10dB FD through SC with residual SI=10dB FD through relay with residual SI=20dB FD through SC with residual SI=20dB FD through relay with residual SI=30dB FD through SC with residual SI=30dB 15

20

25

30

35

40

45

50

SNR(dB) Fig. 3.11 Overall outage probability with and without SC at destination node of full- and halfduplex systems with respect SNR in different residual SI ∈ (10, 20, 30) dB

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3.6 Conclusions In this chapter, we investigated the system performance of full- and half-duplexed UAV network for a wireless cooperative communication system using the SWIPT technique with TS protocol. In the presence of a direct link between source and desired user, we derived closed form mathematical expressions for an outage probability and average throughput for a dual-hop decode and forward UAV system. For the system analysis, we used a generalised Weibull fading channel, which has never been studied before in the field of UAV-aided systems. We observed that the performance of our recommended UAV-aided full-duplex architecture model acts better based on numerical results, when the self-interference at the UAV is less. Furthermore, using a selection combining technique at the receiver helps to mitigate the self-interference effect in high SNR regime. Numerical simulations are used to verify the analytical derivations, indicating that they could be used in future wireless communication networks.

References 1. M. Dohler, Y. Li, Cooperative Communications: Hardware, Channel and PHY (John Wiley & Sons, 2010) 2. M.F.J. Pinkney, D. Hampel, S. DiPierro, Unmanned aerial vehicle (UAV) communications relay, in Proceedings of MILCOM ’96 IEEE Military Communications Conference, McLean, VA, vol. 1 (1996), pp. 47–51. https://doi.org/10.1109/MILCOM.1996.568581 3. M. Mozaffari, W. Saad, M. Bennis, Y. Nam, M. Debbah, A tutorial on UAVs for wireless networks: applications, challenges, and open problems. IEEE Commun. Surv. Tutorials 21(3), 2334–2360, thirdquarter (2019) 4. K.P. Valavanis, G.J. Vachtsevanos, Handbook of Unmanned Aerial Vehicles (Springer Publishing Company, Incorporated, 2014) 5. J. Anandpushparaj, V. Palliyembil, L.G. Nadiminti, M. Magarini, P. Muthuchidambaranathan, Performance analysis of UAV cellular communications, in 2019 TEQIP III Sponsored International Conference on Microwave Integrated Circuits, Photonics and Wireless Networks (IMICPW), Tiruchirappalli (2019), pp. 370–373. https://doi.org/10.1109/IMICPW.2019. 8933212 6. X. Lu, P. Wang, D. Niyato, D.I. Kim, Z. Han, Wireless networks with RF energy harvesting: a contemporary survey. IEEE Commun. Surv. Tutorials 17(2), 757–789, Secondquarter (2015). https://doi.org/10.1109/COMST.2014.2368999 7. H.J. Visser, R.J.M. Vullers, RF energy harvesting and transport for wireless sensor network applications: principles and requirements. Proc. IEEE 101(6), 1410–1423 (2013). https://doi. org/10.1109/JPROC.2013.2250891 8. I. Krikidis, S. Timotheou, S. Nikolaou, G. Zheng, D.W. Ng, R. Schober, Simultaneous wireless information and power transfer in modern communication systems. IEEE Commun. Mag. 52(11), 104–110 (2014) 9. H. Chen, Y. Li, J.L. Rebelatto, B.F. Uchoa-Filho, B. Vucetic, Harvest-then-cooperate: Wirelesspowered cooperative communications. IEEE Trans. Signal Process. 63(7), 1700–1711 (2015) 10. A.A. Nasir, X. Zhou, S. Durrani, R.A. Kennedy, Relaying protocols for wireless energy harvesting and information processing. IEEE Trans. Wirel. Commun. 12(7), 3622–3636 (2013). https://doi.org/10.1109/TWC.2013.062413.122042

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Chapter 4

UAV-Assisted Wireless Power Sensor Networks Stefan Panic and Caslav Stefanovic

4.1 Introduction Enhancing reliability of wireless communication systems with low latency and energy consumption is critical for emergency situations, safety missions, freight, and agriculture. Therefore, using UAVs has been a subject of concerted research over the past few years, owing to their autonomy, flexibility, and broad range of application domains. Indeed, UAVs have been considered as enablers for various applications that include military, surveillance and monitoring, telecommunications, delivery of medical supplies, and rescue operations. In particular, UAV-assisted relaying is able to serve existing networks by enabling communication between two nodes suffering from blockages and by recovering the network in inaccessible disaster affected areas. However, there also exist challenges in UAV-assisted relaying including frequent power shortages resulting from the limited size and weight of a battery in particular for the case of small-size UAVs developed recently as an attempt to relieve the limited battery size and life problem. In rural areas, since agriculture is a major source of income, UAVs are starting to make way toward

The authors would like to acknowledge the CONEX-Plus project. The CONEX-Plus has received research funding from UC3M and the European Union’s Horizon 2020 programme under the Marie Skłodowska-Curie grant agreement No. 801538. S. Panic () Faculty of Natural Science, University of Pristina, Kosovska Mitrovica, Serbia e-mail: [email protected] C. Stefanovic Department of Signal Theory and Communications, Universidad Carlos III de Madrid, Leganes, Spain e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 D. N. K. Jayakody et al. (eds.), Integration of Unmanned Aerial Vehicles in Wireless Communication and Networks, Unmanned System Technologies, https://doi.org/10.1007/978-3-031-03880-8_4

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optimizing the agriculture operations to increase crop production and monitor crop growth. In this, many applications UAV harvest energy from sensors in downlink and then collect and process the small data at low power in uplink. In addition, UAV trajectory optimization and optimization based on channel quality are some of the major open challenges to the global RD community. This chapter focuses on a critical study of coverage, mobility, energy efficiency, and data rates under practical system constraints and imperfections. The potential use of UAVs for data collection in wireless sensor networks (WSNs) has procured significant interest recently. Cost effectiveness and deployment flexibility with changing trajectory are the major advantages of UAV-assisted WSNs. Various numbers of applications have been studied in the literature, for instance, mobile base stations [1, 2] and mobile relays in cooperative communication [3–5]. In [1], the authors have studied the optimal deployment of multiple UAVs equipped with directional antennas used as aerial base stations. The results obtained in the work of [1] have shown that the number of available UAVs, the antenna gain, and beamwidth can determine the UAV optimal altitude and the location. A new polynomial time successive mobile base station placement solution for UAV ground terminals has been proposed in [6]. A new mobile relaying technique with high mobility UAV relays to maximize throughput has been introduced in [3]. WSNs usually consist of a large number of power-constraint low-cost sensor nodes (SNs). They are typically powered using rechargeable batteries and difficult to be recharged after depletion [7]. Considerable interest has been received to radio frequency (RF) energy harvesting (EH) techniques, i.e., wireless power transfer (WPT) and simultaneous wireless information and power transfer (SWIPT), to prolong battery life of power-constraint wireless SNs. Recent advances and challenges in RF-EH have been extensively studied in [8]. The outage performance of an EH-enabled UAV-based wireless relay system has been studied in [4]. A new unified energy harvesting scheme for full-duplex UAV to assist cooperative communication system is proposed in [5] to improve the operational time of the UAV while maintaining the expected quality of service (QoS). A UAV with WPT capability to collect sensor observations has been investigated in [9]. The authors exploited the mobility of the UAV to maximize the energy transfer to all SNs by optimizing the UAV trajectory. A new framework to improve energy efficiency in deadline-based WSN data collection with multiple UAVs has been proposed in [10]. A novel data gathering framework in the UAV-assisted WSNs has been developed in [11]. The authors have introduced a priority-based data access scheme considering the mobility of the UAV to increase data gathering efficiency of the system. Flight time minimization of UAV for data collection over WSNs has been investigated in [12]. The authors have formulated the flying time minimization problem as a dynamic programming problem and solved the optimization problem in a onedimensional sensor network. In this chapter, a UAV-assisted WSN has been considered, in which all SNs located within the UAV’s coverage area are powered by the UAV using the WPT EH technique. Recharging or powering up SNs through WPT by the assistance of data collecting UAV is a promising approach, especially when the SNs are located in a hazardous location or manual replacement of SN batteries is challenging. Here is

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emphasized on fading channels between the UAV and SNs and explored the effect on efficient power transfer and data collection in the presence of fading channel. Assuming that the ground-to-air channels are experiencing both Hoyt fading and Rician-shadowed fading, we derive outage probability (OP) and obtain the optimal time ratio to minimize the OP numerically.

4.2 System Model We consider a UAV-assisted WSN as illustrated in Fig. 4.1, where a UAV collects sensor observation in a circular service area of radius R = rk . The UAV is hovering at the center of the circular service area with the height of H . We assume that the k number of SNs are randomly located within the UAV’s coverage area. In addition, all SNs and the UAV are equipped with a single antenna. Furthermore, it is assumed that the SNs do not have any prior power supply or charge in its inbuilt batteries for information transmission, while the UAV is equipped with two batteries. One battery of the UAV is used for its mobility, while the other will be used as a constant power source with the transmission power P0 that exclusively used for the WPT.

Fig. 4.1 A reference system model for wireless-powered wireless sensor network with energy transfer in downlink and information transmission in the uplink Fig. 4.2 Transmission block diagram of the proposed system

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Once UAV reaches the center of the service area, data collection process starts and the total operational data collecting time is denoted by T . The TS protocol structure is used in the system as shown in Fig. 4.2. During the first time phase T τ , where τ ∈ (0, 1), the UAV will broadcast the WPT signal to power up the SNs. At the remnant, time slice T (1 − τ ) is used by the SNs to send sensor notices to the UAV. Let i ∈ {1, 2, ..., N} denote the index of the SNs and hi = husi and gi = hsui represent the channel coefficient for the UAV-to-ith SN link and for the ith SN-toUAV link, respectively. Moreover, husi and hsui are presumed to be independent for all SNs. Here, polar coordinates on the ground plane (ri , φi ) describe position of the ith SN. Therefore, the squared Euclidean distance between the UAV and the ith SN can be determined as di2 = H 2 + ri2 , where ri stands for the range between the ith SN and the center of the UAV’s zone of service. Let us express the path loss between the ith SN and UAV with mi , m2i = κ/di2α , where α denotes the path loss exponent, while κ denotes the constant coefficient of the path loss. Furthermore, we presume that all of the SNs are attempting to transmit at a constant information rate denoted by R per channel use. Since it is assumed that all SNs are assigned to different orthogonal channels, then, there no interference would occur among the SNs during the second time instant of TS protocol. Correspondingly, the portion of energy harvested by each SN during the first time instant in TS protocol can be expressed as Ei = η|husi |2 mi P0 τ T ,

(4.1)

where η is EH efficiency of the EH circuitry in SN. Thus, transmit power of the ith SN can be calculated as Psi =

τ Ei =η |husi |2 mi P0 . (1 − τ )T 1−τ

(4.2)

Then, the SNR of the signal received by the UAV from the ith SN can be expressed as γui = |hsiu |2 |hsui |2 m2i η

τ P0 , 1 − τ N0i

(4.3)

where N0i is the power of additive Gaussian white noise (AWGN) between ith SN and the UAV. Finally, the achievable information rate for sensor observations of the ith SN can be written as Ci = (1 − τ ) log2 (1 + γui ). Let us first observe the case when due to the flying altitude of the UAV, the channels do not contain a line-of-sight (LoS) component but are often modeled by Hoyt fading [13]. Assuming both husi and hsi u are experiencing Hoyt fading, the power of Xi of the desired signal follows a Hoyt distribution. Thus, probability density function (PDF) of X can be expressed as [14] fX (x) =

(1 + q 2 ) exp 2qΩX

 −

   (1 − q 4 ) x (1 − q 2 )2 x I , 0 4q 2 ΩX 4q 2 ΩX

(4.4)

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where I0 (x) is the zeroth-order modified Bessel function of the first kind [15], ΩX is the mean of X and denotes the channel average SNR value, while qi is the Nakagami-q fading parameter, which ranges from 0 to 1. The main issue in characterizing the random nature of majority of the fading models for wireless communications can be reduced to the task of characterizing of complex transformations of Gaussian random process. Hoyt fading model is used for modeling short-term signal variations that occur due to mutual impact of randomly scattered waves. Hoyt random process can be described as a complex Gaussian random process consisting of two zero-mean in-phase and in-quadrature components with arbitrary variance values [16]. Furthermore, the Hoyt fading model could stand as a good represent of the random process consisting of two correlated in-phase and in-quadrature components [14]. In addition, it is acknowledged that the Hoyt model could be used for modeling fading scenarios that are more general and more severe than the scenarios that are modeled with the Rayleigh model, since the Hoyt model can be reduced to the Rayleigh model. Since the Rayleigh model is the widely most used model for the modeling propagation scenarios when there is no direct LOS component between the transmitter and the receiver, analyzing wireless propagation characteristics based on the Hoyt model delivers significant generalization of provided results. In [17], the authors presented how, by relaying on results obtained for the Rayleigh fading model, the Hoyt fading model characteristics could be approximated. In [18], the authors have provided performance analysis of half-duplex WSN with TS-based EH relaying protocol over Hoyt fading channels. As previously mentioned, it is interesting to observe general scenario in which due to the flight conditions of the UAV, the channels content a LOS components affected by the shadowing effect, so the corresponding PDF of Xi , Xi ∈ (|gk |2 , |hk |2 ), can be modeled as   i mm (1 + κi )Xi i (1 + κi ) exp − fXi (Xi ) = (κi + mi )mi x¯i x¯i   κi (1 + κi )Xi , ×1 F1 mi , 1, x¯i (mi + κi )

(4.5)

where 1 F1 (x) denotes the confluent hypergeometric function [15], parameter 2bi denotes the average power of scatter component, while parameter mi denotes Ωi fading severity parameter. Parameter κi is defined as ratio of powers, κi = 2b , i where Ωi denotes the average power of LOS component, while x¯i , x¯i = E[Xi ], represents average channel SNR value. Rician-shadowed link parameter values for corresponding shadowing mode are provided in [19] as heavy shadowing (mg = mh = 0.739, bg = bh = 0.063, κg = κh = 0.00711, x¯g = x¯h = 8.97 × 10−4 ), average shadowing (mg = mh = 10.1, bg = bh = 0.126, κg = κh = 4.0828, x¯g = x¯h = 0.835), overall shadowing (mg = mh = 5.21, bg = bh = 0.251, κg = κh = 0.55387, x¯g = x¯h = 0.278), and light shadowing (mg = mh = 19.4, bg = bh = 0.158, κg = κh = 2.64241, x¯g = x¯h = 1.29). There arises a need

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to study the case when obstacles block the LOS link in between network nodes and fluctuations of the LOS signal are brought by shadowing effect. In order to account for the fluctuations of the LOS or scattered signal contributions brought by shadowing effect, several composite fading models have been proposed in the literature [2, 19, 20].

4.3 Performance Analysis In this section, the system performance of the system model is investigated by deriving the mathematical expression for its outage probability.

4.3.1 Outage Probability Under the described system model and given the target information rate R, the outage probability can be written as P r(Ci < R) = P r(

R > log2 (1 + γui )) 1−τ R

= P r(γui < 2 1−τ − 1) = P r(

R τ P0 |hsi u |2 |husi |2 κη < (2 1−τ − 1)) 2 2 α 1 − τ N0i (H + ri )

= P r(

|hsi u |2 |husi |2 < L(τ, R, P0 /N0i )), (H 2 + ri2 )α

where L(τ, R, P0 /N0i ) = equation can be written as



(4.6)

1 1−τ N R 0i 2 1−τ − 1 . For given ri , the above κη τ P0

P r(Ci < R|ri )   ) = P r |hsi u husi | < L(τ, R, P0 /N0i )(H 2 + ri2 )α .

(4.7)

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67

Thus, the distribution of zk = |hsi u husi | can be expressed as fzi (z) =

∞ ∞   (1 − qg4 )2i (1 − qh4 )2l (1 + qg2 )2l−2i+1 i=0 l=0

×

(1 + qh2 )2l−2i−1 qh2l+2i+1 qg2l+2i+1  √  (1+qg2 )(1+qh2 ) z i+l √ z K(2l−2i) 2qg qh

Ωgi+l+1 Ωhi+l+1 26i+6l+1 Γ (i

Ωg Ωh

+ 1)Γ (l + 1)i!l!

(4.8)

,

where g = husi and h = hsi u . The OP of Eq. (4.7), P r(zi < Z|ri ), P r(zi < Z|ri ) = * Z(ri ) fzi (z)dz can be expressed as Eq. (4.8) (the infinite series with respect to i and 0 l should be truncated. We have chosen the summation upper limit as 10, which is found to be large enough such that the truncation error is negligible in our simulation setups), where P r(zi < Z|ri ) =

∞ ∞   (1 − qg4 )2i (1 − qh4 )2l (1 + qg2 )2l−2i+1

(1 + qh2 )2l−2i−1 qh2l+2i+1 qg2l+2i+1     −i − l 2,1 i+l  (Z(ri )) G1,3 bZ(ri )  l − i, i − l, −i − l − 1

(4.9)

i=0 l=0

×

Ωgi+l+1 Ωhi+l+1 26i+6l+1 Γ (i + 1)Γ (l + 1)i!l!

b=

Z(ri ) =

)

(1 + qh2 )2 (1 + qg2 )2 16qg2 qh2 Ωg Ωh

,

L(α, R, P0 /N0i )(H 2 + ri2 )α .

.

(4.10)

(4.11)

Proof The proof is provided in the Appendix. Now, a case of Rician-shadowed environment is considered. Starting from Eq. (4.5) and by following the same procedure like in the previous case, as it is shown in the Appendix, the PDF of zk = |gk hk | is given in the form of t+s t+s m ∞ ∞  h  2 +1 (1 + κh ) 2 +1 2mg g mm h (1 + κg ) fzk (z) = (kg + mg )mg +s (kh + mh )mh +t (s!)2 (t!)2 s=0 t=0 )

t+s z(1+κg )(1+κh ) Γ (mg + s)Γ (mh + t)κgs κht z 2 K(t−s) 2 x¯g x¯h , × t+s t+s +1 +1 x¯g 2 x¯h 2 Γ (mg )Γ (mh )

(4.12)

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where Γ (x) denotes the Gamma function, given with Eq. (8.310) from [15], while Kv (z) denotes the vth-order modified Bessel function of the second kind, given with Eq. (8.807) from [15]. Now, the OP of Eq. (4.12), as explained in the Appendix, can be expressed as P r(zk < Z|rk ) t+s t+s ∞ ∞   (1 + κg ) 2 +1 (1 + κh ) 2 +1 = (kg + mg )mg +s (kh + mh )mh +t

s=0 t=0 m

×

h s t mg g mm h Γ (mg + s)Γ (mh + t)κg κh

x¯g

t+s 2 +1

× G2,1 1,3



t+s +1 h 2

x¯

Γ (mg )Γ (mh

)(s!)2 (t!)2

(Z(rk ))

s+t 2 +1

   (1 + κg )(1 + κh ) − s+t Z(rk )  s−t t−s 2 s+t , x¯g x¯h 2 , 2 ,− 2 − 1

(4.13)

where G2,1 1,3 (x) denotes Meijer G function, given with Eq.(9.301) from [15]. The closed-form expressions from Eq. (4.13) rapidly converge, since it only needs to sum up 15–20 terms in order to obtain accuracy to the 5th significant digit, which corresponds to the case when the truncation error is negligible.

4.3.2 Time Switching Factor Optimization Here, an attention was made to optimize the value for α, which minimizes the outage probability. As we can observe from (4.6), when the SN location ri is fixed, outage probability minimization is equivalent to L(α, R, P0 /N0i ) in (4.7). Therefore, for the given values for P0 and N0i and rate R, by selecting a value for α ∈ {0, 1}, the outage probability can be minimized. To satisfy the local optimally, partial derivatives of L(α, R, P0 /N0i ) with respect to α should be equal to zero. Thus, adhering to the local optimal condition, we can represent the partial derivatives of L(α, R, P0 /N0i ) with respect to α as follows: ∂L(α, R, P0 /N0i ) = (1 − α) − 2R/(1−α) (1 − α − αR ln 2) = 0. ∂α

(4.14)

As it can be observed from (4.15), α ∗ depends on the value of rate R, which involves joint computations of α and rate R making it challenging to obtain an exact solution and cannot be expressed by an explicit equation with respect to rate R. Therefore, we have obtained α ∗ numerically below.

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4.4 Numerical Results Here, the numerical results are provided to demonstrate and validate the theoretical analysis presented. Unless otherwise stated, in all simulations, the parameters listed in Table 4.1 have been used. In Fig. 4.3, the accuracy of analytically obtained OP in (4.10) has been validated, with respect to transmission power of the UAV Pu in different τ values, where α ∈ {0.2, 0.5, 0.8}. Two different scenarios have been considered during the simulation based on the SN location within the UAV’s service area. In the first scenario, SNs are located uniformly in the circular service area of radius rk , where ri < rk . The Table 4.1 Observed values of system parameters

Parameter Distance from ground to UAV Targeted data rate of each sensor Energy conversion coefficient Path loss exponent Noise power Constant coefficient of path loss Radius of the UAV’s service area

Numerical value h = 500 m R = 1 bit η = 0.9 m=3 N0 = −150 dBm κ = 1.3 rk = 100 m

Fig. 4.3 Outage probability versus the transmit power of UAV P0 (solid lines: sensor cell edge results; dash lines: the worst-case node)

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Fig. 4.4 Outage probability versus information rate R

other one corresponds to the worst-case scenario where each SN is located at the edge of the circular service area, where ri = rk . Outage probability decreases with the increase in UAV’s transmission power in both scenarios. This observation makes sense since the increase in UAV’s transmission power increases the amount of energy harvested by the SNs, which increase the SNs’ transmission power. As expected SNs located within the service area show superior outage performance compared to SNs located at the edge of the service area. It can also be observed from Fig. 4.3 that the increase in TS factor, τ , first decreases the outage probability and then increases as expected. This is due to the fact that the increase in α leads to reduction of transmission time, which eventually increases the overall outage probability of the system. Next, OP has been presented versus transmission rate R in Fig. 4.4 with respect to different values of α and Hoyt fading severity parameter. As it can be clearly seen from Fig. 4.4, regardless of α value OP increases with the increase in information transmission rate. This observation also clearly depicts that there is a tradeoff relationship between the information rate and resulting outage probability. In addition, Fig. 4.4 shows that the optimum value of α ∗ changes based on the information transmission rate. It is interesting to note that the SNs need more time allocated for information transmission in order to minimize the outage probability, which can lead to a decrease in the value of α ∗ . In order to find the optimal α value, which minimized the OP, the OP has been plotted versus α, where 0 < α < 1 as illustrates in Fig. 4.5. Figure 4.5 shows

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Fig. 4.5 Outage probability versus the time ratio α in the function of Hoyt fading severity parameter

that the OP decreases as α increases from 0 to optimal α ∗ (≈ 0.6), but later it starts increasing as α increases from its optimal value. This is due to the fact that for values of α smaller than the optimal value α ∗ , there is less time allocated for EH. Hence, less energy is harvested and larger values for outage probability can be observed due to smaller SN’s transmission power (see (4.7)). On the other hand, for α values greater than α ∗ , less time is available for information transmission. As a result, again outage probability increases at the UAV due to smaller value (1 − α)/2 (see Fig. 4.2). Furthermore, it can also be observed from Fig. 4.5 that an increase in Hoyt fading severity parameter q decreases the outage probability. Finally, in Fig. 4.6, the relationship between the OP and UAV’s hovering altitude over uniformly distributed SNs in the given service area has been investigated. It can be easily observed that, regardless of UAV’s hovering altitude, always the lowest OP is recorded in α ∗ . Furthermore, Fig. 4.6 shows that the OP increases with the increase in UAV’s hovering altitude. However, in practical scenarios, the altitude of UAV is either fixed or at least higher than the threshold altitude defined according to the operational environment where the effect of buildings and other obstacles becomes negligible. Also in practice, for a given UAV’s altitude determined as mentioned earlier, the information rate R should be adjusted to obtain an acceptable outage probability or QoS for the users who have worst channel condition (in this scenario, the users located at the edge of the service area).

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Fig. 4.6 Outage probability versus the distance from ground to UAV, as a function of Hoyt fading severity parameter for P0 = 40 dB

First, in Fig. 4.7, it is observed how shadowing severity affects OP for a given set of system parameters. Here, the OP values are depicted versus the transmit power of UAV P0 for the case of α = 0.2, 0.5, 0.8 and rk = 200. It can be seen how system performances deteriorate as shadowing severity parameters spans from light shadowing through overall shadowing case to heavy shadowing case. In Fig. 4.8, OP is depicted when averaged over the sensor node locations. First, it is assumed that SNs are uniformly located within the circular area of radius rk , while later is considered worst-case scenario when it is assumed that SN is located at the edge of the circle, i.e., ri = rk . For both scenarios, the case of overall shadowing severity is observed. As it can be seen from Fig. 4.8, OP decreases with the increase in the UAV transmit power. In Fig. 4.9, OP values are depicted as a function of time ratio α, for observed value of transmit power of UAV PN = 40 dB. Effects of shadowing severity on OP values for various values of system parameters are also examined. It can be noticed from Fig. 4.9 that while increasing the time ratio value, α, OP values decrease at first, but then its values start to increase. Namely, at first, because of an initial increase in α value, the SNs obtain more time to harvest energy from UAV, which reduces OP values to some extent, and however, further increase in α value leads to reduction of transmission time, which consequently leads to the increase in OP values. Shadowing severity conditions also affect OP values change due to time ratio α value switching. Namely, less dynamic OP change is present for the average

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Fig. 4.7 Outage probability versus the transmit power of UAV P0

Fig. 4.8 Outage probability in the function of transmit power of UAV P0

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Fig. 4.9 Outage probability versus the time ratio α of UAV

shadowing condition case than comparing to the dynamism of OP change for light shadowing condition case and overall shadowing condition case. In Fig. 4.10, OP is presented as a function of information rate value, R, when value of transmit power of UAV is set at PN = 40 dB and is assumed that SNs are uniformly distributed in the circular area of service. It is interesting to notice here that an increase in information rate leads also to OP values increase. With the increase in information rate, each SN requires more time to complete its information transmission, so α parameter value change effects more significantly to OP change than in previous occasions. The obtained results are graphically presented and discussed in the function of system parameters.

4.5 Conclusion In this chapter, a UAV-assisted WSN has been studied, where SNs are powered by the UAV using WPT over Hoyt fading channels and Rician-shadowed channels. SNs harvest energy from the WPT link broadcasted by the UAV and all the harvested energy is used to transmit sensor observation data to the UAV. Rapidly converging OP closed-form expressions are derived for the cases of system operating over Hoyt fading channels and Rician-shadowed fading channels. Furthermore, an optimal time allocation, which minimizes the OP, has been obtained. The results suggested

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Fig. 4.10 Outage probability versus the transmit rate

that there is a trade-off between the outage probability and transmission rate. Also an optimal time ratio should be obtained depending on the required information rate. Finally, it also identifies that the achievable OP is determined by the threshold altitude of the UAV and the optimal time ratio calculated based on the required transmission rate, and however, these parameters are specific to the operational environment.

Appendix In order to obtain PDF of zi = |hsi u ||husi |, we must perform following transformation of random variables:    ∞ zi 1 f|husi | (|husi |) d|husi |, fzi (z) = f|hsi u | (4.15) |husi | |husi | 0 where |hsi u | and |husi | have the PDFs given with Eq. (4.5) and corresponding PDF parameters. After using series expressions of 1F1 confluent hypergeometric functions and introducing into Eq. (4.15), we obtain the following integral expression:

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fzi (z) =

∞ ∞   (1 − qg4 )2i (1 − qh4 )2l (1 + qg2 )2 (1 + qh2 )2

qh4l+1 qg4i+1 Ωh2l+1 Ωg2i+1  ∞ z2l × |husi |2i−2l−1 Γ (i + 1)Γ (l + 1)26i+6l+1 i!l! 0     (1 + qg2 )2 z (1 + qh2 )2 |husi | × exp − 2 d|husi |, exp − 4qg Ωg |husi | 4qh2 Ωh i=0 l=0

(4.16) which can be solved using Eq. (3.471.9) from [15]. In that way, we are obtaining expression from Eq. (4.11) expressed in the form of modified Bessel function of second kind. Now, by transforming expression for modified Bessel function of second kind into expression for Meijer G function, by using Eq. (03.04.26.0008.01) from [21], we can obtain its CDF form expressed as Eq.13.

References 1. M. Mozaffari, W. Saad, M. Bennis, M. Debbah, Efficient deployment of multiple unmanned aerial vehicles for optimal wireless coverage. IEEE Commun. Lett. 20(8), 1647–1650 (2016) 2. G. Stamenovic, S. Panic, D. Rancic, C. Stefanovic, M. Stefanovic, Performance analysis of wireless communication system in general fading environment subjected to shadowing and interference. EURASIP J. Wirel. Commun. Netw. 2014, 124 (2014) 3. Y. Zeng, R. Zhang, T.J. Lim, Throughput maximization for UAV-enabled mobile relaying systems. IEEE Trans. Commun. 64(12), 4983–4996 (2016) 4. L. Yang, J. Chen, M.O. Hasna, H.-C. Yang, Outage performance of UAV-assisted relaying systems with RF energy harvesting. IEEE Commun. Lett. 22(12), 2471–2474 (2018) 5. D.N.K. Jayakody, T.D.P. Perera, P. Muthuchidambaranathan, M.O. Hasna, Self-energized full duplex UAV-assisted cooperative communication systems, in 2019 IEEE 7th Black Sea Conference on Communications and Networking (IEEE, Sochi, 2019) 6. J. Lyu, Y. Zeng, R. Zhang, T.J. Lim, Placement optimization of UAV-mounted mobile base stations. IEEE Commun. Lett. 21(3), 604–607 (2017) 7. C. Zhan, Y. Zeng, R. Zhang, Energy-efficient data collection in UAV enabled wireless sensor network. IEEE Wirel. Commun. Lett. 7(3), 328–331 (2018) 8. T.D.P. Perera, D.N.K. Jayakody, S.K. Sharma, S. Chatzinotas, J. Li, Simultaneous wireless information and power transfer (SWIPT): Recent advances and future challenges. IEEE Commun. Surv. Tutorials 20(1), 264–302 (2017) 9. J. Xu, Y. Zeng, R. Zhang, UAV-enabled wireless power transfer: Trajectory design and energy optimization. IEEE Trans. Wirel. Commun. 17(8), 5092–5106 (2018) 10. A.T. Albu-Salih, S.A.H. Seno, Energy-efficient data gathering framework-based clustering via multiple UAVs in deadline-based WSN applications. IEEE Access 6, 72275–72286 (2018) 11. S. Say, H. Inata, J. Liu, S. Shimamoto, Priority-based data gathering framework in UAVassisted wireless sensor networks. IEEE Sensors J. 16(14), 5785–5794 (2016) 12. J. Gong, T. Chang, C. Shen, X. Chen, Flight time minimization of UAV for data collection over wireless sensor networks. IEEE J. Sel. Areas Commun. 36(9), 1942–1954 (2018)

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13. X. Liu, Amount of log-square-Hoyt fading in satellite optical communications. IEEE Commun. Lett. 16(5), 666–669 (2012) 14. S. Panic, M. Stefanovic, J. Anastasov, P. Spalevic, Fading and Interference Mitigation in Wireless Communications (CRC Press, Boca Raton, 2013) 15. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, 2014) 16. M. Simon, M. Alouini, Digital Communication over Fading Channels (Wiley, New York, 2001) 17. J.M. Romero-Jerez, F.J. Lopez-Martinez, A new framework for the performance analysis of wireless communications under Hoyt (Nakagami-q) Fading. IEEE Trans. Inf. Theory 63, 1693–1702 (2017) 18. S. Panic, D.N.K. Jayakody, S. Garg, Self-energized bidirectional sensor networks over Hoyt Fading channels under hardware impairments, in Proceedings of 2019 IEEE 90th Vehicular Technology Conference (VTC2019-Fall), Honolulu, HI, USA, 22–25 September 2019 (2019) 19. A. Abdi, W. Lau, M.S. Alouini, M. Kaveh, A new simple model for land mobile satellite channels: First- and second-order statistics. IEEE Trans. Wirel. Commun. 2, 519–528 (2003) 20. S.K. Yoo, N. Bhargav, S.L. Cotton, P.C. Sofotasios, M. Matthaiou, M. Valkama, G.K. Karagiannidis, The κ-μ/inverse gamma and η-μ/inverse gamma composite fading models. IEEE Trans. Inf. Theory 63, 1693–1702 (2017) 21. http://functions.wolfram.com/ (2019). [Online; accessed September 2020]

Chapter 5

Reliable Capacity of A2G Drone Communications Using 5G NR Marco Corrente, Ricardo Sacoto-Martins, Luis Bernardo, Rui Dinis, Rodolfo Oliveira, Paulo Pinto, and Luis Campos

5.1 Introduction Unmanned autonomous vehicles (UAVs), commonly known as drones, are envisioned to support an extensive set of services in the civilian and commercial domains, including remote control and surveillance and communications relaying, acting as a flying base station (BS), a mobile backhaul for the cellular network or as a cellular terminal that relays other communication technologies [1–3]. This chapter addresses the use of UAV to deploy critical communications, which require low latency and high reliability [4]. It estimates the coverage range and network

M. Corrente Faculdade de Ciências e Tecnologia, FCT, Universidade Nova de Lisboa, Caparica, Portugal Instituto de Telecomunicações, Lisboa, Portugal e-mail: [email protected] R. Sacoto-Martins Faculdade de Ciências e Tecnologia, FCT, Universidade Nova de Lisboa, Caparica, Portugal Beyond Vision, Lisboa, Portugal e-mail: [email protected] L. Bernardo () · R. Dinis · R. Oliveira · P. Pinto Dep.o de Eng.a Electrotécnica, Faculdade de Ciências e Tecnologia, FCT, Universidade Nova de Lisboa, Caparica, Portugal Instituto de Telecomunicações, Lisboa, Portugal e-mail: [email protected]; [email protected]; [email protected]; [email protected] L. Campos PDMFC, Lisboa, Portugal e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 D. N. K. Jayakody et al. (eds.), Integration of Unmanned Aerial Vehicles in Wireless Communication and Networks, Unmanned System Technologies, https://doi.org/10.1007/978-3-031-03880-8_5

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capacity in the presence of hard reliability requirements, comparing it with when they do not exist. The integration of UAV in cellular networks has been evaluated for advanced Long-Term Evolution (LTEadv) networks [5, 6]. UAV support has been enhanced in the fifth generation (5G) networks [7]. Besides acting as terminals, 5G introduced the slicing concept, which enables service-oriented configuration of wireless networks in a flexible and agile manner supported by the core [8]. The flexible resource allocation introduced makes the 5G new radio (NR) interface a promising choice for the radio interface. The height of the UAV connected to a terrestrial BS not only allows a broader coverage range but also produces more interference in neighbour BS. In order to evaluate the level of reliability achievable in the air-to-ground (A2G) link, for uplink transmissions, a reliable channel model is required. Several A2G and ground-to-air channel models have been proposed over the years [9–15], supported by measurement campaigns and theoretical studies. 3GPP also published a reference model [16] covering three scenarios: urban-macro with aerial vehicles (UMa-AV), urban-micro with aerial vehicles (UMi-AV) and rural-macro with aerial vehicles (RMa-AV). A critical parameter in the communication range is the probability of having line-ofsight (LoS) or non-LoS (NLoS) communication. In all cases, these models define statistically the characteristics of the channel. Critical communications on a 5G A2G channel must be resilient to the channel variations. When very high reliability is a critical issue, some authors also propose the use of machine learning techniques to estimate the evolution of the channel [4]. This chapter considers a UAV deployed on a rural scenario connected to a macro BS and uses the RMa-AV channel model defined in the [16] to derive the statistics of the signal-to-noise ratio (SNR) at the BS for different settings of a physical uplink shared channel (PUSCH). It estimates the statistics of the 5G NR transmission performance considering throughput maximization with hard reliability constraints—a 1% block error rate (BLER). The one percent percentile metric was used to assert the reliable throughput achieved. Four different numbers of resource blocks (RBs) are considered (25, 52, 78 and 105) associated, respectively, with the bandwidths 5, 10, 15 and 20 MHz for a 15-kHz subcarrier spacing. A multiple input multiple output (MIMO) configuration was considered with 2 UAV transmission antennas and 8 receiving antennas at the BS. UAV A2G communication optimization involves not only setting a tolerable transmission power and adjusting the height and bandwidth but also using 5G NR adapted modulation and coding settings (MCS) [17] to achieve the required bit rate and reliability. This chapter calculates the MCS indexes that maximize the throughput with and without reliability concerns and analyses the cost of reliability in terms of throughput and of coverage range. This chapter is organized as follows: the system model is presented in Sect. 5.2. Section 5.3 analyses the performance of 5G NR receiver and proposes a configuration approach. Section 5.4 defines the A2G channel model used. Section 5.5 presents the simulation results that specify the coverage range providing reliable communications. Section 5.6 concludes and presents the future work.

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5.2 System Model This chapter analyses the A2G channel capacity of the UAV to BS channel, when the 5G NR interface is used over a dedicated slice. As shown in Fig. 5.1, the capacity is influenced by the UAV position, which is defined by the height, hU T , and the horizontal distance, d2D , which define the total distance, d3D . The notations h and d were adopted in the axis of the figures below, respectively, to represent hU T and d2D . The channel capacity is influenced by several parameters, including: • UAV position • MIMO configuration, related with the number of transmitting and receiving antennas and antenna gains • Transmission power • Bandwidth, related with the number of resource blocks (RBs) allocated for the channel • 5G NR Modulation and Coding Scheme (MCS) For this study, a fixed 2 × 8 multiple input multiple output (MIMO) configuration was considered, with 2 transmitting antennas at the UAV and 8 receiving antennas at the BS. The UAV transmits with a power PT = 18 dBm, the maximum transmission power defined for a terminal in 5G NR [17]. The chapter focuses mainly on the selection of the index of the MCS, IMCS , and of the bandwidth to satisfy a reliable bandwidth constraint, considering the A2G channel model. The approach followed was to start studying the influence of the signal-to-noise ratio (SNR) on the 5G NR channel capacity considering a bandwidth of 5, 10, 15 and 20 MHz, which correspond approximately to 25, 52, 78 and 105 RBs. By testing all the possible IMCS configurations, Sect. 5.3 calculates the threshold SNR values associated with a maximum reliable throughput, which guarantees a block error rate (BLER) below 1%. Second, in Sect. 5.4, the A2G channel model in [16] was used to study the SNR and throughput probability distribution for different heights and horizontal Fig. 5.1 System model

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distances. The 5G NR settings are calculated to maximize the throughput and to provide reliability guarantees. In a final Sect. 5.5, the two models combined are simulated and the throughput and error are measured for different UAV positions. The coverage regions are estimated in function of the UAV height.

5.3 5G NR PUSCH IMCS defines the modulation and coding scheme used in a transmission. This chapter considers a physical uplink shared channel (PUSCH) configured to use the higher modulation (256-QAM) with scheduled transmissions (in the downlink control channel) using the downlink control information (DCI) format 0_1, where the IMCS configurations shown in Table 5.1 can be used [17]. A numerology of 0 is assumed (i.e. a subcarrier spacing of 15 kHz). The values were copied from Table 5.1.3.1-2 in [17] (referred in section 6.1.4.1 for the selected PUSCH mode), denoting a trade-off between throughput and error resilience—higher IMCS values correspond to higher modulation orders (from QAM, 16-QAM, 64-QAM to 256QAM) and higher spectral efficiency but lower error resilience. Therefore, require a higher SNR to be selected. A second trade-off is due to the number of RBs, which increases the throughput due to the larger bandwidth, at the cost of requiring a higher SNR to use the same IMCS .

5.3.1 5G NR Performance The 5G NR performance study was conducted using the 5G toolbox and MATLAB R2020a. This software supports link performance analysis by computing BLER and throughput metrics. A tapped delay line (TDL) channel model was considered for this initial analysis with a delay spread of 30 ns and a maximum Doppler shift of 10 Hz and with hybrid-ARQ enabled. Seven hundred samples were collected for each configuration, using 7 random seeds. The measurements were collected for 25, 52, 78 and 105 RBs, for all the 28 IMCS values, and considering a 0.25 dB step SNR in the range of −20 dB to 30 dB. A 0.005 dB step was used on the SNR interval where BLER zero is reached. Figures 5.2 and 5.3 show the BLER for a subset of 13 IMCS values, including all the QAM modulations and the ones corresponding to the maximum and minimum coding rates for 16-QAM, 64-QAM and 256-QAM modulations. As expected, both figures show that BLER zero is achieved for higher SNR values as IMCS is increased. Comparing Figs. 5.2 and 5.3, they show that BLER zero SNR values for 105 RBs are a shifted copy to a higher SNR of the 25 RB ones. The throughput for the same subset of 13 IMCS values with 25 RBs and 105 RBs is presented respectively in Figs. 5.4 and 5.5. As expected, the steady throughput gain from 25 RBs to 105 RBs is proportional to the ratio 25–105, although it starts

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Table 5.1 MCS index table for PUSCH with DCI format 0_1 [17] MCS index IMCS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Modulation order Qm 2 2 2 2 2 4 4 4 4 4 4 6 6 6 6 6 6 6 6 6 8 8 8 8 8 8 8 8

Target code rate x[1024] 120 193 308 449 602 378 434 490 553 616 658 466 517 567 616 666 719 772 822 873 682.5 711 754 797 841 885 916.5 948

Spectral efficiency 0.2344 0.377 0.6016 0.877 1.1758 1.4766 1.6953 1.9141 2.1602 2.4063 2.5703 2.7305 3.0293 3.3223 3.6094 3.9023 4.2129 4.5234 4.8164 5.1152 5.332 5.5547 5.8906 6.2266 6.5703 6.9141 7.1602 7.4063

for a higher SNR value. The maximum throughput can be obtained selecting the IMCS value that maximizes the throughput for each SNR value. However, a different approach is needed when reliability is a concern. For instance, for SNR below -10 dB, it is not satisfied the BLER 1% constraint. The selection of a higher IMCS value should also occur only when the BLER constraint is satisfied. Figures 5.6 and 5.7 redraw the throughput plots above showing only the SNR values that satisfy the 1% BLER constraint. The IMCS value that maximizes the reliable maximum throughput is defined in this set of curves. It does not affect the maximum throughput but reduces the SNR ranges supported, with consequences for the coverage range.

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Throughput(BLER 0 then Go to Block-A Reduce i =i+1

6.4.5 Numerical Simulation and Discussion Performance of the proposed approach is analyzed through extensive numerical simulation. Also, we compared the fairness of the approach against a similar approach proposed in [13]. Figure 6.10 illustrates the minimum achievable rate among the users achieved through our proposed approach in four typical environments. Also, it illustrates the same matrix achieved in a similar approach proposed in [13]. It is observable that

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the minimum achievable rate obtained in our approach is relatively higher compared to the approach proposed in [13]. The reason is that the proposed approach aims to increase the achievable rate at the same time try to maximize fairness among the users. Figure 6.11 illustrates the deviation of the minimum achievable rate among the users with respect to the threshold rate. It illustrates the deviation in the proposed approach as well as the similar approach proposed in [13]. Moreover, it illustrates the achieved gain through the proposed approach compared to [13]. The gain achieved (GR ) is calculated as follows:  GR =

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Fig. 6.11 Deviation of minimum achievable rate from the average threshold value in various environments. Indicates the fairness gain achieved through our proposed approach compared to the similar approach proposed in [13]: channel bandwidth = 1 MHz; noise variance = −70 dB

6.5 Conclusion The UAV applications are exponentially increasing with the continuous development of various features. UAV in wireless communication can be illustrated with respect to two angles. Initially, how the emerging wireless communication use cases paved the path for several UAV related applications by providing the demand in various factors by including real-time command and control, massive connectivity, and enormous data transfer. Conversely, UAVs can also be integrated into wireless communication systems to provide various services such as ubiquitous coverage, edge computing, aerial relay, data dissemination, and data collection. An extensive discussion of above scenarios was presented in this chapter. A disaster-resilient system is one of the prominent applications among those. Ease of deployment, low implementation cost, and ability to deploy in any geographical area make it a well-suited candidate in disaster-resilient applications. However, all these advantages come with several challenges to overcome which were not there in classical, such as real time placement, crucial energy constraints, moving cells, etc. Here, we have discussed the most common challenges with the nature of the problem. Finally, we have discussed a sample scenario to methodologically realize the problems related to application of UAV in disaster resilient system. The

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problem studies the placement and the user association of UAV aerial base station to temporarily enable the coverage in a region where the terrestrial communication infrastructure is destroyed due to a disaster. The objective of the problem was identified as maximizing the achievable rate while increasing fairness among the users. The main problem is analyzed by dividing it into three subproblems. Those are user association and clustering, intra-cluster positioning, and altitude selection. User association and clustering problem is addressed through k-means clustering and Gale–Shapley algorithm. The intra-cluster placement subproblem is addressed through a modified pattern search algorithm. The altitude selection subproblem is solved by understanding the impact on the achievable rate with the elevation angle between the user and the UAV. The performance of our proposed approach is compared through numerical simulation with the benchmark approach provided in the current literature. Simulation results witness that our proposed approach gives at least 43% gain compared to the benchmark approach.

References 1. (2021) DJI FPV - Videos - DJI, in DJI Official. https://www.dji.com/dji-fpv/video 2. A. Kosta, N. Pappas, V. Angelakis, Age of Information: A New Concept, Metric, and Tool (Now Foundations and Trends, 2017). http://dx.doi.org/10.1561/1300000060 3. R. Alghamdi et al., Intelligent Surfaces for 6G wireless networks: a survey of optimization and performance analysis techniques, in IEEE Access, vol. 8 (2020), pp. 202795–202818. https:// doi.org/10.1109/ACCESS.2020.3031959 4. S. Kahveci, Some cooperative relaying techniques for wireless communication systems, in 2014 22nd Signal Processing and Communications Applications Conference (SIU) (2014), pp. 1690–1693. https://doi.org/10.1109/SIU.2014.6830573 5. X. Lin, W. Mei, R. Zhang, A new store-then-amplify-and-forward protocol for UAV mobile relaying. IEEE Wirel. Commun. Lett. 9(5), 591–595 (2020). https://doi.org/10.1109/LWC. 2019.2961668 6. T.D.P. Perera, S. Panic, D.N.K. Jayakody, P. Muthuchidambaranathan, J. Li, A WPT-Enabled UAV-assisted condition monitoring scheme for wireless sensor networks, in IEEE Transactions on Intelligent Transportation Systems. https://doi.org/10.1109/TITS.2020.3018493 7. A. Sharma, P. Vanjani, N. Paliwal, C. M. W. Basnayaka, D. N. K. Jayakody, H.-C. Wang, P. Muthuchidambaranathan, Communication and networking technologies for UAVs: a survey. J. Network Comput. Appl. 168 (2020), 102739. ISSN 1084-8045 8. D.N.K. Jayakody, T.D.P. Perera, A. Ghrayeb, M.O. Hasna, Self-energized UAV-assisted scheme for cooperative wireless relay networks. IEEE Trans. Vehic. Technol. 69(1), 578–592 (2020) 9. T.D.P. Perera, S. Panic, D.N.K. Jayakody, P. Muthuchidambaranathan, J. Li, A WPT-enabled UAV-assisted condition monitoring scheme for wireless sensor networks, in IEEE Transactions on Intelligent Transportation Systems. 10. H. Hydher, D.N.K. Jayakody, K.T. Hemachandra, T. Samarasinghe, Intelligent UAV deployment for a disaster-resilient wireless network. Sensors 20(21), 6140 (2020) 11. T.D.P. Perera, S. Panic, D.N.K. Jayakody, P. Muthuchidambaranathan, UAV-assisted data collection in wireless powered sensor networks over multiple fading channels, in IEEE INFOCOM 2020 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS) (2020), pp. 647–652

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12. E. Turgut, M. Cenk Gursoy, I. Guvenc, Energy harvesting in unmanned aerial vehicle networks with 3D antenna radiation patterns. IEEE Trans. Green Commun. Network. 4(4), 1149–1164 (2020) 13. H. El Hammouti, M. Benjillali, B. Shihada, M. Alouini, Learn-As-You-Fly: a distributed algorithm for joint 3D placement and user association in multi-UAVs networks. IEEE Trans. Wirel. Commun. 18(12), 5831–5844 (2019) 14. M. Ibrahim, H. Arslan, Air-ground Doppler-delay spread spectrum for dense scattering environments, in MILCOM 2015–2015 IEEE Military Communications Conference (2015), pp. 1661–1666 15. K. Daniel, M. Putzke, B. Dusza, C. Wietfeld, Three dimensional channel characterization for low altitude aerial vehicles, in 2010 7th International Symposium on Wireless Communication Systems (2010), pp. 756–760 16. D.W. Matolak, R. Sun, Air–ground channel characterization for unmanned aircraft systems— part I: methods, measurements, and models for over-water Settings. IEEE Trans. Vehic. Technol. 66(1), 26–44 (2017) 17. W. Khawaja, I. Guvenc, D. Matolak, UWB channel sounding and modeling for UAV air-toground propagation channels, in 2016 IEEE Global Communications Conference (GLOBECOM) (2016), pp. 1–7 18. Y. Liu, S. Xie, Y. Zhang, Cooperative offloading and resource management for UAV-enabled mobile edge computing in power IoT system. IEEE Trans. Vehic. Technol. 69(10), 12229– 12239 (2020) 19. Y. Zhou et al., Secure communications for UAV-enabled mobile edge computing systems. IEEE Trans. Commun. 68(1), 376–388 (2020) 20. Y. Chen, N. Zhao, Z. Ding, M. Alouini, Multiple UAVs as relays: multi-hop single link versus multiple dual-hop links. IEEE Trans. Wirel. Commun. 17(9), 348–6359 (2018) 21. Z. Hu, Z. Zheng, L. Song, T. Wang, X. Li, UAV offloading: spectrum trading contract design for UAV-assisted cellular networks. IEEE Trans. Wirel. Commun. 17(9), 6093–6107 (2018) 22. A. Omran, L. Sboui, M. Kadoch, Z. Chang, J. Lu, R. Liu, 3D deployment of multiple UAVs for emergent on-demand offloading, in 2020 International Wireless Communications and Mobile Computing (IWCMC) (2020), pp. 692–696. https://doi.org/10.1109/IWCMC48107. 2020.9148252 23. A. Al-Hourani, S. Kandeepan, S. Lardner, Optimal LAP altitude for maximum coverage. IEEE Wirel. Commun. Lett. 3(6), 569–572 (2014). https://doi.org/10.1109/LWC.2014.2342736

Chapter 7

Analysis of Age of Information in Wireless Communication Networks Tharindu D. Ponnimbaduge Perera and Dushantha Nalin K Jayakody

7.1 Introduction The exponential growth of Internet-of-Things (IoT) applications in next-generation communications has led to increasingly connected devices in the communication infrastructures. These connected devices are responsible to generate and exchange information within different entities of the communication setup to support decision taking processes in IoT applications. In general, wireless communications over the last two decades have achieved technological advances, which enable seamless connectivity, higher reliability, and higher quality of service (QoS) even considering higher mobility of the devices. With those advancements, a requirement of realtime applications for monitoring and control emerges in the domain of IoT. Thus, the future IoT applications will heavily depend on sharing of time-sensitive information within the application to satisfy the requirements of such applications, i.e., intelligent transportation systems (ITSs), autonomous vehicles, smart cities, homes, etc. For example, sensors in ITS need to exchange infrastructure condition with the vehicles to avoid catastrophic accidents, self-driving vehicles need to exchange real-time information with other vehicles to avoid accidents, and swarms of unmanned aerial vehicle (UAV) in communication system need to exchange its real-time position to avoid collision and to improve system performance. Therefore,

T. D. P. Perera Centre for Telecommunication Research, School of Engineering, Sri Lanka Technological Campus, Padukka, Sri Lanka e-mail: [email protected] D. N. K. Jayakody () COPELABS, Lusófona University, Lisbon, Portugal e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 D. N. K. Jayakody et al. (eds.), Integration of Unmanned Aerial Vehicles in Wireless Communication and Networks, Unmanned System Technologies, https://doi.org/10.1007/978-3-031-03880-8_7

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Fig. 7.1 Position monitoring application in intelligent transportation system. The base station receives current position of the vehicle and forwards the information to the data processing server. Red color rectangle represents the position uncertainty of the vehicle with respect to the data processing server

it is essential to maintain freshness of the information received since outdated information can jeopardize reliability of the system output given rise to safety risks. Data freshness at the destination is a quite difficult objective to achieve in wireless communication. It is also noteworthy that data freshness is different and goes beyond low latency. Data freshness can be defined as regular delivery of low-delay data packets over time to destination communication node in the network. A reference position monitoring system is given in Fig. 7.1 to illustrate this challenging problem, where a vehicle moves with the velocity V toward its destination generating its position information with the rate of τ data packets per second. Then, the vehicle transmits these data packets to the data processing center through base station in uplink communication. The latest data packet received from the vehicle containing its position at time t is given by δ(t). Thus, uncertainty about vehicle’s current position can be represented as v(t − δ(t)), which is illustrated in red color rectangle in Fig. 7.1. The equation v(t − δ(t)) can be used to identify the data freshness from the perspective of data processing center. For an example, t − δ(t) = 3 seconds denotes that at time t the data processing server knows the location of the vehicle three seconds ago. With relation to Fig. 7.1, data processing server then knows the location of the vehicle as Q1 [x, y], while in reality current position of the vehicle is Q0 [x, y]. If vehicle continuously generates its position information and transmits to the data processing server without any delays, then t = δ(t), and there will be no position uncertainty in the application, i.e., v(t − δ(t)) = 0. Nerveless, this ideal condition of data freshness at the destination cannot be achieved in current communication networks due to intrinsic sources of latency, i.e., data buffers, and limited resources and non-optimal resource

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allocation policies in communication networks. Therefore, it is required to consider the entire communication network as a whole and optimize generation of data packets, queuing policies at data buffers and polices of transmission scheduling to maintain data freshness at the destination.

7.2 Age of Information The most popular conventional critical performance metrics used in current and future wireless communication networks are achievable throughput, outage probability, end-to-end delay, service reliability, and overall energy efficiency. However, with the increase in real-time applications in IoT, data freshness at the destination became critical. Therefore, a performance metric to capture data freshness at the destination communication node is required to maintain quality of service (QoS) in real-time IoT applications. In order to facilitate this requirement, a performance metric named age of information (AoI) is introduced in 2011 to quantify the freshness of information received with respect to its generated time. The AoI captures the time elapse since the last received information update was generated. A significant attention from both academia and industry has attracted by AoI due to its ability to characterize freshness of the information received in wireless communication networks illustrating its uniqueness compared to the latency performance metric. Time critical information in real-time monitoring applications is categorized as real-time status update in the form of data packets. Each of these data packets consists of modulated bits of status update information along with the time stamp of its generation. Information within the status update packets is different from application to application, i.e., sensor observations, location coordinates, stock market updates, etc., and these status updates need to be transmitted from its generation point to a required destination within the communication network. Furthermore, AoI reflects the practical constraints on the transmission of status updates based on data buffers in communication nodes and time-varying wireless channels between the communication nodes. In particular, AoI captures the time taken to generate status update, time spent at data buffers/queues, and time spent at the wireless channel by each status update. In the recent literature, various performance metrics derived in relation to AoI are submerged to extend characterization of timeliness of status update, i.e., average age of information (AAoI), peak age of information (PAoI), nonlinear age penalty function also known as cost of update delay, the value of information update (VoIU), age of synchronization (AoS), and age of incorrect information (AoII). In this direction, closed-form expressions for AoI of modeled communication systems along with upper bound and lower bounds have been studied and investigated in the literature. Regardless of the communication setup, the primary objective of AoI-based research works arises in the direction of designing optimal policies to

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minimize average or instantaneous AoI of the status updates. To facilitate this requirement, most of the recent research works have been focused on formulation of optimization problems and algorithms, which contribute to the system design of real-time information update applications. It is also noteworthy that optimizing timeliness of status updates with the effective utilization of available resources is one of the main critical objectives in future generation of applications in beyond 5G. Therefore, there are a wide range of objectives to be considered in communication system design depending on the QoS requirements. Another fruitful research direction of AoI can be found in the literature is the way of AoI, and its relevant metrics can be integrated with latest trends of machine learning techniques, i.e., game theory, reinforcement learning, etc. Quite diverse domains in wireless communications considered AoI as a tool to achieve expected timeliness of status update while preserving QoS requirement. Some of these domains are radio frequency energy harvesting (RF-EH), cooperative communication, IoT wireless sensor networks, resource allocation and optimization, channel coding, caching, and UAV communications.

7.2.1 AoI Literature in Nutshell The AoI as a performance metric was introduced in [1] and since then AoI in wireless communications has been receiving significant attention in the literature from both academia and industry. Early stages of AoI research were mainly focused on characterizing AoI based on queuing techniques in communication node’s data buffers under heterogeneous service policies [1–4]. Information theory has been used to design channel coding schemes to increase AoI performance in [5]. The impact of interference on AoI performance is analyzed using game theory in [6, 7]. AoI-based link scheduling optimization was considered recently in many works available in the literature [8–11]. AoI in different applications of WSNs, i.e., vehicular networks, cellular networks, investigated in [12–15]. The most recent works of AoI have focused on AoI in EH-enabled communication networks, in which EH is performed via RF-WPT [16–19]. The problems associated with AoI optimal policies in UAV-assisted communication systems have been investigated very recently in [20–22]. The list of research works related to AoI listed in this section is not exhaustive, thus, for a comprehensive survey on AoI read [23, 24] and the references therein.

7.2.2 AoI Performance Metric For better understating, the following use case scenario is assumed. Extract samples from a stochastic process X(t) of sensor observations collect by the data source in two-node communication setup are illustrated in Fig. 7.2. Sensor observations

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Fig. 7.2 Extracted samples of the stochastic process X(t) sensed by the data source

contain information about the status update of the process at the data source. Each collected sample needs to be transmitted to the destination over a wireless communication link to assist real-time decision-making. The data buffer equipped in data source stores sensor observations temporarily in the form of data packets. Each data packet contains the value of the process X(ti ) of the i sample at the time ti and the time stamp ti . Then, each data packet in the data buffer will be transmitted toward the destination providing a status update. For simplicity, a firstcome-first-serve (FCFS) queuing model is assumed at the data buffer in data source. Furthermore, storage of data packets at the data buffer is instantaneous, and thus, data packet arrival at the data buffer is denoted by sampling rate of X(t). The average rate of stochastic process is denoted by λ and average service rate of data packets represented by R. By definition, AoI is defined as the time elapse since the last received status update was generated at the data source. Let ti be the time stamps at the destination of the status update received. Thus, at given time τ , the index of the recently received status update can be given as S(τ ) = max{i|ti ≤ τ }.

(7.1)

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The time stamp of the recently received status update can be written as u(τ ) = tS(τ ) .

(7.2)

Therefore, AoI of the system can be expressed as the random process Δ(t) = t − u(t).

(7.3)

7.2.3 Evolution of AoI AoI evolution of the two-node communication system given in Fig. 7.2 is illustrated in Fig. 7.3. Status update generate in the data source waits in the data buffer before being transmitted to the destination by the base station. Observation of the system starts at when t = 0, while the data buffer is empty, and thus, the AoI at the destination is Δ(0) = 0. Status update data packet i is generated at time ti and is successfully received at the destination at time ti . Time difference of ti−1 − ti reflects the age of previously received status update at the destination. The value of AoI linearly increases over time until the freshest status update is received, reflecting the last received status update getting older. When the next status update is received at the destination, the time stamp of τ (t) is updated and AoI is reset to the packet delay, which is caused by the queuing policy and transmission medium. The main

Fig. 7.3 AoI evolution of two-node communication system

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two parameters that have higher influence in AoI are status update inter-delivery time and packet delay, which are denoted by the two random variables Xi and Y i. It is also noteworthy that the controlling only one of these parameters is insufficient for achieving better AoI performance in the communication system. Referring to Fig. 7.3, the inter-delivery time Xi can be given as Xi = ti − ti−1 .

(7.4)

Similarly, system time of status update i can be written as Yi = ti − ti,

(7.5)

which is corresponding to the combination of queue waiting time and service time within the communication setup. Furthermore, assuming the AoI observation time interval from t = 0 to the given time τ , the number of status update arrival can be written as N(τ ) = max{n|tn ≤ τ }.

(7.6)

Therefore, at time ti , where i = 1, 2, ..., N (τ ), AoI Δ(ti ) is reset to ti − ti . This captures the reduction in age (freshness of the information) for each received status update at the destination with respect to its generation at the data source. Within the observation of age, when the time is not in the set I = t1 , t1 , ..., tN (tau) causes an increase in age as time passes by creating a saw-tooth wave in evolution of AoI as depicted in Fig. 7.3. Furthermore, AoI can also be calculated by calculating the gray color area of Qi illustrated in Fig. 7.3.

7.3 Analysis of Age of Information As discussed in the previous section, the main objective of the communication system is to maintain timeliness of received data at the destination as best as possible while maintaining expected QoS requirements. At the same time, it is noteworthy that the tips of the saw-tooth illustrated in Fig. 7.3 do not reflect the timeliness of the communication system. It reflects the instantaneous age of information before a status update received at the destination. This maximum value of AoI, which reflects by the tip of the saw-tooth in Fig. 7.3, can also be described as the maximum value of AoI immediately before a status update named as peak age of information (PAoI). As can be clearly seen from Fig. 7.3, there can be either a small or drastic reduction of AoI immediately after the PAoI. Therefore, timely update required at the destination refers to time average AoI, but the PAoI.

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7.3.1 Time Average AoI For the given AoI process Δ(t) assuming ergodicity, the time average age can be defined as using sample average, which converges to its corresponding stochastic average. Thus, the time average age for a given interval (0, τ ) can be expressed as ΔA =

1 τ



τ

Δ(t)dt.

(7.7)

0

This integral represents the area under the Δ(t). Also, it is noteworthy that the time average age ΔA reflects the average AoI (AAoI) as Δ = lim ΔA . τ →∞

(7.8)

Considering the area of Qi , where i ≥ 1, given in Fig. 7.3, the AAoI of the system illustrated in Fig. 7.3 can be obtained as Δ=

E[XY ] + E[X2 ]/2 , E[X]

(7.9)

where E[.] denotes the expectation operator, X denotes the inter-delivery time, Y denotes the system time and data arrival rate at the data source λ = z/E[X]. This core foundational work was derived and introduced in [1]. It is also noteworthy that no assumptions have been made regarding the distribution of random variables X and Y . It is also observed that the X and Y are dependent. Thus, computation of AAoI complicates due to the limited knowledge on their joint distribution. Furthermore, having fixed data arrival rate and reducing inter-delivery time, which correspond to data packets filling up at data buffer, lead to an increase in system time. Nevertheless, having larger inter-delivery times will make the data buffer empty causing reduction in delays. Therefore, it can be clearly identified that X and Y are negatively correlated to each other. For the better understanding of numerical results of AAoI, inter-delivery time and packet delay with respect to the data packet arrival rate at the source is illustrated in Fig. 7.4 considering M/M/1 first-come-firstserve (FCFS) queue at the data buffer. To summarize, AoI of a given status update communication system mainly depends on the two factors, i.e., transmission delay corresponding to the system time and status update arrival pattern at the source. The way each of these two factors affects the system AAoI is illustrated in Fig. 7.4. It is also observed that the inter-delivery time is inversely proportional to the status update arrival rate, which can be written as λ = 1/E[X]. Smaller inter-delivery time results high average system time and high AAoI. However, when inter-delivery time is larger, it leads to high AAoI and low system time. Thus, careful optimization of X and Y is needed to achieve minimum AAoI within the communication system.

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AoI (FCFS) Inter-delivery Time Packet Delay

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0 0

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Arrival Rate Fig. 7.4 AoI, packet delay, and inter-delivery for M/M/1 queue with fixed service rate 1 packets/sec

7.3.2 Peak Average Age of Information PAoI is one of the alternate definitions derived in relation to AoI to cater different requirements of status update applications. There are two main objectives of PAoI, i.e., work as a proper alternative to age and average age, and it is more tractable in complicated communication models. PAoI is the peak value of saw-tooth illustrated in Fig. 7.3, which categorized the maximum values of AoI immediately before a status update is received at the destination. The metric PAoI is more applicable in communication application, in which a threshold restriction is needed on age of each status update or when there is an interest in the maximum age of each status update. Moreover, PAoI has much simpler formulation as compared to the AAoI. Considering Fig. 7.3, the PAoI before receiving the ith status update can be written as Ai = Xi + Yi ,

(7.10)

where PAoI is a discrete stochastic process. Considering age observation interval (0, τ ), the time average PAoI can be expressed as

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AA = lim

(7.11)

i=1

where N (tau) denotes the number of status updates successfully received at the destination by the time τ . Thus, the average PAoI can be obtained as AA = E[X + Y ],

(7.12)

where PAoI serves as the upper bound for AoI in communication systems.

7.3.3 Cost of Update Delay With the introduction of AoI to characterize the age of status update at the destination, capturing of information characteristics at the source by updating the definition of AoI to a nonlinear cost function is submerged in wireless communication systems. The main objective of this requirement is to identify the reasons for the absence of status update at the destination with respect to the non-negative, monotonically increasing category of functions related to the source characteristics. Therefore, the concept of AoI is expanded by introducing another new metric named cost of update delay (CoUD) in [25]. CoUD characterizes the cost of having outdated status update at the destination. The requirement of further extending the concept of AoI mainly depends on the communication application setup and the data generating statistic at the data source. For an example, consider we are observing freshness of the status update at time instant t and the freshest status update of the process X(t) received at the destination is arrived at t − Δ, where Δ denotes a random value. If the status update at t and t − Δ is independent from each other, destination cannot estimate the information with the knowledge of t − Δ. Hence, this simply indicated the transmission delay. On the other hand, if t and t − Δ are dependent, δ directly affects the estimation accuracy at the destination. Thus, it can be concluded that smaller age Δ increases the accuracy of the estimation at the destination. The CoUD can be written as C(t) = fs (t − u(t)),

(7.13)

where t and u(t) denote the time of most recent status update received at the destination and its generation at the data source, respectively. It is also noteworthy that the function fs (.) is a non-negatived and monotonically increasing function, which represents the evolution of CoUD with relevance to the data characteristics at the data source. More information about the selection of fs (.) is given in [25]. The average CoUD needs to be maintained smaller to achieve increased status update freshness at the destination. The time average CoUD for the given observation interval of (0, τ ) can be written as

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1 CA = lim τ →∞ τ



τ

C(t)dt.

(7.14)

0

Similar to the AAoI, this integration represents the area under the saw-tooth shape of C(t).

7.3.4 Value of Information Update Apart from AoI and CoUD, the timeliness of status update received at the destination can be characterized based on the degree of importance of the status update received at the destination for the application. Therefore, another new metric named value of information update (VoIU) is introduced in [25]. VoIU captures the reduction in uncertainty of the destination, which is directly related to the definition of AoI. The metric VoIU for the communication system illustrated in Fig. 7.2 can be defined as Vi =

fs (ti − ti−1 ) − fsi (ti − ti ) , fs (ti − ti−1 )

(7.15)

where i denotes the index of status update, ti represents the time stamp of status update generation at the data buffer, ti denotes the time stamp of status update received at the destination and at time ti , the C(ti ) = fs (ti − ti−1 ). The value of VoIU comes within the interval of [0, 1] since it is a bounded fraction as in (7.15). When the inter-delivery time of status update goes toward infinity, the VoIU value takes its maximum value 1. On the other, if packet delay/system time is larger, VoIU gets its minimum value reflecting that the particular status update is not as timely except by the communication application to maintain the status update freshness of the system. Minimizing average CoUD or maximizing average VoIU has to be decided according to the requirements of the communication application. Similar to (7.11), the average VoIU for the given time interval (0, τ ) of a status update communication system can be written as N (τ ) 1  Vi . τ →∞ τ

VA = lim

(7.16)

i=1

VoIU reflects the impact of the received status update in reducing the CoUD. Therefore, VoIU needs to be maximized in communication applications to maintain data freshness at the destination.

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7.4 AoI in SWIPT-Enabled Two-Way Relay Network This section considers an AoI analysis of SWIPT-enabled amplification-andforward (AF) two-way relay network (TWRN) as depicted in Fig. 7.5. In this communication setup, relay node assists status update exchange between two terminals S1 and S2 adopting simultaneous wireless information and power transfer (SWIPT) power-splitting (PS)-based energy harvesting (EH) to power up its communication capabilities. Furthermore, it is assumed that there is no feasible direct link available between the terminals. All communication nodes are equipped with a single antenna, which operates in the half-duplex mode. The block diagram of the AF relaying with the presence of additive white Gaussian noise (AWGN) and 2 ) hardware impairments (HI) is illustrated in Fig. 7.5. The symbol nxy ∼ CN (0, σxy is to denote the AWGN with x, y ∈ {S1 , S2 , r}. In addition, we assume that all channels experience Rayleigh fading with path loss exponent (m), where the channel gain is constant during each transmission block, while hi and gi denote the uplink and downlink channels, respectively. First, both terminals S1 and S2 broadcast the status update packets x1 and x2 , respectively. The received signal at the relay can be written as

Fig. 7.5 Reference system model of wireless powered two-way relay network

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yr =

  P (1 − ρ)h1 (x1 + ζ ts1 ) + P (1 − ρ)h2 (x2 + ζ ts2 ) + ζ r + ns1 r + ns2 r , (7.17)

where Pi denotes the transmit power of Si , with P1 = P2 = P , ζtsi ∼ CN (0, κ12 ) represents the HI at the transmitter of Si , ζrr ∼ CN (0, κ22 (1 − ρ)P (|h1 |2 + |h2 |2 )) denotes the HI caused by the receiver of the UAV, and ρ denotes the power-splitting ratio. The symbols κ1 and κ2 characterize the HI levels of both the transmitter and the receiver, respectively. The received power at the relay’s energy harvesting circuitry can be written as PR = Pρ(|h1 |2 + |h2 |2 ).

(7.18)

Considering (7.18), the harvested energy from the received power PR can be written as ti Er = η(PR ) , 2

(7.19)

where ti denotes the transmission time of status update by each terminal and η(x) denotes the nonlinear EH function. This EH function adopts the sigmoid nonlinear EH function as in [26], which can be modeled as 

1 − exp (−μ(PR − ωa )) η(PR ) = λ 1 + exp (−μ(PR − ωc ))

+ ,

(7.20)

where λ ≥ η(PR ) denotes the maximum saturation power at the output, and ωa and ωc are the input power that change the curvature sign and the input sensitivity threshold such that η(PR ) = 0 if PR ≤ ωa , respectively. Thus, the transmit power of the relay can be written as Pr =

Er T 2

= η(PR ).

(7.21)

Once the uplink transmission of status update finished, the relay amplifies the received signal yr using an amplification factor β and transmits to the terminals. Thus, the received signal at the terminal Si can be written as ysi =



Pr gi (yr β + ζ tr ) + ζ rsi + nrsi ,

(7.22)

where ζtr ∼ CN (0, κ12 ) represents the HI introduced by the transmitter of the UAV, and ζrsi ∼ CN (0, κ22 Pr |gi |2 ) is the HI introduced by the receiver of Si . Considering (7.17), the SNDR at the UAV can be given as γr =

a1 Ω , ((a2 + a3 )(Ω + Ψ )) + a1 Ψ + 2

(7.23)

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where a1 = P /σ 2 (1 − ρ), a2 = a1 κ12 , a3 = a1 κ22 , Ω = |h1 |2 , |g1 |2 , and Ψ = |h2 |2 , while |g2 |2 denotes the average channel power gain of the data packet transmission. 2 = σ 2 . Similarly, by considering (7.17), For simplicity, we assume that σs2i r = σrs i (7.21), and (7.22), the SNDR at the Si can be written as γ S1 =

I1 Ψ Ω , I2 ΩΨ + I3 Ω + I4 Ω(Ω + Ψ ) + I5 Ψ Ω + 1

(7.24)

2 P2 ρ(1 − ρ)η(PR )β 2 , I2 = I1 (1 + κ12 ), I3 = Pσ 2 ρη(PR )[2β + κ12 + κ22 ], σ2 I κ2 I1 κ22 , and I5 = β1 21 . The closed-form expression of the outage probability at

where I1 =

I4 = S1 can be derived as Pout = 1 − 2μ3

∞  l  m  n  ∞   Kμk (μ2 γ0 ) 1

k=0 l=0 m=0 n=0 p=0

  × K(m−2n+p+k+l) (2 μ2 μˆ3 γ0 c3 ) ,

μˆ3

3m−2n+p+k+l 2

m−2n+p+k+l 2

m−p+k+l 2

c4m−n c3

p

c2

(k!)2 l!p!(n − p)!(m − n)!

(7.25) where μi denotes the mean value of the random variable Xi , Kv (.) is the vth order modified Bessel function of the second kind, and μˆ3  μ1 + c4 μ2 γ0 . Proof See Appendix 1.

7.4.1 AoI Formulation In information theories, it is well known that utilizing a relay node can improve the system performance in terms of throughput or equivalently decreasing outage probability, especially when the establishment of direct link is infeasible between the nodes. However, integrating SWIPT-PS with nonlinear EH scheme into the relay in the proposed communication setup can introduce the cost of increasing the overhead delay due to EH and a number of retransmission requests by the respective terminals. Thus, it is not evident in what way or manner AF-TWRN with nonlinear SWIPT-PS affects the AoI performance. In order to fill this void, the AoI of the proposed system is analyzed in the following section, considering the outage probability. In AF relay scheme, the relay node is not capable of decoding and storing the received information in data buffers. Thus, the end-toend data transmission and age evolution of the proposed system can be modeled as a single-hop communication network. Thus, AoI evolution of the proposed system is equivalent to the age evolution shown in Fig. 7.3. The AAoI of the system for the observation time period (0, τ ) can be written as

7 AoI

141 N (τ ) 1  Δi . τ →∞ τ

ΔA = lim

(7.26)

i=1

Moreover, the average AoI can be calculated by obtaining the average area of the graph illustrated in Fig. 7.3, which can be written as   N (τ )−1 1 Qi + QN (τ ) , ΔA = lim Q1 + τ →∞ τ

(7.27)

i=1

where QN (τ ) = 12 ΔN (τ ) (ΔN (τ ) + 1). For a given data packet of length n, the service time Yi can be written as Yi = (αn + cd + rAF )(m + 1),

(7.28)

where α denotes the symbol duration, cd represents the channel-induced delay, rAF denotes the time spent by the AF process at the relay, and m denotes the number of retransmissions by the source terminal. The variable m is geometrically distributed with Pout due to effect of having i.i.d. channel state information over time. The expected number of retransmission attempts from the source terminal can be expressed as E[M] =

∞ 

(m−1)

m(1 − Pout )Pout

.

(7.29)

m=0

Therefore, considering (7.25), (7.27), and (7.28), time average AoI can be written as ΔA = lim

i→∞

E[

* ti

Δi dt] . E[ti ] 0

(7.30)

The numerator of (7.29) can be further simplified by using (7.27) as 

ts +Yi +ta

Δ[t]d(t) =

ts

1 ((ts + Yi + ta )2 − ts2 ), 2

(7.31)

where ta denotes the time taken to receive the acknowledgement of successful transmission from the destination and ts = αn + cd + rAF . Therefore, applying (7.31) into (7.30), time average AoI can be expressed as ΔA =

E[(ta + Yi )ts + 12 (ta + Yi )2 ] . E[ta + Yi ]

(7.32)

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As it can be clearly observed from (7.31), the time average AoI depends on the Yi and ts . The variable Yi can be further derived as E[Yi ] =

∞ 

m Pout (1 − Pout )(m + 1)E[ts ] =

m=0

ts . 1 − Pout

(7.33)

By using (7.32), the second-order moment of E[Yi2 ] can be written as E[(Yi )2 ] =

∞ 

m E[(m + 1)2 (1 − Pout )Pout ]

m=0

= (1 − Pout )E[(ts )2 ]

(7.34) Pout + 1 3 1 − Pout

(ts )2 (Pout + 1) = . 2 1 − Pout

Then, applying (7.33) and (7.34) into (7.32), a closed-form expression for time average AoI can be obtained as ΔA =

2 − 4P ts ta (Pout (ts )2 (3 − Pout ) + ta2 (1 − Pout ) out + 3) + . 2(1 − Pout )(ts + ta (1 − Pout )) 2(1 − Pout )(ts + ta (1 − Pout )) (7.35)

7.4.2 AoI Minimization It is comprehensible that there is a trade-off between the amount of energy harvested by the relay and AoI performance at the terminals for the proposed system. Principally, when ρ increases, a higher available transmission power can be obtained as per the used nonlinear EH model. However, this may lead to a decrease in transmission rate causing an increase in AoI due to the increase in the number of retransmissions. Thus, there exists an optimal PS ration ρ ∗ that provides the best achievable AoI and throughput. The corresponding optimization problem of AoI minimization can be written as

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143

(P 1) : Minimize ρi

subject to:

(ΔA )

(C1) : γr ≥ 22R − 1, (C2) : γS1 ≥ 22R − 1, (C3) : 0 < βi ≤ βmax ,

(7.36)

(C4) : 0 < ρi < 1, (C5) : 0 < P < P ∗ , (C6) : Pr ≤ λ, where βmax =

0

Pr π0 (1−ρ)[1+(κ12 +κ22 )(Ω+Ψ )+Ψ ]+2

and P ∗ denotes the maximum

power limit at the transmitter. Constraints (C1) and (C2) are to assure that the endto-end SNDR of the signals falls below a desired threshold value of γ th . Constraint (C6) asserts that the transmission power of the UAV does not surpass the maximum saturation power of the EH circuitry. Due to the complicated nature of the Bessel function and infinite series in (7.25), finding a closed-form expression for an optimal ρ ∗ that minimizes AAoI in (7.35) is not possible. Thus, the suggested minimization problem (P1) can be solved by golden section search method without resorting to derivatives under the given constraints. Let us assume that within the interval [a, b], the ρ ∗ is found. Accordingly, p and q can be written as p = b − (b − a)ψ √ and q = a + (b − a)ψ, where ψ = 5−1 is the golden ratio conjugate. After 2 completing the evaluation of AAoI in (7.35) at points p and q, a new interval for searching is identified adhering to the condition AoI (ejp ) ≤ AoI (ej q ) or AoI (ejp ) > AoI (ej q ). The modified algorithm to find ρ ∗ is given in Algorithm 1.

Algorithm 1: Optimal ρ ∗ that minimized AoI 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Data: [a = 0, b = 1], (7.35), tolerance . Result: ρ ∗ Initialize ψ, p and q fp = AoI (p) fq = AoI (q) while (b − 1) ≥  do if fp ≤ fq then q → b and p → q p = b − (b − 1)ψ fq = fp and fp = AoI (p) else p → a and q → p q = a + (b − a)ψ fp = fq and fq = AoI (q) end end return ρ ∗ ← (a + b)/2

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Fig. 7.6 Achievable AoI together with the outage probability at the destination, where n = 12bits

7.4.3 Numerical Results Without loss of generality and unless otherwise stated, all simulation parameters are set as follows. It is assumed that κ1 = κ2 = 0.1, σ 2 = −80 dBm, α = 2, γ th = 0, L0 = −60 dB, fixed service rate of R = 2, and arrival rate λ = 1/E[Y ]. For the nonlinear EH model, parameters are set as λ = 50 mW, μ = 0.064 mW, and ωa = ωc = 0.003 mW, and it is noteworthy that these parameters can be changed according to the characteristics of the EH circuitry. Furthermore, we have set RMS delay spread for 1 m as rm = 1 × 10−6 , AF delay as rAF = 3.18 × 10−3 in digital domain and rAF = 2 × 10−6 in analog domain, and s = 1 × 10−6 s. For the Monte Carlo simulation, we have used the number of realization as Ntrials ≥ 1000. First, we investigate the achievable pairs of AoI and outage probability to understand the relationship between the variables and the system boundary of the considered communication system setup in terms of AoI. Figure 7.6 illustrates the AoI performance of the proposed system versus the outage probability at the destination. It can be clearly seen from the figure that service time Y is increasing with the increase in outage probability causing an increase in AoI toward infinity showing similar behavior illustrated in Fig. 7.4. The boundary in Fig. 7.6 shows that there is an intrinsic relationship between service time/packet delay and the outage probability.

7 AoI

145

90

M.Sim. P = 10 dBm

80

Analytic P = 10 dBm *

70

M.Sim. P = 20 dBm

60

AoI

-> P = 10 dBm

Analytic P = 20 dBm

18.85 18.8 18.75 18.7

50

0.7

*

-> P = 20 dBm

18.822

40 18.82 0.75

30 20 10 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Fig. 7.7 Optimal values for AoI with respect to transmission power P

In Fig. 7.7, the optimal value of PS ratio ρ is assessed with respect to the transmission power P for AoI given in (7.35). To verify the obtained theoretical results, the Monte Carlo simulation results are also provided for the comparison. It can be observed from Fig. 7.7 that there exists an optimal point of ρ for AoI metric. Furthermore, it can be observed that the optimal point decreases with the increase in transmission power. This observation makes sense since the amount of energy harvested is saturated due to the nonlinearity of the EH circuitry as in (7.20). Thus, the optimal value reduces accordingly to maximize the portion of information processing signal to improve the system performance, which leads to higher SNDR at the terminal. The minimum AoI is achieved at 0.7 and 0.75 for transmission power of 20 dBm and 10 dBm, respectively. It can also be seen that the numerical optimal values obtained via Algorithm (1) tally with the Monte Carlo simulation results showing the accuracy of the low complexity Algorithm (1). In Fig. 7.8, the impact of data packet size on the AoI with respect to the outage probability is evaluated. It can be clearly seen from the figure that AoI converges to AoI floor when the outage probability decreases. AoI floor approximately equals service time when there is fixed inter-arrival time with m = 0 due to the zero-

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5000

dp=12 bits

4500

dp=32 bits dp=64 bits

4000

dp=128 bits 3500

dp=256 bits

AoI

3000 2500 2000 1500

AoI converges to AoI Floor

1000X 0.1 Y 412.5 500

X 0.1 Y 19.34

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Outage Probability Fig. 7.8 Time average AoI versus outage probability with n ∈ 12, 32, 64, 128, 256 bits, and P = 30 dBm

outage probability. However, service time increases with the increase in size of the data packet as in (7.28) causing an increase in AoI with respect to the size of the data packet. It can also be observed from Fig. 7.8 that if the data buffer at the terminal has a higher number of bits, sending the entire data vector in multiple small data packets can lead to a higher AoI as compared to sending in larger data packets. For an instance, let us consider AoI values of the given data points in Fig. 7.8 when the outage probability is equal to 0.1. If the data vector has 256 bits to be transmitted to the destination, sending the entire data vector as a one data packet makes the AoI value as 412.5. However, transmitting data vector by using 22 data packets with the size of 12 bits gives the AoI value as 425.48, which is larger than the previous case. Thus, the size of the update data packet needs to be decided carefully with respect to the data vector that needs to be transmitted to the destination. It is clearly seen from Fig. 7.8 that the impact of outage probability and data packet size on the AoI affects similarly with minor changes.

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7.5 Applications and Recommendations Migrating from tradition performance metrics toward new performance metrics such as AoI can be treated as a tool to address different requirements of communication applications toward beyond 5G. AoI has started evolving as a performance metric due to the growing literature. Especially, this evolving AoI can be used to achieve a wide range of objectives in communication networks, in which critical real-time information is shared among the communication nodes. Energy replenishment via RF signals is an important aspect of wireless powered communication networks. Time-varying availability of energy to replenish the inbuilt battery along with its constraints can decrease the sampling rate at the data source and the status update freshness at the destination. Thus, investigation of the way that stochastic EH affects the system AAoI at the destination is timely required. Furthermore, optimal information age-related policies are required to make EH techniques such as SWIPT, WPT, etc. a practical reality in the next 3GPP releases. Optimizing AoI while maintaining expected QoS in wireless sensor networks is also known as another challenging research area. Characterization of AoI distribution as a random process is the next crucial step in AoI-related research. Thus, a promising avenue for the future work is to build mathematical foundation for the stationary distribution of AoI in terms of system delay between any two consecutive time instants of update data packet at the reception. This can be further extended by considering the general cost of information staleness. This will be useful to investigate second-order properties related to the randomness of AoI, i.e., auto-correlated function, etc. In cellular networks, base stations need to estimate the channel responses from the active end users. This channel response information is utilized by the base stations when processing the uplink and downlink signals for each user. The knowledge of the current channel responses is also known as channel state information (CSI). In one-way wireless links, base station gets to know CSI via a CSI feedback sent by the end user. Thus, this can affect the age of available information at the end user over time causing limited access to timely information. The CSI aging can be caused by multiple factors, i.e., measuring time, transmission delay, processing time, time to execute adaptation functions, frame time, and time interval between consecutive acknowledgements. Thus, the way of CSI aging can incorporate with the AoI framework of a communication system required significant attention from the researchers. Caching and content placement are another promising research avenue in AoI. Critical investigations are required on caching policies that are aimed to minimize cache misses using request rates and popularity along with the content age and updating latest content in a cache to minimize the AAoI on cache data. Message caching has become critically important in high-demand online services and IoT applications i.e., online gaming, smart grids, smart cities, augmented reality, etc. Overall, in wireless communication applications, there is a vast opportunity of possible application domains associated with the concept of timeliness information captured by the metric AoI.

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7.6 Conclusion AoI in wireless communication has emerged as an end-to-end performance metric to measure the timeliness of received status updates at the destination. The concept of age is common that age-based optimizations can be found almost in all network layers. These age policies are substantially different from the maximization of achievable throughput. Moreover, age-based status update mechanisms are quite practical since the transmitters, receivers, routers, and servers easily understand the time stamps as compared to the other application-specific measurements, i.e., outage probability, throughput, latency, etc. The introduction of AoI has lead the scientific world into the development of new analytical models for status update freshness and tools for age analysis. It is also noteworthy that the AoI metric is now beginning to be applied in UAV-assisted communication networks, IoT application, etc. However, it is clear that there are still lots of answered questions, open problems, and unexplored potential applications related to AoI performance metric. As a foundation for the topic AoI, in this chapter, we have described AoI performance metric in detail giving examples and mathematical foundation. Furthermore, evolution of AoI along with the other performance metrics emerged from AoI, i.e., peak AoI, cost of update delay, and value of information update were explained along with its mathematical formulations. Then, a SWIPT-PS-enabled two-way relay network was used to formulate the AoI performance metric in EH-enabled wireless setup following the mathematical formulations described earlier. After obtaining a closed-form expression for time average AoI, an optimization problem was formulated to identify the optimal power-splitting factor that minimizes the AoI performance. Furthermore, it was shown the relationship between AoI and the traditional performance metric outage probability. Finally, potential applications and recommendation were provided for future investigation of AoI performance metric in different research domains. In each of these recommendations, there are likely to be informative problem formulations. These informative problem formulations will provide the answer for the question of whether AoI performance metric will become a practical performance metric to assist design and operations of real-time cyberphysical applications yet to come in future generations of communications.

Appendix 1 The outage probability of the proposed system can be defined as the probability that the end-to-end average SNDR of the update data packet falls below a desired threshold value γ th . Therefore, the system outage probability at the S1 1 can be expressed as

1 Due

to the similarity between S1 and S2 , from here onward, we focus on terminal S1 .

7 AoI

149

Pout = P r(γS1 < γ th ),

(7.37)

where γ th = 22R − 1 and R is the transmission rate of the terminals. In order to have a closed-form expression for outage probability, considering (7.37), we fix X1 at some value x1 and obtain the outage probability with respect to x1 . Next, the average of the obtained function in terms of x1 with respect to the distribution of X1 is considered to acquire the closed-form expression for outage probability at S1 . Thus, (7.37) can be rewritten as  Pout =

∞

γ0 (C4 x1 + c3 x1 + c2 )fX1 (x1 )dx1 .

0

(7.38)

Now, (7.38) can be rewritten as pout = 1 − μ1 e−2K



∞ ∞  ∞

0

l  (μ2 γo )m K l+k (c4 x1 (k!)2 m!l!

k=0 l=0 m=0

(7.39)

+ c3 x1 + c2 )m × e−μ2 γ0 (c4 x1 +c3 x1 +c2 ) (μ1 x1 )k e−μ1 x1 dx1 . Then, having μ3 = μ1 e2K e−c2 μ2 γ0 and by applying probability mass function with binomial coefficient, we can obtain Pout = μ3  × "0

∞  l  m  n ∞  m m−n cn−p cp  K l+k μk1 μm 2 γ0 c4 3 2 (k!)2 l!p!(m − n)!(n − p)! l=0 k=0 m=0 n=0 p=0 " #$ % V1

∞

m−2n+k+p −(μ1 +c4 μ2 γ0 )x1 −μ2 γ0 c3 x1 x1 e

#$

(7.40)

dx1 ,

%

V2

whereby using (8.321.1) in [27], V2 can be represented as the complete Gamma function, and thus, (7.40) can be expressed as Pout =μ3

∞  l  m  n ∞  

V1 Γ (1 + k + m − 2n + p)(μ1 + μ2 γ0 (c4 + c3 ))−l−k−m−2n−p ,

k=0 l=0 m=0 n=0 p=0

(7.41) where only if (k + m − 2n + p) > 1 && μ1 + μ2 γ0 (c4 + c3 ) > 0. Thus, by letting μˆ3 = μ1 + c4 μ2 γ0 and considering Equation (3.471.9) in [27], a closedform expression for the outage probability is obtained as in (7.25).

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Index

A Aerial base station (ABSs), xii, 62, 114, 116–122, 125 Age of information (AoI), ix, xii, xiii, 107, 127–149 Amplify-and-forward relay, 41, 109

C Channel estimation, ix, 7–14, 25, 112 Channel tracking, 1–25 Coverage, xi, xii, 1, 32, 39, 40, 62, 63, 79, 80, 82, 83, 87, 92, 93, 95–101, 108–109, 113, 115, 116, 125

D Data freshness, 128, 129, 137 Decode and forward (DF), x, 41, 58, 109, 110 Disaster-resilient system, ix, 105–125 Dual-hop relay, 41

H Hardware impairment (HI), 138, 139 Hoyt fading channels, 65, 74

M Minimum achievable rate, 119, 122–124 Modulation, ix, 1, 18, 28, 48, 80–87 Moving cells, xii, 114, 124

O Orthogonal frequency-division multiplexing (OFDM), x, 5, 27–34, 36, 37 Outage probability (OP), xi, 45–54, 63, 67–72, 74, 75

R Reliability, xi, xii, 7, 25, 35, 39, 40, 61, 79, 80, 82, 83, 87, 95, 96, 98, 101, 106, 127–129 Rician Shadowed fading channels, xi, 63, 74

E Equalization, ix, x, 1–25, 27–30, 33–35

F Fairness, xii, 118, 122–125 Fifth generation (5G) networks, ix, x, xi, xiii, 28, 39, 79–103, 106, 107, 130, 147

S Self-Interference (SI), 41, 47, 49, 52–54, 57, 114 Simultaneous wireless information and power transfer (SWIPT), x, xii, 40–42, 44, 52, 58, 62, 138, 140, 147, 148

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 D. N. K. Jayakody et al. (eds.), Integration of Unmanned Aerial Vehicles in Wireless Communication and Networks, Unmanned System Technologies, https://doi.org/10.1007/978-3-031-03880-8

153

154 Single-carrier modulations combined with frequency-domain equalization (SC-FDE), ix, x, 1, 5, 28, 33–36 T Throughput, x, xi, 40, 41, 51–58, 62, 80–83, 85–89, 91–102, 129, 140, 142, 148 U UAV data collection, xi

Index UAV positioning, xi, 81, 82, 93, 101, 122 Unmanned aerial vehicle (UAV), 1, 27, 39, 61, 79, 105, 128 User association, xii, 112, 114, 119, 122, 125

W Weibull fading channel, x, 52, 58 Wireless energy transfer (WET), xi Wireless sensor network (WSN), xi, 62, 63, 65, 74, 111, 112, 130