Reconfigurable Intelligent Surface-Enabled Integrated Sensing and Communication in 6G (Wireless Networks) 9819982987, 9789819982981

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Wireless Networks

Xiaoling Hu Chenxi Liu Mugen Peng Caijun Zhong

Reconfigurable Intelligent Surface-Enabled Integrated Sensing and Communication in 6G

Wireless Networks Series Editor Xuemin Sherman Shen, University of Waterloo, Waterloo, ON, Canada

The purpose of Springer’s Wireless Networks book series is to establish the state of the art and set the course for future research and development in wireless communication networks. The scope of this series includes not only all aspects of wireless networks (including cellular networks, WiFi, sensor networks, and vehicular networks), but related areas such as cloud computing and big data. The series serves as a central source of references for wireless networks research and development. It aims to publish thorough and cohesive overviews on specific topics in wireless networks, as well as works that are larger in scope than survey articles and that contain more detailed background information. The series also provides coverage of advanced and timely topics worthy of monographs, contributed volumes, textbooks and handbooks.

Xiaoling Hu . Chenxi Liu . Mugen Peng . Caijun Zhong

Reconfigurable Intelligent Surface-Enabled Integrated Sensing and Communication in 6G

Xiaoling Hu State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications Beijing, China

Chenxi Liu State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications Beijing, China

Mugen Peng State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications Beijing, China

Caijun Zhong School of Information and Electronic Engineering Zhejiang University Hangzhou, Zhejiang, China

ISSN 2366-1186 ISSN 2366-1445 (electronic) Wireless Networks ISBN 978-981-99-8298-1 ISBN 978-981-99-8299-8 (eBook) https://doi.org/10.1007/978-981-99-8299-8 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 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 Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Paper in this product is recyclable.

Preface

The sixth-generation mobile system (6G) is expected to have both high-rate communication and high-accuracy sensing capabilities, supporting various novel applications, such as smart factories, the Internet of Vehicles, and immersive services. Against this background, integrated sensing and communication (ISAC) emerges as a new paradigm, due to its advantages of high spectral efficiency, low hardware cost, and mutual enhancement of communication and sensing. With rich spectral resources and miniaturized hardware modules, high-frequency bands such as millimeter waves and terahertz are promising for realizing ISAC. However, due to the severe wireless propagation conditions in high-frequency bands, ISAC faces challenges of limited coverage and limited communication-sensing performance caused by uncontrollable wireless environments. Reconfigurable intelligent surface (RIS) provides a new way to tackle these challenges, by actively shaping wireless propagation environments. RIS-enabled ISAC can help comprehensively improve 6G multi-dimensional performances such as communication capacity, sensing accuracy, and coverage. In this book, we aim to deliver a thorough understanding of RIS-enabled ISAC from three perspectives, namely, performance evaluation, signal processing technologies, and air interface technologies. First, in Chap. 1, we give an introduction to RIS-enabled ISAC, including its background and motivations, potential applications, fundamentals, and state of the art. In particular, we discuss the challenges faced by the high-frequency ISAC system, including limited coverage, high cost and power consumption, and limited communication and sensing performance due to uncontrollable environments, and point out the benefits of introducing RIS, namely, extending system coverage, reducing system cost and power consumption, and enhancing both communication and sensing performances. Second, we present the theoretical performance analysis of RIS-Enabled ISAC in Chap. 2. In the state of the art of ISAC technologies, communication and sensing functionalities are co-designed to offer unprecedented synergies and acquire integration gain. However, in general, communication performance is mostly measured by channel capacity, while sensing performance is mostly measured by mean squared error (MSE). For the RIS-enabled ISAC systems, this divergence in performance v

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Preface

evaluation metrics makes it difficult to investigate the joint communication-sensing performance. Responding to this, we present a new theoretical framework for performance evaluation of the RIS-enabled ISAC systems, and reveal the impacts of some key system setups (such as RIS passive beamforming, the randomness of communication signals, time resources, transmit power, and so on) on the communication-sensing tradeoff. Third, we discuss spatial and delay-Doppler signal processing technologies of RIS-enabled ISAC in Chaps. 3 and 4, respectively. For spatial signal processing, by exploiting the additional spatial freedom provided by RIS, higher angle of arrival (AoA) estimation accuracy can be achieved, thereby enabling more accurate location sensing. AoA-based location sensing with the assistance of a distributed RIS is addressed under various system setups, from single users to multiple users. For delay-Doppler signal processing, the acquisition of delay-Doppler information relies on the processing of the received echo signals. However, due to the introduction of RIS, the transmitted signals in RIS-enabled ISAC systems undergo reconfigurable and cascaded echo channels. Taking into account these new echo channel characteristics, we discuss the coarse-grained and fine-grained sensing via delay-Doppler estimation. Fourth, we discuss the air interface technology, i.e., beamforming, in RISenabled ISAC. In Chap. 5, by exploring the inner relationship between communication channels and sensing parameters in the RIS-enabled ISAC system, we study sensing-assisted beamforming schemes to avoid high-overhead channel estimation or beam training while ensuring communication performance. In addition, in RISenabled ISAC systems, the beamforming requirements for communication and sensing are different and even contradictory, making it difficult to balance their performance. Responding to this, in Chap. 6, we discuss RIS multi-beam design for simultaneous communication and sensing enhancement. Finally, Chap. 7 presents future trends and open issues of RIS-enabled ISAC from four aspects, namely, new information theory and practical measurement, air interface technologies, signal processing technologies, and hardware design and practical deployments. Acknowledgments The authors would like to thank Zhouyuan Yu, Xiaowei Qian, Shuyang Lv, Xin Peng, and Sitong Li for their assistance in preparing some of the technical content of this book. Many thanks as well to technical reviewers and language and graphic editors, who have all contributed to the book-compiling process. Beijing, China Beijing, China Beijing, China Hangzhou, China August, 2023

Xiaoling Hu Chenxi Liu Mugen Peng Caijun Zhong

Contents

1

Introduction of RIS-Enabled ISAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Background and Motivations of RIS-Enabled ISAC . . . . . . . . . . . . . . . . . . 1.1.1 Requirements of 6G . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Basics and Challenges of ISAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Basics and Advantages of RIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.4 Motivations of RIS-Enabled ISAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Potential Applications of RIS-Enabled ISAC. . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Smart Transportation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Smart Factory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 UAV Application. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Fundamentals of RIS-Enabled ISAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 RIS Response Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Overview of RIS-Enabled ISAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 RIS-Enabled DF ISAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 RIS-Enabled DB ISAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 1 1 3 5 6 6 6 8 8 9 9 11 15 15 18 20 21

2

Theoretical Performance Analysis of RIS-Enabled ISAC . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 System Model of RIS-Enabled NO-ISAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 NO-ISAC Transmission Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Performance Evaluation of RIS-Enabled NO-ISAC System . . . . . . . . . . 2.4 Modified CRLB-Based Beamforming Design . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 BS Active Beamforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 IRS Passive Beamforming. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25 25 25 26 27 28 29 35 36 36

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2.5 Numerical Results and Discussions on the Performance of RIS-Enabled ISAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 RIS-Enabled NO-ISAC System vs. RIS-Enabled Localization System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 RIS-Enabled NO-ISAC System vs. RIS-Enabled TD-ISAC System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3 Tradeoff Between Communication Performance and Localization Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38 39 41 44 48 49

3

Angle Information Acquisition in RIS-Enabled ISAC . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Single-User Localization via AoA Estimation. . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Proposed Location Sensing Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Numerical Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Simultaneous Multi-User Localization via AoA Estimation . . . . . . . . . . 3.3.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Multi-User Location Sensing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Numerical Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51 51 52 52 54 59 62 62 65 72 75 76

4

Delay-Doppler Information Acquisition in RIS-Enabled ISAC . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Transmission Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Coarse-Grained Sensing via Delay-Doppler Estimation . . . . . . . . . . . . . . 4.3.1 Hierarchical Codebook Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 3D Hierarchical Beam Training Based on a DSP Detector . . . 4.3.3 Beam Refinement for High-Accuracy Direction Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Fine-Grained Sensing via Delay-Doppler Estimation . . . . . . . . . . . . . . . . . 4.4.1 Maximum Likelihood Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Numerical Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Performance of the Hierarchical RIS 3D Beam Training . . . . . 4.5.2 Performance of the Distance and Velocity Estimation . . . . . . . . 4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77 77 77 78 79 80 81 83 86 90 91 93 95 96 98 99 99

Contents

5

Sensing-Assisted Beamforming in RIS-Enabled ISAC . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Sensing-Assisted Beamforming in the Single-User Case . . . . . . . . . . . . . 5.2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Beamforming Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Numerical Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Sensing-Assisted Beamforming in the Multi-User Case . . . . . . . . . . . . . . 5.3.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Sensing-Based Joint Active and Passive Beamforming . . . . . . . 5.3.3 Numerical Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

Beamforming for Simultaneous Communication and Sensing Enhancement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Beamforming for Joint Performance Enhancement of Device-Based RIS-ISAC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 System Model of Device-Based RIS-ISAC . . . . . . . . . . . . . . . . . . . 6.2.2 Sensing-Based Beamforming for Joint Performance Enhancement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Numerical Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Beamforming for Joint Performance Enhancement of Device-Free RIS-ISAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Wideband Beamforming for Simultaneous Communication and Sensing Enhancement . . . . . . . . . . . . . . . . . . 6.3.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

Future Trends and Open Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 New Information Theory and Practical Measurement. . . . . . . . . . . . . . . . . 7.1.1 New Information Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.2 Practical Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Air Interface Technologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Waveform Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 Beamforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Signal Processing Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Hardware Design and Practical Deployments . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Wideband and High-Frequency the RIS . . . . . . . . . . . . . . . . . . . . . . . 7.4.2 Deployment and Control of the RIS . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

101 101 101 101 105 110 113 113 118 126 132 132 135 135 136 136 141 152 158 158 163 168 171 171 173 173 173 174 174 174 175 176 176 176 177 177

Acronyms

3D AWGN AO AoA AoD BS CP CPI CRLB CSI DB DF DFRC DoF ECSI EDA EM ESPRIT FBSS FPGA ISAC KKT LoS LS MIMO Mmwave MRC MUI MUSIC NO-ISAC NLoS

Three-Dimensional Additive White Gaussian Noise Alternating Optimization Angle of Arrival Angle of Departure Base Station Cyclic Prefix Coherent Processing Interval Cramer-Rao Lower Bound Channel State Information Device-Based Device-Free Dual-Function Radar-Communication Degree of Freedom Effective Channel State Information Estimation of Distribution Algorithm Electromagnetic Estimation of Signal Parameters via Rotational Invariance Technique Forward-backward Spatial Smoothing Field Programmable Gate Array Integrated Sensing and Communication Karush-Kuhn-Tucker Line of Sight Local Search Multiple-Input Multiple-Output Millimeter wave Maximum Ratio Combining Multi-User Interference Multiple Signal Classification Non-Orthogonal ISAC Non-Line of Sight xi

xii

OFDM PIN PSO RCC RF RIS RSS SINR SV TLS TOA UAV ULA UPA ZF

Acronyms

Orthogonal Frequency Division Multiplexing Positive-Intrinsic-Negative Particle Swarm Optimization Radar-Communication Coexistence Radio Frequency Reconfigurable Intelligent Surface Received Signal Strength Signal-to-Interference-plus-Noise Ratio Saleh-Valenzuela Total Least Square Time of Arrival Unmanned Aerial Vehicles Uniform Linear Array Uniform Rectangular Array Zero-Forcing

Chapter 1

Introduction of RIS-Enabled ISAC

1.1 Background and Motivations of RIS-Enabled ISAC 1.1.1 Requirements of 6G As shown in Fig. 1.1, 6G will be oriented to new vertical application scenarios represented by smart manufacturing, smart transportation, and smart home, and supports diverse new applications and services such as digital twins, multi-sensory extended reality, autonomous driving, and holographic communication. In order to realize the above vision, the future 6G network will evolve from a single communication facility to a multi-functional comprehensive platform including wireless communication, sensing, computing and artificial intelligence. In addition to traditional wireless communication capabilities, multi-dimensional environment sensing capabilities are also necessary for acquiring physical space information. Hence, integrated sensing and communication (ISAC) has become a mainstream trend of 6G, and it is also a hot spot in the current 6G air interface technology research.

1.1.2 Basics and Challenges of ISAC ISAC is a new type of information processing technology based on software and hardware resource sharing or information sharing to realize concurrent sensing and communication functions, which can effectively improve system spectrum efficiency, hardware efficiency, and information processing efficiency. Through air interface and protocol joint design, time-frequency-space resource sharing, hardware device sharing and other means, the unified design of communication and sensing functions is realized. This allows the wireless network to simultaneously © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Hu et al., Reconfigurable Intelligent Surface-Enabled Integrated Sensing and Communication in 6G, Wireless Networks, https://doi.org/10.1007/978-981-99-8299-8_1

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2

1 Introduction of RIS-Enabled ISAC

smart home smart manufacturing smart transportation

Fig. 1.1 New vertical application scenarios

carry out high-quality communication interaction and high-accuracy, fine-grained sensing, thereby improving the overall performance of the network and its service capabilities. The core design concept of the ISAC is to realize two independent functions of communication and sensing in a single system and realize the mutual enhancement of the two. Sensing, like communication, will become a native capability of 6G networks. On the one hand, the communication system can provide various types of sensing services through spectrum sharing, hardware or signal processing module multiplexing. On the other hand, sensing information can also be used to assist communication (e.g., channel estimation, beamforming, intelligent scheduling, etc.), improving communication service quality and efficiency. High-frequency bands such as millimeter waves (Mmwave) and terahertz are especially promising for realizing ISAC. On the one hand, compared with sub6G and other low-frequency bands, the large bandwidth provided by millimeter wave or terahertz can support higher-rate communication and higher-resolution sensing services, and can provide low-latency information exchange and sharing for communication and sensing modules. On the other hand, small Mmwave antennas are also conducive to the hardware integration of the two modules. However, the ISAC system operating in the high-frequency band faces the following three major challenges in practice. • The first challenge is the limited coverage. Since high-frequency signals suffer from severe propagation path loss, the ISAC system usually has a very small coverage. What is worse, the line-of-sight (LoS) path is easily blocked by environmental objects due to the high penetration loss, leaving a lot of blind spots. For example, MmWave signals have a high penetration loss of more than

1.1 Background and Motivations of RIS-Enabled ISAC

3

10 dB when passing through common environment objects such as the human body, leaves, vehicles, and concrete buildings. • The second challenge is the high cost and power consumption. In order to compensate for the high path loss of high-frequency signals, a large-scale multiple-input multiple-output (Multiple-Input Multiple-Output, MIMO) technology is usually used, which brings problems of high hardware cost and high power consumption. • The third challenge is that both communication and sensing performances are limited to the uncontrollable environment. In terms of communication performance, Shannon channel capacity reveals that the maximum communication rate for error-free transmission is determined by the channel condition (i.e., the wireless propagation environment). Traditional communication systems can only passively adapt to the uncontrollable environment through the design of transceivers. In terms of sensing performance, the theory of detection and estimation reveals that the effective improvement of sensing resolution depends on a large number of independent observation samples. However, due to the uncontrollable wireless environment, the correlation between observation samples is strong, and the improvement of sensing resolution is limited only by increasing the number of observation samples.

1.1.3 Basics and Advantages of RIS Developed based on the technology of electromagnetic metamaterials, RIS is an artificial two-dimensional surface with special electromagnetic properties. Figure 1.2

Middle layer Inner layer

Outer layer

Intelligent controller Fig. 1.2 Typical hardware architecture of RIS

4

1 Introduction of RIS-Enabled ISAC

illustrates the typical hardware architecture of RIS, which is composed of three layers and an intelligent controller. • The outer layer is a two-dimensional surface, which consists of a large number of regularly arranged electromagnetic elements and is responsible for directly interacting with incident signals. These electromagnetic units are usually composed of metals, dielectrics, and adjustable elements. Typical adjustable elements are varactor diodes, and positive-intrinsic-negative (PIN) diodes. By controlling the bias voltage of the adjustable element, the electromagnetic properties of the RIS element can be adjusted, and then the electromagnetic parameters (such as phase, amplitude, etc.) of the incident signals can be changed in a programmable way, so as to manipulate the electromagnetic wave achieve intelligent manipulation of the electromagnetic wave. • The Middle layer is a copper plate that is responsible for preventing signal energy leakage. • The Inner layer is a control circuit board, its main function is to apply control signals to each RIS element, and then adjust the electromagnetic properties of each element. • The intelligent controller is connected to the control circuit board and is responsible for triggering the control signal. In practical applications, a field programmable gate array (FPGA) can be used as the intelligent controller of RIS. Due to the above special hardware architecture, RIS has the following advantages, compared with the traditional active antennas. • Low hardware cost: For traditional phased arrays, its components such as phase shifters and power amplifiers need to be connected to each antenna element to achieve beamforming in the analog domain. In contrast, RIS does not need to configure a large number of devices such as phase shifters and power amplifiers, but only integrates devices with low hardware costs such as PIN diodes or varactor diodes in each electromagnetic element. By controlling the bias of these adjustable devices, the phase response of each electromagnetic element can be changed by setting the voltage, thereby realizing beamforming in the analog domain. Hence, compared with the traditional phased array, the hardware cost of RIS is relatively low. • Low power consumption: The electromagnetic element of the RIS is mainly a passive unit, and its main function is to intelligently adjust the phase of the incident signal, without the ability to amplify the power of the signal. In addition, compared with traditional communication equipment, RIS does not have devices (such as radio frequency(RF) chains) with high power consumption, so RIS has a great advantage in terms of power consumption. • Easy deployment: RIS is a two-dimensional metasurface. Since its thickness is much smaller than the wavelength of wireless electromagnetic waves, RIS is relatively light and thin overall. And it does not integrate a large number of complex hardware devices. These characteristics make the deployment of RIS

1.1 Background and Motivations of RIS-Enabled ISAC

5

more flexible than that of traditional active equipment. It can be easily deployed on common environment objects such as vehicles, the surface of buildings, and indoor walls. In addition, the number of RIS elements can be adjusted according to actual requirements, which greatly increases the flexibility of its deployment. • No additional delay and thermal noise: Traditional transceivers introduce additional processing delays and thermal noise when receiving, processing, and transmitting signals. However, RIS only relies on the physical characteristics of the passive electromagnetic unit to complete the phase adjustment of the incident signal, without the process of signal processing, so it will introduce neither additional signal processing delay or thermal noise.

1.1.4 Motivations of RIS-Enabled ISAC The emergence of the reconfigurable intelligent surface (RIS) provides a new way to solve the problems faced by the practical application of ISAC systems. As mentioned above, RIS has the advantages of low cost, low power consumption, easy deployment, and no additional delay or thermal noise. It can actively control the wireless environment in a programmable manner, transforming the traditional design paradigm that passively adapts to the wireless environment to a new paradigm that intelligently shapes the environment. This new paradigm will facilitate the overall improvement of 6G communication and sensing capabilities. Especially, RIS-enabled ISAC has the following advantages. • Extending system coverage: When the LoS path is blocked, RIS solves the problem of blind area coverage by constructing a virtual line-of-sight path; When the LoS path exists, RIS can enhance the received signal strength, thereby expanding the coverage radius of the ISAC system. • Reducing system cost and power consumption: The application of RIS makes the design of ISAC systems transform from traditional large-scale MIMO systems to RIS-enabled medium-sized MIMO systems. By mining aperture and beamforming gains, RIS can achieve better communication and sensing performances with lower hardware costs and power consumption. • Enhancing both communication and sensing performances: The introduction of RIS incorporates the wireless propagation environment into the design of the ISAC system, providing additional spatial freedom. For communication, RIS can enhance communication performance by actively improving the channel condition, breaking through the original channel capacity determined by the uncontrollable environment. There are two main ways to improve the channel condition. One is to create more abundant scattering paths, thereby providing additional multiplexing gain and supporting multi-stream transmission in hot spot areas. Another is to realize the superposition of signals with the same phases, thereby providing additional diversity gain and serving weak signal areas such as cell edges. For sensing, RIS helps to shape a low-correlation

6

1 Introduction of RIS-Enabled ISAC

electromagnetic environment through time-space encoding. As such, a large number of independent observation samples about the sensing target can be obtained, which greatly improves the sensing resolution.

1.2 Potential Applications of RIS-Enabled ISAC RIS-enabled ISAC can facilitate the capabilities expansion and performance enhancement of 6G networks, thereby forming industrial synergy and cluster effects, and giving birth to more new applications. Sensing, like communication, will become the native capability of 6G networks. With the “integration gain”, mutual enhancement of communication and sensing can be realized, and with the “collaboration gain” of RIS, multi-dimensional performance such as communication rate, sensing accuracy, and coverage will be further improved. Typical applications of RIS-enabled ISAC include smart transportation, smart factories, and unmanned aerial vehicles (UAVs).

1.2.1 Smart Transportation By adopting ISAC technology, the future intelligent transportation system will realize the efficient collaboration and interconnection of people, vehicles, and roadside infrastructures. The roadside unit can accurately acquire the vehicle’s states such as positions and speeds. And the vehicle can quickly interact with other vehicles, roadside units, pedestrians, etc. while extracting the surrounding environment information with high precision and resolution. However, due to the strong dynamics of vehicles, the limited distance of the Internet of Vehicles, and the occlusion of buildings, it is difficult to guarantee effective communication and sensing services between multiple vehicles, between vehicles and the surrounding environment, and between users in the vehicle and the base station. As shown in Fig. 1.3, the combination of RIS and ISAC technologies can improve the coverage of vehicles, expand the communication distance, and effectively solve the problem of communication and sensing performance loss caused by non-line-of-sight (NLoS) propagation. In addition, the introduction of the transmissive RIS can ensure that the signal sent by the base station is focused on the users in the vehicle through the RIS on the roof, thereby enhancing the received signal strength in the vehicle.

1.2.2 Smart Factory Future factories tend to be highly intelligent, requiring a large amount of equipment and robots to cooperate to complete complex industrial tasks. Ultra-high-precision

1.2 Potential Applications of RIS-Enabled ISAC

7

RIS

transmissive RIS

Fig. 1.3 Smart transportation

Fig. 1.4 Smart factory

sensing and extremely low communication delay are necessary to achieve close cooperation between robots, between robots and equipment, and between equipment and equipment. ISAC technology will play an important role in the development of smart factories, which is reflected in various aspects. First, ISAC assists in the realization of functions such as positioning, imaging, and environmental map construction. Secondly, by sensing channel state information, it reduces signaling overhead and thus ensures extremely low-latency communication. In addition, by uploading the sensing information to the cloud, joint sensing can be realized, guiding the robot or equipment to make correct decisions. As illustrated in Fig. 1.4, RIS can be deployed on factory walls and on the surface of large equipment to

8

1 Introduction of RIS-Enabled ISAC

Fig. 1.5 UAV application

enhance both communication and sensing performance, meeting the requirements for high reliability and low latency of communication when a large amount of equipment is connected.

1.2.3 UAV Application Owing to the high mobility of UAVs, UAVs can be quickly deployed in target areas, supporting applications such as emergency communications, monitoring and reconnaissance, which are closely related to communication and sensing services. With the help of ISAC technology, the base station or UAV can realize concurrent communication and sensing functions on the same platform and time-frequency resource blocks, thereby improving spectrum efficiency and energy efficiency. As shown in Fig. 1.5, the UAV use cases based on the RIS-enabled ISAC technology can be divided into two categories. One is to deploy the RIS as a small lowpower reflective antenna array on the UAV. Based on the sensing results of ground users’ location, quantity, distribution, etc., UAVs can adaptively adjust the reflection coefficients of RIS to enhance link quality and achieve wide coverage. Another is to deploy RIS as a passive relay On the ground building. The reflection coefficients of RIS are adjusted through the BS’s sensing of the UAV, thereby improving the communication rate with the UAV and supporting real-time communication services such as UAV high-definition video transmission.

1.3 Fundamentals of RIS-Enabled ISAC In this section, we introduce the fundamentals of RIS-enabled ISAC systems, including the RIS response model, signal model, and channel model.

1.3 Fundamentals of RIS-Enabled ISAC

9

1.3.1 RIS Response Model RIS is a planar array consisting of a large number of reconfigurable passive elements, and each element can induce a certain phase shift independently on the incident signal [1]. Specifically, each element of the RIS receives the superposed multi-path signals from the transmitter, and then scatters the combined signal with adjustable amplitude and/or phase as if form a single point source [2]. Let .θ = [θ1 , · · · , θM ] and define a diagonal matrix ) ( 0 = diag β1 ej θ1 , · · · , βM ej θM ,

.

(1.1)

as the reflection-coefficients matrix of the RIS, where .θm ∈ [0, 2π ) and .βm ∈ [0, 1] denote the phase shift and the amplitude reflection coefficient of the n-th element of the RIS, respectively. To characterize the fundamental performance of the RIS, we assume that the phase shifts can be continuously varied in .[0, 2π ), while in practice they are usually selected in a digital way, i.e., from a finite number of discrete values from 0 to .2π for the ease of circuit implementation. For the sake of practical implementation, the phase shift of each RIS element takes values from the .Q = 2b discrete values, where b denotes the number of bits used for quantizing the phase shifts. If the discrete phase shifts within .[0, 2π ) are uniformly quantized, then the set of discrete phase shifts is given by B = {0, Aθ, · · · , (Q − 1) Aθ } ,

.

(1.2)

where .Aθ = 2π/Q. For example, if the number of bits used for quantizing is .b = 1, then the phase shift .θm ∈ {0, π }. It is noticeable that such quantization may lead to the loss of performance and this has been investigated in a large amount of literature and experiments [3]. Also, this issue will be discussed in the subsequent chapters.

1.3.2 Signal Model With the assistance of an RIS, the dual-function radar-communication (DFRC) BS simultaneously communicates with a blind-zone user and conducts sensing of the target. The DFRC BS is able to carry out communication and sensing by using the OFDM waveform, and the sensing is realized by using the communication signals.1 The BS has .NBS transmitting/receiving antennas arranged in a uniform linear array (ULA) along the y axis, and the passive RIS has an .M = My × Mz uniform rectangular array (URA) lying on the y-o-z plane. The total bandwidth

1 OFDM is adopted in the RIS-enabled ISAC system because it is widely used in the communication systems and is also able to be implemented in the radar system.

10

1 Introduction of RIS-Enabled ISAC

of the system (denoted by B) is equally divided into N sub-carriers with a carrier frequency/wavelength .fc /.λ.2 The frequency of the n-th (.n ∈ N A {0, · · · , N − 1}) sub-carrier is .fn = fc + nAf , where .Af = B/N denotes the sub-carrier spacing. We denote the transmitted OFDM symbol as s = [s1 , s2 , · · · , sN ]T ∈ CN ×1 ,

.

(1.3)

where .sn represents the OFDM symbol on the n-th sub-carrier with unit power (i.e., E{|sn |2 } = 1). The compact transmit precoding matrix on all sub-carriers is given by

.

) ( WBST = diag wBST,1 , · · · , wBST,N ∈ CN NBS ×N ,

.

(1.4)

|| ||2 where .wBST,n ∈ CNBS ×1 , satisfying .||wBST,n || = 1, represents the transmit precoding vector on the n-th sub-carrier. For the signal transmitting process, the symbol vector .s is first precoded by the transmit precoder in the frequency domain, which yields the precoded symbol vector x = WBST s = [x1 , x2 , · · · , xN ]T ,

.

(1.5)

where .xn = wBST,n sn ∈ CNBS ×1 is the baseband precoded OFDM symbol vector on the n-th sub-carrier.

1.3.2.1

Communication Signal Model

The received baseband frequency-domain communication signals of the user on the n-th sub-carrier at the l-th OFDM symbol can be written as √ yu,n,l = pT,n Hc,n (0 (l)) xn,l + nu,n,l ,

.

n ∈ N , l ∈ L A {0, · · · , L − 1} ,

(1.6)

where .pT,n denotes the transmit power allocated on the n-th sub-carrier. The additive white Gaussian noise (AWGN) at the user is denoted by .nu,n,l , whose elements follow the complex Gaussian distribution .CN (0, σ02 ). In addition, .Hc,n (0 (l)) denotes the effective cascaded BS-RIS-user channel at the n-th sub-carrier which is defined as Hc,n (0 (l)) = hI2T,n 0 (l) HB2I,n ,

.

(1.7)

2 Narrowband scenario is considered where the bandwidth is much smaller than the carrier frequency (i.e., .B 0, σ02

(4.46)

based on which, we calculate the false alarm rate of each element in .r l as ) ( pF A,each = P [r l ]nD > κ|H0 =

f

∞

f (z|H0 ) dz

.

f

∞

= κ

z

κ κ

− 2 1 − σ2 e 0 dz = e σ0 . 2 σ0

(4.47)

When .ND = N, the false alarm rate can be expressed as [3] )N ( pF A = 1 − 1 − pF A,each .

.

(4.48)

Finally, for a DSP detector with the false alarm rate of .pF A , the false alarm threshold κ can be designed according to (4.48) and (4.47) as

.

) ( 1 κ = −σ02 ln 1 − (1 − pF A ) N .

.

(4.49)

4.3.3 Beam Refinement for High-Accuracy Direction Estimation After the beam training process, we determine that the target is within the coverage of the RIS phase shift beam ( ) ) ( 2iˆK − 1 2jˆK − 1 ˆ ˆ = bI −1 + .ξ iK , jK . , −1 + M M

(4.50)

4.4 Fine-Grained Sensing via Delay-Doppler Estimation

91

Since the beam training result is selected from the pre-defined codebook, the training accuracy is limited by the resolution of the codeword in the last layer. Responding to this, we propose a beam refinement approach to achieve superresolution beam training. Specifically, there are totally 4 adjacent areas around { } .ξ (iˆK , jˆK ), which belong to the set .ψ A ξ (iˆK + iA , jˆK + jA )|iA , jA ∈ {−1, 1} . In the beam refinement stage, we first remove the 2 searched areas in the K-th layer from the set .ψ. Then, we sequentially search for the two remaining areas in .ψ, and calculate the corresponding DSPs based on the received echo signals. Combining the DSPs of .ξ (iˆK , jˆK ) (denoted by .PDSP (iˆK , jˆK )) and its four adjacent areas, we update the azimuth/elevation index based on linear interpolation as ( ) ( ) ( ) fI iˆK −1, jˆK +fI iˆK , jˆK +fI iˆK +1, jˆK ) ( ) ( ) ,. ( .i˜K = P iˆK −1, jˆK +P iˆK , jˆK +P iˆK +1, jˆK ( ( ) ( ) ) fJ iˆK , jˆK − 1 +fJ iˆK , jˆK +fJ iˆK , jˆK +1 ) ( ) ( ) , j˜K = ( P iˆK , jˆK −1 +P iˆK , jˆK +P iˆK , jˆK +1

(4.51)

(4.52)

where .fI (i, j ) A iP (i, j ) and .fJ (i, j ) A j P (i, j ). As such, we obtain the final RIS phase shift beam as ( ) ( ) ˜ ˜ 2 j − 1 − 1 2 i K K opt ˜ , −1+ iK , j˜K = bI −1+ .ξ . M M

(4.53)

Recall (4.14), and we can find that the final RIS phase shift beam has the largest beamforming gain along the direction ) 2j˜K − 1 2i˜K − 1 A A + uB2I , −1 + + vB2I , −1 + M M

( .

(4.54)

( ) D which can be treated as the estimated target direction . uˆ D I2T , vˆ I2T .

4.4 Fine-Grained Sensing via Delay-Doppler Estimation During the fine-grained sensing period, we adopt the RIS phase shift beam (4.53) obtained in the previous beam training period, and estimate the distance and velocity of the target by extracting delay-Doppler information from the DFBS received echo signals.

92

4 Delay-Doppler Information Acquisition in RIS-Enabled ISAC

First, we denote the transmitting symbols during the fine-grained sensing period by an .N × TFS -matrix, whose .(n, l)-element is given by .

[SFS ]n,l = sn,(l+TCS ) , n ∈ N, l ∈ LFS A {0, · · · , TFS − 1} .

(4.55)

Similarly, according to (4.1), (4.2), and (4.10), we denote the DFBS received echo signals during the fine-grained sensing period by an .N × TFS -matrix, whose .(n, l)element is given by .

[YFS ]n,l =

√

( ) opt opt,T pT,n αTG wBS He,n 0opt wBS [SFS ]n,l ej 2π (l+TCS )TO fD

opt,T

+ wBS nBS,n,l ( ) √ opt 2 opt,T = pT,n αTG hI2T,n 0opt HB2I,n wBS [SFS ]n,l ej 2π (l+TCS )TO fD + wBS nBS,n,l =

√

pT,n αFS ejβFS e−j 2π nAf τ [SFS ]n,l ej 2π lTO fD + wBS nBS,n,l , opt,T

(4.56)

where |( ( ) ( ))2 || | 2 2 | H D D opt A A | ,. b u 0 u αFS A NBS αTG aI2T aB2I , v b , v I I2T I2T B2I B2I | I |

.

βFS A angle

(4.57)

(( ( ) ( ))2 ) D D opt A A +2π (TCS TO fD−fc τ ) . u 0 u , v b , v bH I I I2T I2T B2I B2I (4.58)

As such, all path losses and all phase shifts, which remain constant during the finegrained sensing period, are summarized into the amplitude term .αFS and the phase term .βFS . Then, by using the known transmitting symbol matrix .SFS , we processes the echo signals .YFS , which yields the auxiliary matrix .F, whose .(n, l)-element is given by .

[F]n,l =

[YFS ]n,l √ = pT,n αFS ejβFS e−j 2π nAf τ ej 2π lTO fD + [NFS ]n,l , [SFS ]n,l

(4.59)

where ) ( wBS nBS,n,l ∼ CN 0, σ02 , [SFS ]n,l opt,T

.

[NFS ]n,l =

(4.60)

denotes the noise term. After that, the auxiliary matrix .F would be passed on to the estimator for the delay .τ and the Doppler shift .fD of the target.

4.4 Fine-Grained Sensing via Delay-Doppler Estimation

93

4.4.1 Maximum Likelihood Estimation First, we stack the unknown parameters (i.e. .αFS , .βFS , .τ , and .fD ) to be estimated into a 4 dimensional vector .θ which is given by θ = [αFS , βFS , τ, fD ]T .

.

(4.61)

Since each symbol in .F is uncorrelated, the likelihood function can be expressed as f (F|θ ) =

−1 N −1 TFS || ||

.

n=0 l=0

( ) |2 1 1 || √ j (2π (lTO fD −nAf τ )+βFS ) | exp − 2 |[F]n,l − pT,n αFS e | , π σ02 σ0 (4.62)

and the corresponding log-likelihood function can be calculated as l (F|θ) =

N −1 TΣ FS −1 Σ

.

( − log π σ02 −

n=0 l=0

) |2 1 || √ j (2π (lTO fD −nAf τ )+βFS )| |[F]n,l − pT,n αFS e | . σ02 (4.63)

Then, the maximum likelihood estimate (MLE) for the unknown parameter vector can be expressed as θˆ ML = arg max l (F|θ) .

.

(4.64)

θ

To simplify the log-likelihood function, we ignore its first term since it does not depend on any of the estimation parameters and would not affect the maximization of the likelihood function. The same goes for the constant positive factor .1/σ02 in the second term. As such, the log-likelihood function maximization problem becomes (P2) : max

N −1 TΣ FS −1 Σ

.

θ

|2 | √ | | − |[F]n,l − pT,n αFS ej (2π (lfD −nAf τ )+βFS ) | .

(4.65)

n=0 l=0

Then, we further reformulate the above objective function as N −1 TΣ FS −1 Σ .

|2 | √ | | − |[F]n,l − pT,n αFS ej (2π (lfD −nAf τ )+βFS ) |

(4.66)

n=0 l=0

=

N −1 TΣ FS −1 Σ n=0 l=0

} { | |2 √ 2 − |[F]n,l| . 2αFS pT,n Re [F]n,l e−j (2π (lTO fD −nAf τ )+βFS ) − pT,n αFS

94

4 Delay-Doppler Information Acquisition in RIS-Enabled ISAC

By ignoring the constant terms that are independent of .θ , the objective function is reduced to lˆ (F|θ ) =

N −1 TΣ FS −1 Σ

.

} { Re [F]n,l e−j (2π (lTO fD −nAf τ )+βFS ) .

(4.67)

n=0 l=0

As such, .θˆ ML can be obtain as θˆ ML = arg max lˆ (F|θ) .

.

(4.68)

θ

To facilitate the parameter estimation, we reformulate (4.67) as ⎧ ⎫ ⎛ ⎞ N −1 TΣ FS −1 ⎨ ⎬ Σ ˆ (F|θ ) = Re ejβ ⎝ .l [F]n,l e−j 2π lTO fD ⎠ ej 2π nAf τ . ⎩ ⎭ n=0

(4.69)

l=0

Noticing that both the inner and the outer sum share a high resemblance with the Discrete Fourier transform (DFT), we design a DFT-based approach in the following steps. First, we quantize .τ and .fD as τnD =

.

nD τmax , nD = 0, · · · , NDFT − 1, . NDFT

fD,lD =

lD

fD,max , lD = −TDFT , · · · , TDFT − 1,

TDFT

(4.70) (4.71)

where .τmax = 1/2Af and .fD,max = 1/2TO are the maximum unambiguous time delay and the maximum unambiguous Doppler shift [4]. Since .fD can be negative, .lD is shifted symmetrically around zero. According to [5], it can be easily verified that the MLE for .τ and .fD is that which maximizes the Delay-Doppler spectrum N ×2TDFT , whose .(n , l )-th element is given by .A ∈ R DFT D D

.

[A]nD ,lD

| |2 ⎛ ⎞ |N −1 TFS −1 | |Σ Σ | −j 2π lTO fD,lD ⎠ j 2π nAf τnD | | ⎝ =| e [F]n,l e | . | n=0 | l=0

(4.72)

Then, by calculating .

( ) nˆ D , lˆD = arg max [A]nD ,lD , (nD ,lD )

(4.73)

4.5 Numerical Results and Discussions

95

we estimate the time delay and Doppler shift as τˆ =

.

nˆ D τmax , . NDFT

lˆD fD,max . fˆD = TDFT

(4.74) (4.75)

The velocity of the target and the distance between the RIS and the target are estimated as fˆD λ ,. 2 cτˆ . = 2

νˆ TG =

(4.76)

dˆI2T

(4.77)

.

Furthermore, combining the estimated distance .dˆI2T and the estimated AoDs ( D ) [ ]T D , we calculate the target location as . xˆ , yˆ , zˆ ˆ I2T , vˆI2T . u TG TG TG , where ˆ yˆTG = yRIS − uˆ D I2T dI2T , .

.

D ˆ zˆ TG = zRIS − vˆI2T dI2T , . / 2 2 2 − (y xˆTG = xRIS + dˆI2T RIS − yTG ) − (zRIS − zTG ) ,

(4.78) (4.79) (4.80)

where .[xRIS , yRIS , zRIS ]T denotes the location of the RIS.

4.5 Numerical Results and Discussions In this section, we present simulations to demonstrate the effectiveness of the proposed delay-Doppler information acquisition schemes in the RIS-enabled system. The RIS and the DFBS are located at .qRIS = [0, 0, 10]T m and .qBS = [35, −20, 10]T m, respectively. The normalized azimuth and elevation AoDs from the RIS to the target are randomly generated from .[−0.5, 0.5] with the distance .dI2T = 10 m. The total transmit power is set to be 25 dBm and the noise power spectral density is .−174 dBm/Hz. The path loss exponents of the BS-RIS and RIStarget links are set as .2.3 and .2.2, respectively, and the path loss at the reference distance of 1 m is set as 30 dB. Following the 5G new radio standard, we set .fc = 28.5 GHz, .B = 100 MHz, .Af = 120 KHz, .N = 833, .TO = 8.33 us, .TCP = 0.58 us. Unless otherwise specified, the following setups are adopted: 2 .M = 64, .NBS = 64, .TCS = 4 log2 M = 24, .TFS = 42, .σ 0 = −123.2 dBm, 2 16 .νTG = 20 m/s, .ζ TG = 1, .pF A = 0.01, .ND = 833, .NDFT = TDFT = 2 .

96

4 Delay-Doppler Information Acquisition in RIS-Enabled ISAC

4.5.1 Performance of the Hierarchical RIS 3D Beam Training First, we compare the beam training overhead of the proposed hierarchical beam training with the exhausted beam searching scheme in Fig. 4.6. It is obvious that the proposed hierarchical beam training scheme has much lower beam training overhead than the exhausted beam searching scheme, and the overhead gap becomes larger with the number of RIS elements. This is because the beam training overhead of the former scheme has a logarithmic relationship with .M 2 , while that of the latter scheme has a linear relationship with .M 2 . Moreover, adopting the beam refinement adds only a small beam training overhead that is almost negligible. Figure 4.7 compares the target detection success rates of the hierarchical RIS 3D beam training with the proposed DSP detector and the traditional RSS detector, where the target detection success rate is defined as the probability that the target falls into the beam coverage of .ξ (iˆK , jˆK ). As expected in Proposition 1, the proposed DSP-based beam training scheme outperforms the RSS-based training scheme, due to its ability to leverage the advantage of multiple sub-carriers in resisting noise. In addition, the success rates of both two hierarchical beam training schemes improve as the number of sub-carriers increases, especially in the case of a small number of sub-carriers, since collecting observation data from more subcarriers helps suppress the adverse effect of noise. In Fig. 4.8, we present the beam alignment error (i.e., direction estimation error of the target) of the proposed hierarchical beam training scheme. For comparison, the following three beam training schemes are presented as benchmarks: (1) Hierarchical beam training without beam refinement process; (2) Hierarchical

140

Exhausted beam searching, no refinement Proposed hierarchical beam training Hierarchical beam training, no refinement

Required OFDM symbols

120 100 80 60 40 20 0 20

40

60

80

100

120

M2 Fig. 4.6 Beam training overhead versus the number of RIS element .M 2

140

4.5 Numerical Results and Discussions

97

1 0.95 0.9

Success Rate

0.85 0.8 0.75 0.7 0.65 0.6

Proposed hierarchical IRS beam training RSS-based hierarchical IRS beam training

0.55 0.5 0

100

200

300

400

500

600

700

800

900

N Fig. 4.7 Target detection success rate of the hierarchical RIS 3D beam training versus the number of sub-carriers

Beam Alignment Error (rad)

10

10

1

0

Proposed hierarchical beam training Hierarchical beam training, no refinement Hierarchical beam training, no compensation Exhaustive beam searching, no refinement

10-1

10-2

10-3

50

100

150

M Fig. 4.8 Beam alignment error versus M

200

250

98

4 Delay-Doppler Information Acquisition in RIS-Enabled ISAC

beam training without beam compensation process; (3) Exhaustive beam searching scheme [6]. We adopt the beam alignment error to measure the performance of the target direction estimation, which is defined as } { / ( ) ) ( D 2 + v D − vˆ D 2 , ε = E π uD − u ˆ I2T I2T I2T I2T

.

(4.81)

In the case of a small number of RIS elements, the hierarchical beam training schemes perform worse than the exhaustive beam searching scheme, which results from the insufficient beamforming gain in the initial stages of the hierarchical beam training. However, as the number of RIS elements increases, the performance of the proposed hierarchical beam training gradually surpasses that of the exhaustive beam searching scheme, due to the fact that the proposed beam refinement process can achieve super-resolution beam training. In addition, we can observe that the beam alignment errors of all beam training schemes improve with the number of RIS elements. This improvement is due to the following two reasons. On the one hand, the resolution of the codeword (i.e., .2/M) increases with the number of RIS elements. On the other hand, a larger RIS beamforming gain can be acquired by adding RIS elements, thus benefiting the target detection process. Moreover, without either the beam refinement or compensation process, the hierarchical beam training performance becomes worse, which demonstrates the necessity of the beam refinement/compensation process.

4.5.2 Performance of the Distance and Velocity Estimation Finally, Fig. 4.9 investigates the impacts of the different beam training schemes on the fine-grained sensing performance, i.e. the distance and velocity estimation performance. Since the final result of beam training is applied to the fine-grained sensing period, the performance of both distance and speed estimation in the finegrained sensing period varies with different beam training schemes. In the lower SNR region, the exhaustive searching scheme achieves the best distance and speed estimation accuracy, due to its low beam alignment error. However, in the medium and high SNR region, the proposed hierarchical beam training scheme achieves the highest distance and speed estimation accuracy, due to its super-resolution beam refinement. In addition, without the compensation process, the performance of both distance and speed estimation degrades significantly, which demonstrates the importance of the compensation process for improving the fine-grained sensing accuracy.

References

99

10-1 10-2 10-3 10-4 10-5 10 -6 10-7

10 1

Proposed hierarchical beam training Hierarchical beam training, no refinement Hierarchical beam training, no compensation Exhaustive beam searching, no refinement

5

Proposed hierarchical beam training Hierarchical beam training, no refinement Hierarchical beam training, no compensation Exhaustive beam searching, no refinement

10 0

Speed Estimation

Distance Estimation Accuracy (m)

10 0

10-1 10-2 10-3 10-4 10-5

10

15

20

(a)

25

30

35

10-6

5

10

15

20

25

30

35

(b)

Fig. 4.9 Distance and velocity estimation accuracy versus .ρ. (a) Distance estimation. (b) Velocity estimation

4.6 Summary In this chapter, we investigated the delay-Doppler information acquisition in the RIS-enabled ISAC system. First, we designed a hierarchical codebook of RIS 3D beamforming by invoking sub-array partitioning and beam broadening approaches. Then, we proposed a low-overhead DSP-based beam training strategy for target direction estimation. A beam refinement scheme was designed to further improve the accuracy of direction estimation. Finally, we estimated the distance and velocity of the target by extracting delay-Doppler information from the received echo signals. It was shown that the proposed hierarchical beam training strategy achieves a much lower overhead of .4 log2 M than the exhaustive beam training scheme with the overhead of .M 2 . The proposed DSP detector can achieve a high detection success rate of .99.7%, which is .10% higher than that of the traditional power detector. Moreover, investigations also found that the proposed RIS beam training strategy and distance/velocity estimation scheme are more suitable for the case with a large number of RIS elements, in which the proposed schemes can achieve .10−3 rad level direction estimation accuracy and .10−5 -m/.10−4 -m/s level distance/velocity estimation accuracy, even better than the exhaustive beam searching scheme, which is attributed to the adoption of the beam refinement process.

References 1. Wang Y, Wen X, Chen Y, Jing W, Pan Q (Istanbul, Turkey, 2019) Joint 3D codebook design and beam training for UAV millimeter-wave communications. In: Proc. IEEE Int. Symposium on Personal, Indoor and Mobile Radio Commun., pp 1–6 2. Xiao Z, He T, Xia P, Xia XG (2016) Hierarchical codebook design for beamforming training in millimeter-wave communication. IEEE Trans Wireless Commun 15(5):3380–3392, https://doi. org/10.1109/TWC.2016.2520930

100

4 Delay-Doppler Information Acquisition in RIS-Enabled ISAC

3. Skolnik MI (2008) Radar handbook. McGraw-Hill Education 4. Richards MA (2014) Fundamentals of radar signal processing. McGraw-Hill Education 5. Rife D, Boorstyn R (1974) Single tone parameter estimation from discrete-time observations. IEEE Transactions on Information Theory 20(5):591–598, https://doi.org/10.1109/TIT.1974. 1055282 6. Ning B, Chen Z, Tian Z, Han C, Li S (2022) A unified 3D beam training and tracking procedure for terahertz communication. IEEE Trans Wireless Commun 21(4):2445–2461, https://doi.org/ 10.1109/TWC.2021.3112493

Chapter 5

Sensing-Assisted Beamforming in RIS-Enabled ISAC

5.1 Introduction In general, there are two schemes for beamforming design in RIS-enabled systems, namely channel estimation-based beamforming and codebook-based beam training. For the channel estimation-based beamforming scheme, based on the estimated RIS cascaded channels, beamforming problems under various setups are formulated and solved, yielding the final passive beamforming results. For the codebook-based beam training scheme, a codebook of passive beams is first generated, and then these beams will be trained to find the best one. Due to a large number of RIS elements, both schemes have the disadvantage of high beamforming overhead. In this chapter, by exploring the inner relationship between communication channels and sensing parameters in the RIS-enabled ISAC system, sensing-assisted beamforming schemes are studied, which avoids high-overhead channel estimation or beam training while ensuing communication performance [1, 2].

5.2 Sensing-Assisted Beamforming in the Single-User Case 5.2.1 System Model As shown in Fig. 5.1, we consider an RIS-enabled system operating in the mmWave band, where a distributed semi-passive RIS with M reflecting elements assists the uplink transmission between the BS and a single-antenna user. The distributed semi-passive RIS consists of 3 sub-RISs. The first sub-RIS is passive with .M1 passive reflecting elements, while the i-th (.i = 2, 3) sub-RIS is semi-passive with .Mi (φ)2 (t), φ(3 (t)) , t )∈ ( ) (0, and the ) phases ( {T1 + n|n = 1, · · · , 5} are set to be (π, π ), 12 π, 12 π , 12 π, 32 π , 32 π, 21 π and 32 π, 32 π . do Calculate tk* = arg

max

|y(t˜)|.

t˜∈{T1 +5(k−1)+n|n=1,··· ,5}

(5.33)

Let k ←− k + 1. Update the phases (φ2 (t), φ3 (t)) , t ∈ {T1 + 5(k − 1) + n|n = 1, · · · , 5} as ) ( * * ), φ3 (tk−1 ) , φ2 (tk−1 ( π π) * * ) ± k , φ3 (tk−1 )± k . φ2 (tk−1 2 2

(5.34) (5.35)

* ) − y(t * )|| > ε while ||y(tk−1 k−2 ( ) * ), φ (t * ) . Output: φ2 (tk−1 3 k−1

5.2.3 Numerical Results and Discussions In this section, we will provide numerical results to verify the effectiveness of the proposed sensing-assisted beamforming algorithms in the ISAC and PC periods, respectively. The simulation setup is shown in Fig. 5.3, where the user is on the horizontal floor, the BS is 20 meter (m) above the horizontal floor, and the three sub-RISs are respectively 5 m, 7 m and 8 m above the horizontal floor. The distances from the BS to the second sub-RIS and from the second sub-RIS to the user are set to be .dB2I,2 = 50 m and .dI2U,2 = 6 m, respectively. The path loss exponents from the RIS to the BS, from the user to the RIS, and from one sub-RIS to other sub-RISs are set as .2.3, .2.2 and .2.1 respectively. The path loss at the reference distance of 1 m is set as 30 dB. Unless otherwise specified, the following setup is used: .N = 8, .M1 = 16 × 16, .M2 = M3 = Msemi = 4 × 4, .T = 1200, .T1 = 120, .τ1 = 20, 2 .ρ = 20dBm and noise power .σ = −80 dBm. 0 Fig. 5.3 Simulation setup (top view)

5.2 Sensing-Assisted Beamforming in the Single-User Case

111

15

Average achievable rate (bits/s/Hz)

Optimal beamforming Proposed beamforming (M Proposed beamforming (M

semi semi

=36) =25)

Proposed beamforming (M semi=16) Random beamforming

10

5

0 0

5

10

15

20

25

30

Transmit power (dBm)

Fig. 5.4 Performance of the proposed beamforming scheme in the ISAC period

5.2.3.1

Performance of the Proposed Beamforming Algorithms

Figure 5.4 presents the performance of the proposed beamforming scheme in the ISAC period, where the average achievable rate is defined as R¯ ISAC = E {R(t)} , t ∈ {1, 2, · · · , T1 }.

.

(5.37)

The optimal scheme with perfect CSI and the random scheme with randomly generated phase shifts are presented as two benchmarks. The proposed beamforming scheme performs much better than the random scheme, and achieves similar performance to the optimal scheme. Moreover, as the transmit power increases, the gap between the proposed scheme and the optimal scheme gradually vanishes. Also, increasing the number of semi-passive elements improves the performance of the proposed scheme, due to more accurate location sensing. Figure 5.5 presents the performance of the proposed beamforming scheme in the PC period, where the average achievable rate is defined as R¯ PC = E {R(t)} , t ∈ {T1 + 1, T1 + 2, · · · , T1 + T2 }.

.

(5.38)

For comparison, the performance of the AO scheme with perfect CSI [3] and the random scheme with randomly generated phase shifts are presented. The proposed beamforming scheme is superior to the random scheme, and achieves almost the same performance as the AO beamforming scheme with perfect CSI. All the three beamforming schemes improve with the number of passive reflecting elements,

112

5 Sensing-Assisted Beamforming in RIS-Enabled ISAC 16

Average achievable rate (bits/s/Hz)

14 12

AO beamforming (M AO beamforming (M

10

semi semi

=36) =16)

Proposed beamforming (M

semi

=36)

Proposed beamforming (M semi=16)

8

Random beamforming (M

semi

=36)

Random beamforming (M semi=16)

6 4 2 0 100

200

300

400

500

600

700

800

900

1000

M1

Fig. 5.5 Performance of the proposed beamforming scheme in the PC period

due to the increased beamforming gain. Also, adding more semi-passive elements raises the performance of these beamforming schemes, especially in the case of a small number of passive reflecting elements. It is worth noting that the performance improvement of the proposed beamforming scheme is due to both the increased beamforming gain and location sensing accuracy.

5.2.3.2

Performance of the Proposed ISAC Transmission Protocol

Finally, we investigate the performance of the proposed ISAC transmission protocol, and define the average achievable rate as R¯ = E {R(t)} , t ∈ {1, 2, · · · , T1 + T2 }.

.

(5.39)

Figure 5.6 shows the average achievable rate of the proposed ISAC transmission protocol under different ratios of sensing time to the whole transmission time (i.e., 1 .T1 /T ), where we set .τ1 : T1 = 10 and .T = 2000. The optimal ratio of sensing time to the whole transmission time decreases with the transmit power. For a low transmit power of 0 dBm, the optimal ratio is about 1, which indicates that the two semi-passive sub-RISs should always operate in the sensing mode. As the transmit power increases to 10 dBm, the optimal ratio drops to 0.2. With the highest transmit power of 20 dBm, the optimal ratio approaches to 0. This is because the sensing accuracy with a short sensing time is enough high in this case and the two semipassive sub-RISs should operate in the reflecting mode to help data transmission.

5.3 Sensing-Assisted Beamforming in the Multi-User Case

113

Fig. 5.6 Performance of the proposed ISAC transmission protocol with different .T1 /T

Figure 5.7 shows the average achievable rate of the proposed ISAC transmission 1 protocol with different ratios of .τ1 to .T1 (i.e., .τ1 /.T1 ), where we assume .T1 : T = 10 and .T = 2000. For all three configurations of transmit power, it is desired to allocate a very small portion of time slots to the first time block. This is because during the first time block, the BS does not have any CSI to design the RIS phase shifts and the corresponding achievable rate is very low. More time slots should be allocated to the second time block, where a much higher achievable rate can be achieved by properly designing RIS phase shifts according to the estimated user location during the first time block.

5.3 Sensing-Assisted Beamforming in the Multi-User Case 5.3.1 System Model As illustrated in Fig. 5.8, we consider an RIS-enabled multi-user uplink communication system operating in the mmWave band, where a distributed semi-passive RIS with M reflecting elements is deployed to assist the uplink data transmission from K single-antenna users to a multi-antenna BS. We consider that the line-of-sight (LoS) paths between the BS and users are obstructed, and the RIS is deployed to establish strong virtual line-of-sight (VLoS) reflection paths between them. The distributed semi-passive RIS is composed of 3 sub-RISs. The first sub-RIS is passive and consists of .M1 passive reflecting elements, while the i-th (i = 2, 3) sub-RIS is semipassive and consists of .Mi (.Mi 1) transmission period, the users’ locations estimated in the (.i − 1)-th transmission period would be used to design the phase shift of the passive sub-RIS in the first time block of the ISAC period.

116

5 Sensing-Assisted Beamforming in RIS-Enabled ISAC

where .αI2B,i denotes the complex channel gain for the link from the i-th sub-RIS to the BS, .a and .bi are the array response vectors for the BS and the i-th sub-RIS, D respectively. The two effective angles of departure (AoDs) .uD I2B,i and .vI2B,i as well A as the effective AoA .uI2B,i are respectively defined as ( ) ( ) dRIS D D cos γI2B,i sin ϕI2B,i ,. λ ( ) dRIS D sin γI2B,i ,. =2 λ ( ) dBS A sin θI2B,i , =2 λ

uD I2B,i = 2

(5.41)

D vI2B,i

(5.42)

.

uA I2B,i

(5.43)

where .λ denotes the carrier wavelength, .dRIS and .dBS represent the distances between two adjacent reflecting elements of the RIS and two adjacent antennas of A D D the BS, respectively. In addition, .θI2B,i denotes the AoA at the BS, .γI2B,i and .ϕI2B,i are the elevation and azimuth AoDs for the link from the i-th sub-RIS to the BS, respectively. Similarly, the channel from the k-th user to the i-th sub-RIS is modeled as ( ) A hU2I,i,k = αU2I,i,k bi uA U2I,i,k , vU2I,i,k ,

.

i = 1, 2, 3, k = 1, · · · , K,

(5.44)

where .αU2I,i,k denotes the complex channel gain for the link from the k-th user to the i-th sub-RIS, and the two effective AoAs from the k-th user to the i-th sub-RIS are defined as ( ) ( ) dRIS A A cos γU2I,i,k sin ϕU2I,i,k ,. λ ( ) dRIS A sin γU2I,i,k , =2 λ

uA U2I,i,k = 2

(5.45)

A vU2I,i,k

(5.46)

.

A A where .γU2I,i,k /.ϕU2I,i,k denotes the elevation/azimuth AoAs for the link from the k-th user to the i-th sub-RIS. Furthermore, we consider that .dBS = dRIS = λ2 . As such, the array response vectors for the BS and the i-th sub-RIS are respectively given by

]T [ a (u) = 1, · · · , ej π (n−1)u , · · · , ej π (N −1)u , .

.

(5.47)

]T [ bi (u, v) = 1, · · · , ej π (n−1)u , · · · , ej π (My,i −1)u ]T [ ⊗ 1, · · · , ej π (m−1)v , · · · , ej π (Mz,i −1)v .

(5.48)

5.3 Sensing-Assisted Beamforming in the Multi-User Case

5.3.1.3

117

Signal Model

(1) ISAC Period In the ISAC period, only the passive sub-RIS (i.e., the first sub-RIS) operates in the reflecting mode to assist uplink transmission. During the n-th time block, the √ k-th user sends . ρsk (t), satisfying .|sk (t)| = 1, to the BS at time slot .t ∈ Nn = {(n − 1)τ1 + 1, · · · , τ1 + (n − 1)τ2 }, where .ρ denotes the transmit power. The received signal at the BS is given by √ Σ [ (n) ]H (n) wk .y (t) = ρ HI2B,1 01 hU2I,1,k sk (t) K

k=1

+

K [ Σ

] (n) H

wk

nBS (t), t ∈ Nn , n = 1, 2,

(5.49)

k=1 (n)

(n)

where .wk , satisfying .||wk || = 1, represents the BS combining vector of the kth user in the n-th time block. The phase shift matrix of the first sub-RIS in the (n) (n) n-th time block is defined as .01 = diag(ξ 1 ), with the phase shift beam being (n)

(n)

(n)

jϑ

(n)

ξ 1 = [ej ϑ1,1 , · · · , ej ϑ1,m , · · · , e 1,M1 ]T . In addition, .nBS represents the additive white Gaussian noise (AWGN) at the BS, whose elements follow the complex Gaussian distribution .CN(0, σ02 ). The instantaneous achievable rate of the k-th user during the ISAC period is given by ⎛ ⎞ |[ |2 | (n) ]H | (n) | | ρ | wk HI2B,1 01 hU2I,1,k | ⎜ ⎟ ⎜ ⎟ (5.50) .Rk (t) = log2 ⎜1+ ⎟, |[ | 2 ⎝ ⎠ | ΣK | (n) ]H (n) 2 | | ρ j /=k | wk HI2B,1 01 hU2I,1,j | +σ0

.

t ∈ Nn , n = 1, 2.

(2) PC Period In the PC period, all three sub-RISs operate in the reflecting mode to assist uplink √ transmission. The k-th user sends . ρsk (t) to the BS at time slot .t ∈ T2 A {T1 + 1, · · · , T1 + T2 }. The received signal at the BS is √ Σ H y (t) = ρ wk (t) HI2B 0 (t) hU2I,k sk (t) K

.

k=1

+

K Σ k=1

wH k (t) nBS (t), t ∈ T2 ,

(5.51)

118

5 Sensing-Assisted Beamforming in RIS-Enabled ISAC

where .HI2B A [HI2B,1 , HI2B,2 , HI2B,3 ] ∈ CN ×M and .hU2I,k .A [hTU2I,1,k , hTU2I,2,k , hTU2I,3,k ]T ∈ CM×1 denote the baseband equivalent channels from the RIS to the BS and from the k-th user to the RIS, respectively. The phase shift matrix of the whole RIS is defined as .0 (t) = diag(ξ (t)), where .ξ (t) A [ξ T1 (t) , ξ T2 (t) , ξ T3 (t)]T with the phase shift beam being .ξ i (t) = [ej ϑi,1 (t) , · · · , ej ϑi,m (t) , · · · , ej ϑi,Mi (t) ]T . The instantaneous achievable rate of the k-th user during the PC period is given by ⎛

⎞ |2 | | 0 h H ρ |wH (t) (t) I2B U2I,k k ⎠ , t ∈ T2 . .Rk (t) = log2 ⎝1+ Σ | |2 K | H ρ j /=k wk (t) HI2B 0 (t) hU2I,j | +σ02

(5.52)

5.3.2 Sensing-Based Joint Active and Passive Beamforming In this section, We propose two sensing-based beamforming algorithms to maximize the sum rate for the ISAC and PC periods, respectively, by capitalizing on the users’ locations sensed in the ISAC period.

5.3.2.1

ISAC Period

In the ISAC period, we first design the BS combining vectors by adopting the maximum ratio combining (MRC) technique, and then propose an estimation of distribution algorithm (EDA) based beamforming method to optimize the phase shift matrix of the passive sub-RIS. During the n-th time block of the ISAC period, the sum rate of K users is given by ( ) (n) Rsum W(n) , 01 = ⎛ ⎞ |[ |2 | (n) ]H | (n) (n) | | ρ | wk HI2B,1 01 hU2I,1,k | K ⎜ ⎟ Σ ⎜ ⎟ log2⎜1+ ⎟, |[ |2 ]H ⎝ ⎠ | | Σ (n) (n) (n) K | 2 k=1 ρ j /=k | wk HI2B,1 01 hU2I,1,j || +σ0

.

(5.53)

5.3 Sensing-Assisted Beamforming in the Multi-User Case

119 (n)

(n)

where the combining matrix .W(n) is defined as .W(n) A [w1 , · · · , wK ]. As such, the sum rate maximization problem is formulated as (P1) :

max

.

(n)

W(n) ,01

s.t.

( ) (n) Rsum W(n) , 01 , .

(5.54a)

|| || || (n) || ||wk || = 1, .

(5.54b)

(n)

ϑ1,m ∈ Fb , m = 1, · · · , M1 .

(5.54c)

(1) Optimization of BS Combining Vectors (n)

With the given phase shift matrix .01 , the problem (P1) can be reduced to the optimization of .W(n) . By adopting the MRC technique, we obtain the combining vector for the k-th user as (n) (n)

(n) .w k

HI2B,1 01 hU2I,1,k || . = || || || (n) (n) ||HI2B,1 01 hU2I,1,k ||

(5.55)

Since the locations of the BS and all the sub-RISs are fixed, we consider that (n) HI2B,i is perfectly known [7]. Although .hU2I,i,k is unavailable due to the phase ambiguity of its complex channel gain .αU2I,i,k , this phase ambiguity would not affect the A,(n) A,(n) (n) (n) calculation of .Rsum . Therefore, we define .habs,i,k A |αU2I,i,k |bi (uU2I,i,k , vU2I,i,k ),

.

(n)

and design .wk as (n) (n)

HI2B,1 01 habs,1,k (n) || (5.56) wk = || || || (n) (n) ||HI2B,1 01 habs,1,k || | | ( ) ( ) ) ( | A,(n) A,(n) (n) | (n) H uD D b αI2B,1 a uA b 0 u , v , v |α | 1 I2B,1 1 I2B,1 I2B,1 U2I,1,k U2I,1,k 1 U2I,1,k || || . = || || (n) (n) ||HI2B,1 01 habs,1,k ||

.

(n)

Due to .||wk || = 1, it can be easily verified that | | ( ( ) ) | A,(n) A,(n) (n) | (n) D D αI2B,1 bH 1 uI2B,1 , vI2B,1 01 |αU2I,1,k | b1 uU2I,1,k , vU2I,1,k 1 || || = . . || || (n) (n) N ||HI2B,1 01 habs,1,k ||

(5.57)

120

5 Sensing-Assisted Beamforming in RIS-Enabled ISAC (n)

Substituting (5.57) into (5.56) yields .wk = we obtain .W(n) as W(n) =

.

1 A N a(uI2B,1 ).

(n)

Therefore, for any .01 ,

( )] 1 [ ( A ) a uI2B,1 , · · · , a uA ∈ CN ×K . I2B,1 N

(5.58)

(2) Optimization of RIS Phase Shift Matrix With the given combining matrix .W(n) , the problem (P1) can be simplified to the (n) optimization of .01 . Since the user location information is unavailable in the first (1) time block, .01 is randomly generated. Therefore, in the following, we only focus (2) on the design of .01 in the second time block by invoking the users’ locations sensed in the first time block. (2) (2) (2) (2) First, we set the probability matrix as .P1 = [p1,1 , · · · , p1,m , · · · , p1,M1 ] ∈ C2

b ×M 1

(2)

(2)

(2)

, where .p1,m = [p1,m,1 , · · · , p1,m,2b ]T denotes the probability parameter for

(2)

(2)

(2)

ϑ1,m , with its entry .p1,m,l satisfying the probability constraints .0 < p1,m,l < 1 and Σ2b (2) (2) . l=1 p1,m,l = 1. Subsequently, we consider that .ϑ1,m takes a value from .Fb with an .

(2),0

equal probability at first, and initialize the probability matrix as .P1

= 21b ×12b ×M1 . (2),s SISAC }s=1

Then, in the i-th iteration, we randomly generate .SISAC candidates .{01 according to the probability distribution function given by (

(2)

(2),i

E 01 ; P1

.

)

= ⎛

M1 ||

⎛⎛ ⎝⎝

b −1 2|| (

m=1

× ⎝1−

(2),i

p1,m,l

l=1

b −1 2|| (

(2),i

p1,m,l

)r

)r

( )⎞ (2) ϑ1,m ,Fb (l)

⎠

( ) ⎞⎞ (2) ϑ1,m ,Fb (l)

⎠⎠,

(5.59)

l=1 (2)

where .Fb (l) denotes the l-th entry of .Fb , and .r(ϑ1,m , Fb (l)) is a judge function given by ( r

.

(2) ϑ1,m , Fb

)

(l) =

{

(2)

1, ϑ1,m = Fb (l) (2)

0, ϑ1,m /= Fb (l)

.

(5.60)

5.3 Sensing-Assisted Beamforming in the Multi-User Case

121

(2),s

For each phase shift matrix candidate .01 , we calculate the corresponding sum rate ( ) (2),s = .Rsum 0 (5.61) 1 ⎛ ⎞ |[ |2 | (2) ]H | (2),s ˆ (1) | | w ρ H 0 h K I2B,1 ⎟ ⎜ k abs,1,k | 1 | Σ ⎜ ⎟ log2 ⎜1+ ⎟, |[ | 2 ] ⎝ ⎠ H | | Σ k=1 | w(2) HI2B,1 0(2),s hˆ (1) | +σ 2 ρ K j /=k | k 1 abs,1,j | 0 where | ( | ) | (n) | A,(n) A,(n) (n) hˆ abs,1,k = |αˆ U2I,1,k | b1 uˆ U2I,1,k , vˆU2I,1,k , n = 1, 2, .

.

(n)

A,(n) uˆ U2I,1,k

=

yˆU,k − y1 (n)

|| qˆ U,k − q1 ||

1 | | − 20 | (n) | |αˆ U2I,1,k | = 10

(5.62)

(n)

A,(n) , vˆU2I,1,k

=

(

zˆ U,k − z1 (n)

|| qˆ U,k − q1 ||

|| )) || (n) ||qˆ U,k −q1 || d0

,.

(5.63)

( ||||

P L(d0 )+10εU2I log

.

(5.64)

(2),s

ISAC After that, we sort .RISAC = {Rsum (01 )}Ss=1 in descending order and select elite elite largest sum rates the .SISAC phase shift matrix samples corresponding to the .SISAC

(2),s

elite . Based on the selected .S elite samples, we in .RISAC , i.e., .01 q , sq = 1, · · · , SISAC ISAC (2),i+1 with its elements update the probability matrix in the .(i + 1)-th iteration as .P1 given by

(2),i+1 .p 1,m,l

=

1 elite SISAC

elite SISAC

Σ

( ) (2),s r ϑ1,m q , Fb (l) ,

sq =1

m = 1, · · · , M1 , l = 1, · · · , 2b .

(5.65)

Repeat the above process until the difference between the maximum and (2) minimum of .RISAC is less than the threshold .κ, which indicates that .P1 is stable. The procedures of the beamforming algorithm in the second time block of the ISAC period are summarized in Algorithm 5.

122

5 Sensing-Assisted Beamforming in RIS-Enabled ISAC

Algorithm 5 Sensing-based beamforming for the second time block of the ISAC period elite , F . Input: K(1) , HI2B,1 , SISAC , SISAC b (2),0

= 21b × 12b ×M1 , and i = 1. 1: Initialize P1 (2) 2: Calculate W based on the MRC method. 3: repeat (2),s ISAC (2) (2),i 4: Randomly generate SISAC candidates {01 }Ss=1 based on E(01 ; P1 ). (2),s SISAC 5: Calculate the sum rate {Rsum (01 )}s=1 by (5.61). (2),s ISAC in descending order. 6: Sort RISAC = {Rsum (01 )}Ss=1 elite elite largest sum rates in 7: Select SISAC phase shift matrix samples corresponding to the SISAC RISAC . (2),i+1 according to (5.65). 8: Update P1 9: Let i → i + 1. 10: until | max(RISAC ) − min(RISAC )| < κ (2),opt

Output: 01

5.3.2.2

(2),opt

= diag(ξ 1

(2),1

) = 01

, W(2),opt = W(2) .

PC Period

During the PC period, all three sub-RISs operate in the reflecting mode to assist uplink transmission, and the sum rate of K users can be expressed as Rsum (W (t) , 0 (t)) = ⎛ ⎞ |2 | K | Σ 0 h H ρ |wH (t) (t) I2B U2I,k k ⎠, log2 ⎝1 + Σ | |2 K | H ρ j /=k wk (t) HI2B 0 (t) hU2I,j | + σ02 k=1

.

(5.66)

t ∈ T2 , where .W (t) is defined as .W (t) A [w1 (t) , · · · , wK (t)]. As such, the sum rate maximization problem is formulated as (P2) :

.

max

W(t),0(t)

s.t.

Rsum (W (t) , 0 (t)) , .

(5.67a)

||wk (t)|| = 1, .

(5.67b)

ϑi,m (t) ∈ Fb , m = 1, · · · ,Mi , i = 1, 2, 3.

(5.67c)

Note that the calculation of the sum rate involves .hU2I,k , which is unavailable due to the phase ambiguity of .αU2I,i,k . Hence, during the first C time slots of the PC period (.C 1, it is difficult to theoretically prove its convergence. In this case, we will provide some simulation results in the latter section to verify the convergence of the proposed beamforming algorithms. Remark 5.2 It is worth noting that the proposed two beamforming algorithms for both ISAC and PC periods are based on sensed location information instead of perfect CSI, which avoids high channel estimation overhead in the RIS-enabled system.

126

5 Sensing-Assisted Beamforming in RIS-Enabled ISAC

Algorithm 6 Sensing-based beamforming algorithm for the PC period elite , F . Input: K(2) , HI2B , SPC , SPC b

1: Initialize P0 = 21b × 12b ×M , and i = 1. 2: Estimate Ai,k according to (5.72). 3: repeat }SPC { 4: Randomly generate SPC candidates 0s (t) s=1 based on E(0 (t) ; Pi ). s 5: Calculate W (t) based on the ZF method. { ( )}SPC 6: Calculate the sum rate Rsum 0s (t) s=1 by (5.78). { ( s )}SPC 7: Sort RPC = Rsum 0 (t) s=1 in descending order. elite phase shift matrix samples corresponding to the S elite largest sum rate in R . 8: Select SPC PC PC 9: Update Pi+1 based on (5.79). 10: Let i → i + 1. 11: until |max (RPC ) − min (RPC )| < κ Output: 0opt (t) = 01 (t), Wopt (t) = W1 (t)

5.3.3 Numerical Results and Discussions In this section, numerical results are provided to demonstrate the effectiveness of the proposed multi-user location sensing and joint beamforming algorithms as well as to investigate the performance of the RIS-enabled multi-user ISAC system. The simulation setup is shown in Fig. 5.9, where K users are distributed on a ninetydegree sector of the horizontal floor. The BS is 20 meters (m) above the horizontal floor, and the three sub-RISs are respectively 5, 7, and 9 m above the horizontal floor. The distances from the BS to the second sub-RIS and from the second subRIS to the users are set to be .dB2I,2 = 50 m and .dI2U,2 = 10 m, respectively. The path loss at the reference distance of 1 m is set as 30 dB. Other system parameters are set as follows: .K = 3, .N = 8, .M1 = 32 × 32, .M2 = M3 = Msemi = 12 × 12, .T = 1200, .T1 = 120, .τ1 = 20, .εI2B = 2.3, .εU2I = 2.2, .εI2I = 2.1, .b = 3, .bA = 4, elite elite −4 .SISAC = 1500, .S ISAC = 300, .SPC = 2000, .SPC = 400, .κ = 10 , .C = 4, .ρ = 20 2 dBm and .σ0 = −80 dBm (if not specified otherwise). 5.3.3.1

Performance of the Proposed Sensing-Based Beamforming Algorithms

In this subsection, numerical results are presented to illustrate the effectiveness and convergence of the proposed beamforming algorithms in the ISAC and PC periods, respectively. For comparison, the alternating optimization (AO) algorithm [9] with continuous phase shifts and perfect CSI, the low complexity local search (LS) algorithm [10] with perfect CSI, as well as the random phase shift algorithm are presented as three benchmarks for both ISAC and PC periods. In addition, the ZFbased beamforming algorithm is presented as a benchmark for the ISAC period, to demonstrate the advantage of the proposed MRC-based beamforming algorithm in

5.3 Sensing-Assisted Beamforming in the Multi-User Case

127

Sub-IRS 2 5m

5m

1m

y

1m

Sub-IRS 3

Sub-IRS 1

22.5º 22.5º User 3

User 1 User 2 BS x Fig. 5.9 Simulation setup (top view)

the ISAC period. The sum rates in the ISAC and PC periods are respectively defined as .

R¯ ISAC = E {R (t)} , t ∈ {1, 2, · · · , T1 } , .

(5.80)

R¯ PC = E {R (t)} , t ∈ {T1 + 1, T1 + 2, · · · , T1 + T2 } .

(5.81)

Figure 5.10a, b compare the sum rates of different beamforming algorithms versus the number of RIS elements operating in the reflecting mode. It is obvious that the proposed algorithm with discrete phase shifts and sensed location information is superior to the LS algorithm and the random phase shift algorithm, and even achieves comparable performance to the AO algorithm with continuous phase shifts and perfect CSI. Moreover, with the increase of the number of RIS elements, all beamforming algorithms except for the random phase shift algorithm achieve significant performance gains, especially in the case of a small number of RIS elements. For the proposed algorithm and the AO algorithm, the sum rate achieved in the PC period is much larger than that achieved in the ISAC period even with the same number of RIS elements operating in the reflecting mode. This is because there are more distributed sub-RISs assisting uplink data transmission in the PC period, thereby providing a larger spatial multiplexing gain. In contrast, the LS algorithm and the random phase shift algorithm perform worse in the PC period, thus are not suitable for multiple RIS scenarios. In addition, we can observe from Fig. 5.10a that the proposed MRC-based beamforming algorithm for the ISAC period performs slightly better than the ZF-based beamforming algorithm. This is

128

5 Sensing-Assisted Beamforming in RIS-Enabled ISAC

25

10

AO algorithm with perfect CSI Proposed algorithm with sensed location ZF-based beamforming with sensed location LS algorithm with perfect CSI Random phase shift algorithm

5

0 400

Sum rate (bits/s/Hz)

Sum rate (bits/s/Hz)

15

20

AO algorithm with perfect CSI Proposed algorithm with sensed location LS algorithm with perfect CSI Random phase shift algorithm

15

10

5

0 700 800 900 1000 1100 1200 1300 1400 1500

500 600 700 800 900 1000 1100 1200 1300

M1

M

(a)

(b)

Fig. 5.10 Sum rate versus the number of RIS elements operating in the reflecting mode. (a) ISAC period. (b) PC period 14

25

10 8 6

AO algorithm with perfect CSI Proposed algorithm with sensed location LS algorithm with perfect CSI Random phase shift algorithm

4 2 0

2

3

K

(a)

4

Sum rate (bits/s/Hz)

Sum rate (bits/s/Hz)

12 20 AO algorithm with perfect CSI Proposed algorithm with sensed location LS algorithm with perfect CSI Random phase shift algorithm

15 10 5 0

2

3

K

4

(b)

Fig. 5.11 Sum rate versus the number of users K. (a) ISAC period. (b) PC period

because the channel between the BS and RIS is rank-one with only one passive sub-RIS used for communication during the ISAC period. As such, the multi-user interference can not be effectively eliminated by using the ZF-based beamforming algorithm, leading to worse communication performance than the proposed MRCbased beamforming algorithm. Figure 5.11a, b compare the sum rates of different beamforming algorithms versus the user number K, where we set the total transmit power of K users to be 20 dBm (i.e., .Kρ = 20 dBm) and .Msemi = 16 × 16. In both ISAC and PC periods, the performance of all four beamforming algorithms degrades with the increase of the user number, especially for the LS algorithm. For the AO algorithm, the LS algorithm as well as the random phase shift algorithm, this performance degradation is due to more inter-user interference, while for the proposed beamforming algorithm, this performance degradation is due to both more inter-user interference and less accurate sensed users’ locations.

5.3 Sensing-Assisted Beamforming in the Multi-User Case 16

25

12 10 8

b = 3, M1 = 1024 b = 1, M1 = 1024

6

b = 3, M1 = 256

Sum rate (bits/s/Hz)

14

Sum rate (bits/s/Hz)

129

20 15 10 b = 3, M = 1312 b = 1, M = 1312 b = 3, M = 544 b = 1, M = 544

5

b = 1, M1 = 256

4

0

50 100 150 200 250 300 350 400 450 500

Iteration number

(a)

0

0

100

200

300

400

500

600

700

Iteration number

(b)

Fig. 5.12 Convergence of the proposed beamforming algorithms. (a) ISAC period. (b) PC period

Figure 5.12a, b illustrate the convergence of the proposed beamforming algorithms with different numbers of RIS elements and bit-quantization numbers. We can observe that the proposed two beamforming algorithms converge for any number of RIS elements and quantization bits. Adding more RIS elements decreases the convergence speed, due to the increased number of optimization variables. Also, as the bit-quantization number increases, the convergence speed becomes slower, due to the enlarged searching region of RIS phase shifts.

5.3.3.2

Performance of the RIS-Enabled Multi-User ISAC System

Figure 5.13 illustrates the sum rate in the ISAC period versus .τ1 /T1 with different 1 and .T = 2000. The optimal ratio of time values of .ρ, where we set .T1 : T = 10 allocation indicates that, it is desirable to allocate a small portion of time slots to the first time block and more time slots to the second time block. This is because the CSI is unavailable in the first time block, while location information is available in the second time block, which can be used for more effective beamforming design. Moreover, the optimal ratio .τ1 /T1 decreases with the transmit power. With a larger transmit power, the positioning accuracy is sufficiently high and thus it is unnecessary to allocate too much time to the first time block. However, with too little time allocated to the first time block, the communication performance would degrade significantly, due to the fact that low-accuracy localization in the first time block would affect the effectiveness of the beamforming design in the second time block. Figure 5.14 presents the sum rate in the whole transmission period versus the 1 ratio .T1 /T with different .ρ, where .τ1 /T1 = 10 , .T = 1000, and the sum rate is defined as R¯ = E {R (t)} , t ∈ {1, 2, · · · , T1 + T2 } .

.

(5.82)

130

5 Sensing-Assisted Beamforming in RIS-Enabled ISAC 16

= 20 dBm = 10 dBm = 0 dBm

Sum rate (bits/s/Hz)

14 12 10 8 6 4 2 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

/T 1 1 Fig. 5.13 Sum rate of the ISAC period versus .τ1 /T1 30

= 25 dBm = 5 dBm = -5 dBm

Sum rate (bits/s/Hz)

25

20

15

10

5

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

T1/T Fig. 5.14 Sum rate of the transmission period versus .T1 /T

The optimal ratio decreases as the transmit power becomes larger. For instance, with a lower power of .−5 dBm, the optimal .T1 /T is about 1, which indicates that simultaneous location sensing and communication should be conducted during the whole transmission period. As the transmit power increases to 5 dBm, the optimal

5.3 Sensing-Assisted Beamforming in the Multi-User Case

131

16

= 20 dBm = 10 dBm = 0 dBm

14

Sum rate (bits/s/Hz)

region 2 12

region 3

10

region 1

8 6 4 2

10-3

10-2

10-1

100

RMSE (m) Fig. 5.15 Trade-off between communication performance and localization performance of the ISAC period

T1 /T drops to .0.2. With the highest transmit power of 25 dBm, the optimal ratio approaches 0. This is because with high transmit power, an enough high sensing accuracy can be achieved in a short time. Finally, Fig. 5.15 shows the trade-off between the communication performance and localization performance of the ISAC period with different values of .ρ, where 1 and .T = 2000. We can observe that for all three configurations we set .T1 : T = 10 of transmit power, the communication-localization curve includes three regions. Specifically, in region 1, the localization performance is nearly saturated. Despite sacrificing the communication performance a lot, a little localization performance gain can be obtained. For example, when .ρ = 10 dBm, despite sacrificing the sum rate from .9.5 bits/s/Hz to 2 bits/s/Hz, the localization accuracy can only be improved by less than twice. In region 2, the communication performance and the localization performance are properly balanced, and sacrificing the performance of one can effectively enhance that of another. For example, when .ρ = 20 dBm, sacrificing the sum rate from .15.1 bits/s/Hz to .11.6 bits/s/Hz can achieve 10 times higher localization accuracy. In region 3, the location sensing accuracy is too low to promise the effectiveness of the sensing-based beamforming design, thus leading to an unsatisfying communication performance. Hence, in this scenario, it is suggested to allocate more resources to localization for promising good performance of both communication and localization.

.

132

5 Sensing-Assisted Beamforming in RIS-Enabled ISAC

5.4 Summary In this chapter, we focus on RIS beamforming design by using sensing information in an RIS-enabled ISAC system. In the proposed RIS-enabled ISAC system, location sensing and data transmission can be conducted at the same time, occupying the same spectrum and time resources. Furthermore, by exploring the inner relationship between communication channels and sensing parameters, we design beamforming schemes that avoid high overhead while ensuring communication performance. Numerical results show that, although only the imperfect location information is available, the proposed beamforming scheme for the ISAC period achieves almost the same performance as the optimal beamforming scheme with perfect CSI, and the proposed beamforming scheme for the PC period has similar performance to the AO beamforming scheme assuming perfect CSI, demonstrating the effectiveness of beamforming designs using sensed location information. Moreover, we have studied the overall communication performance of the RIS-enabled ISAC system, and numerical results showed that the optimal time ratio of the ISAC period to the PC period decreases with the increase of transmit power, indicating that less time should be allocated to the ISAC period when transmit power is high. In addition, by investigating the trade-off between the sensing and communication performance, we find that increasing the sensing time will always improve the sensing performance, but not always degrade the communication performance.

References 1. Yu Z, Hu X, Liu C, Peng M, Zhong C (2022) Location sensing and beamforming design for IRSenabled multi-user ISAC systems. IEEE Trans Signal Process 70:5178–5193, https://doi. org/10.1109/TSP.2022.3217353 2. Hu X, Liu C, Peng M, Zhong C (2023) IRS-based integrated location sensing and communication for mmwave SIMO systems. IEEE Trans Wireless Commun 22(6):4132–4145, https:// doi.org/10.1109/TWC.2022.3223428 3. Wu Q, Zhang R (Nov. 2019) Intelligent reflecting surface enhanced wireless network via joint active and passive beamforming. IEEE Transactions on Wireless Communications 18(11):5394–5409, https://doi.org/10.1109/TWC.2019.2936025 4. Liu R, Li M, Swindlehurst AL (2022) Joint beamforming and reflection design for RIS-assisted ISAC systems. arXiv:220300265 5. Jiang ZM, et al. (2022) Intelligent reflecting surface aided dual-function radar and communication system. IEEE Systems Journal 16(1):475–486, https://doi.org/10.1109/JSYST.2021. 3057400 6. Yuan J, Liang YC, Joung J, Feng G, Larsson EG (2021) Intelligent reflecting surfaceassisted cognitive radio system. IEEE Trans Commun 69(1):675–687, https://doi.org/10.1109/ TCOMM.2020.3033006 7. Chen X, Zhang Z (2010) Exploiting channel angular domain information for precoder design in distributed antenna systems. IEEE Trans Signal Process 58(11):5791–5801, https://doi.org/ 10.1109/TSP.2010.2062508 8. Mühlenbein H (1997) The equation for response to selection and its use for prediction. Evolutionary computation 5(3):303–346

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9. Guo H, Liang YC, Chen J, Larsson EG (2020) Weighted sum-rate maximization for reconfigurable intelligent surface aided wireless networks. IEEE Trans Wireless Commun 19(5):3064–3076, https://doi.org/10.1109/TWC.2020.2970061 10. Chen W, Ma X, Li Z, Kuang N (2019) Sum-rate maximization for intelligent reflecting surface based terahertz communication systems. In: Proc. 2019 IEEE/CIC Int. Conf. Commun. Workshops China (ICCC Workshops), Changchun, China, pp 153–157, https://doi.org/10. 1109/ICCChinaW.2019.8849960

Chapter 6

Beamforming for Simultaneous Communication and Sensing Enhancement

6.1 Introduction RIS has shown its great potential in facilitating ISAC, where sensing and communication tasks are mostly conducted on different time-frequency resources. While the more challenging scenarios of simultaneous communication and sensing (SC&S) have so far drawn little attention. In RIS-enabled ISAC systems, the beamforming requirements for communication and sensing are different and even contradictory, making it difficult to balance their performance. For communication tasks, it is expected to generate a fixed beam that is precisely aimed at the communication receiver to ensure reliable and stable communication. For sensing tasks, it is expected to generate a scanning beam to achieve a wider sensing range. To meet the different requirements of communication and sensing, this chapter studies beamforming design for simultaneous communication and sensing enhancement in RIS-enabled ISAC systems under various setups, from the device-based case to the device-free case [1]. In particular, narrowband beamforming in a device-based ISAC scenario is first studied, which provides a favorable communication-sensing trade-off and meanwhile avoids the intolerable overhead of the high dimensional cascaded channel estimation. Then, to avoid beam splitting in wideband systems, RIS wideband beamforming is addressed in a device-free ISAC scenario.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 X. Hu et al., Reconfigurable Intelligent Surface-Enabled Integrated Sensing and Communication in 6G, Wireless Networks, https://doi.org/10.1007/978-981-99-8299-8_6

135

136

6 Beamforming for Simultaneous Communication and Sensing Enhancement

6.2 Beamforming for Joint Performance Enhancement of Device-Based RIS-ISAC 6.2.1 System Model of Device-Based RIS-ISAC As shown in Fig. 6.1, we consider an RIS-enabled system operating in the mmWave band, which consists of a BS, a UE, and a distributed RIS. Due to the blockage or the unfavorable propagation environment, the direct link between the BS and the UE does not exist. Hence, a distributed RIS is deployed to assist the concurrent communication and location sensing for the blind-zone UE. The distributed RIS consists of 3 sub-surfaces. The first sub-surface (i.e., sub-surface 1) is composed of .M1 reflecting elements, while the i-th .(i = 2, 3) sub-surface (i.e., sub-surfaces 2 and 3) is composed of .Mi = Ms 0) represents the upper threshold of the difference between .SNR2,d and .SN R3,d . The location sensing accuracy is affected by both .SNR2,d and .SNR3,d and mainly determined by the worse one. It can be easily proved that, maximizing q . SN Rsen in the objective function, together with the constraint (6.27b), is approxζs } { imately equivalent to maximizing .min SNR2,d , SNR3,d , when .ε is very close to 0. By substituting (6.24) and (6.26) into (P1), the problem (P1) is equivalent to (P2) :

.

q Σ ρ 2 (2) (2) wBS ,ξ (2) ,wUE ζs i=2,3 σ0 ' max

|| || || (2) ||2 ||HU2R,i wUE || ''

'

sensing part

+

| ) ( ρ || (2) 1−q (2) |2 × 2 |[wBS ]H HR2B,1 diag ξ (2) HU2R,1 wUE | , . ζc σ '' '0 ' communication part

(6.28a)

||| || || | || ||| || (2) ||2 (2) ||2 || | s.t. |||HU2R,2 wUE || − ||HU2R,3 wUE || | < ε0 , .

(6.28b) (6.28c)

(6.27c), (6.27d), (6.27e), εσ02 ρ .

where .ε0 A

(2)

(2)

To decouple the optimization variables .wBS , .ξ (2) , and .wUE , we recast the problem (P2) as {

(P3) :

.

q1−q max SNR sen + (2) ζ ζc s w UE

[

]} - com max SNR (2)

,.

(6.29)

wBS ,ξ (2)

s.t. (6.28b), (6.28c),

(6.30)

where - sen A SNR

.

|| Σ || || (2) ||2 ||HU2R,i wUE ||

(6.31)

i=2,3

2 By doing this, both the communication and sensing performances become more sensitive to changes in the trade-off factor .q. Otherwise, .q may fail to adjust sensing and communication SNRs due to the great difference between .SN Rsen and .SN Rcom .

6.2 Beamforming for Joint Performance Enhancement of Device-Based RIS-. . .

145

and | | ) ( | (2) (2) |2 SN R com A |[wBS ]H HR2B,1 diag ξ (2) HU2R,1 wUE | .

.

(6.32)

Then, we decompose the problem (P3) equivalently into two sub-problems, i.e., the sub-problem corresponding to the beamforming vectors of the BS and the reflecting sub-surface (P4-a) :

.

- com , . max SNR

(6.33)

s.t. (6.27c), (6.27d),

(6.34)

(2)

wBS ,ξ (2)

and the sub-problem corresponding to the beamforming vector of the UE {

(P4-b) :

.

} q1 − q - max max SNR sen + SN R com , . (2) ζs ζc w

(6.35)

s.t. (6.27e), (6.28b),

(6.36)

UE

max

- com is the optimal value of the objective function in the problem (P4-a). where .SNR First, by substituting (6.3) and (6.7) into (P4-a), we rewrite the problem (P4-a) as | ) ( | (2) (P4-a' ) : max |αcom [wBS ]H a uA R2B,1

.

(2)

wBS ,ξ (2)

| ( ) ( ) ( ) (2) |2 D D (2) A A u diag ξ b u q(w , v , v ) bH 1 1 R2B,1 R2B,1 U2R,1 U2R,1 UE | , . (6.37a)

s.t. (6.27c), (6.27d),

(6.37b)

( ) (2) (2) where .αcom A αR2B,1 αU2R,1 and .q(wUE ) A cH uD U2R,1 wUE . Furthermore, we decompose the problem (P4-a.' ) equivalently into two sub-problems, i.e., .

| )|2 ( | | H A max |[w(2) ] a u | , s.t. (6.27e), R2B,1 BS (2)

(6.38)

wBS

and .

| ( ) ( ) ( )|2 | | D D (2) A b1 uA max |bH 1 uR2B,1 , vR2B,1 diag ξ U2R,1 , vU2R,1 | , s.t. (6.27d). ξ (2)

(6.39)

146

6 Beamforming for Simultaneous Communication and Sensing Enhancement

The optimal solutions to sub-problems (6.38) and (6.39) are respectively given by (2)*

) ( 1 a uA R2B,1 , . NBS )) ( ) ( ( A D D b u = diag b∗1 uA , v , v 1 U2R,1 U2R,1 R2B,1 R2B,1 ( ) ( ) A D D O b u , v , v = b∗1 uA 1 U2R,1 U2R,1 R2B,1 R2B,1 .

wBS = √

.

ξ (2)*

(6.40)

(6.41)

By substituting (6.40) and (6.41) into (6.37a), we obtain the optimal value of the objective function in the problem (P4-a.' ) as | |2 max - com = ||αcom γ q(w(2) )|| , SNR UE

.

(6.42)

] ( ) ( ) ( ) ( ) [ (2)* H (2)* H uD D A A b diag ξ b u where .γ A wBS a uA , v , v 1 R2B,1 1 R2B,1 R2B,1 U2R,1 U2R,1 . Second, we solve the problem (P4-b) using the above results. Specifically, we substitute (6.42) into the problem (P4-b) and obtain (P5) : max

.

(2)

wUE

|| | q Σ || 1 − q || || (2) ||2 (2) |2 ||HU2R,i wUE || + |αcom γ q(wUE )| , ζs ζc i=2,3

s.t. (6.27e), (6.28b).

(6.43)

Next, by substituting (6.3) and (6.7) into (P5), we simplify the above problem as (P6) : max

.

(2)

wUE

| | ( | |2 ) q Σ 1−q | | | (2) |2 |αcom |2 γ 2 |q(w(2) )| , . |αU2R,i |2 Ms |cH uD U2R,i wUE | + UE 2 ζc ζs i=2,3

(6.44a) |2 |2 | ( | ( ) ) | | | H D (2) | uU2R,3 w(2) s.t. 0 < |cH uD U2R,2 wUE | − κ |c UE | < ε1 , (6.27e), (6.44b) where | | |αU2R,3 |2 ε0 . .κ A | | , ε1 A | | |αU2R,2 |2 |αU2R,2 |2 Ms

(6.45)

6.2 Beamforming for Joint Performance Enhancement of Device-Based RIS-. . .

147

| |2 | |2 Let .ζs = 12 (|αU2R,2 | + |αU2R,3 | )Ms and .ζc = |αcom |2 γ 2 . We simplify the problem (P6) as (P7) : max q

Σ

.

(2)

wUE

| ( | ( | | ) ) | H D | (2) |2 (2) |2 w u w ηi |cH uD + (1 − q) |c | U2R,i U2R,1 UE UE | , .

i=2,3

(6.46a) | ( | ( | | ) ) | | H D (2) |2 (2) |2 w u w s.t. 0 < |cH uD − κ |c | U2R,2 U2R,3 UE UE | < ε1 , . || || || (2) || ||wUE || = 1,

(6.46b) (6.46c)

where ηi A

.

2|αU2R,i |2 , i = 2, 3. |αU2R,2 |2 + |αU2R,3 |2

(6.47)

The problem (P7) is a non-convex QCQP. Responding to this, we propose two sensing-based beamforming schemes, i.e., the S-SDR and S-MBS beamforming schemes. S-SDR Beamforming Scheme Note | ( | ) | H D (2) |2 (2) (2) |c uU2R,i wUE | = [wUE ]H Pi wUE ,

(6.48)

) ( ) ( H uD Pi A c uD U2R,i c U2R,i , i = 1, 2, 3,

(6.49)

.

where

.

and the objective function (6.46a) becomes q

Σ

.

(2)

(2)

(2)

(2)

ηi [wUE ]H Pi wUE + (1 − q)[wUE ]H P1 wUE .

(6.50)

i=2,3

Similarly, define ) ( ) ( ) ( ) ( D H D H uD uD .Pκ A c uU2R,2 c U2R,2 − κc uU2R,3 c U2R,3 , (2)

(6.51)

(2)

and the constraint (6.46b) becomes .0 < [wUE ]H Pκ wUE < ε1 . Therefore, we rewrite the problem (P7) as (P8) : max q

Σ

.

(2) wUE

(2) (2) H (2) H ηi [w(2) UE ] Pi wUE + (1 − q)[wUE ] P1 wUE , .

(6.52a)

(2)

(6.52b)

i=2,3 (2)

s.t. 0 < [wUE ]H Pκ wUE < ε1 , (6.27e).

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6 Beamforming for Simultaneous Communication and Sensing Enhancement (2)

(2)

(2)

(2)

Noticing .[wUE ]H Pi wUE = tr(Pi wUE [wUE ]H ), we apply the change of variables (2) (2) (2) H (2) (2) .W UE = wUE [wUE ] , satisfying .WUE > 0 and .rank(WUE ) = 1, and we convert the problem (P8) into (P9) : max q

Σ

.

(2) WUE

(2)

(2)

ηi tr(Pi WUE ) + (1 − q)tr(P1 WUE ), .

(6.53a)

i=2,3 (2)

s.t. 0 < tr(Pκ WUE ) < ε1 , .

(6.53b)

(2)

(6.53c)

rank(WUE ) = 1, . || || || (2) ||2 (2) WUE > 0, ||WUE || = 1.

(6.53d)

To tackle the non-convexity of the rank-one constraint (6.53c), we apply the SDR technique to reduce the problem (P9) to (P10): max q

Σ

.

(2) WUE

(2)

(2)

ηi tr(Pi WUE ) + (1 − q)tr(P1 WUE ), .

(6.54a)

i=2,3

s.t. 0 < tr(Pκ W(2) UE ) < ε1 , (6.53d).

(6.54b)

Problem (P10) is a standard convex semi-definite program (SDP), which can be optimally solved by convex optimization solvers such as CVX [5]. However, due to the relaxation, solving the relaxed (P10) may not lead to a rank-one solution that satisfies constraint (6.53c), which indicates that the optimal objective value of (P10) can only serve as an upper bound of (P7). Nevertheless, many reasonable heuristic methods are proposed to meet the rank-one constraint [6]. Here, we adopt the Gaussian randomization (GR) method to meet the rank-one condition. Specifically, (2) (2) we first obtain the eigenvalue decomposition of .WUE as .WUE = UΣUH , where .U = [e 1 , · · · , e NUE ] and .Σ = diag(λ1 , · · · , λNUE ) are a unitary matrix and a diagonal matrix, respectively. Then, we obtain a suboptimal solution to (P7) as (1/2) r, where .r ∈ CNUE ×1 is a random vector generated according to ¯ (2) .w UE = UΣ ) ) ( ( .r ∈ CN 0, INUE with .CN 0, INUE denoting the CSCG distribution with zero mean and covariance matrix .INUE . Let .lGR denote the number of iterations for the GR process. We independently generate .lGR Gaussian random vectors .r’s and the value of objective function in (P7) is approximated as the maximum one attained by (2) ¯ (2) the best .w UE among all .r’s. Finally, the feasible solution .wUE to the problem (P7) (2)*

can be recovered by .wUE =

¯ (2) w || UE || . || (2) || ¯ UE || ||w

The detailed process of solving the problem

(P1) via the S-SDR beamforming scheme is given in Algorithm 7. S-MBS Beamforming Scheme Although the S-SDR beamforming algorithm can properly solve the problem (P7), it is time-consuming due to the high complexity caused by the use of the SDR technique. To facilitate the practical implementation, we propose a low-complexity S-MBS beamforming algorithm for solving the

6.2 Beamforming for Joint Performance Enhancement of Device-Based RIS-. . .

149

Algorithm 7 Proposed S-SDR beamforming algorithm (1) Input: q, qBS , qi , qˆ UE , lGR and the value of the objective function of (P7) f¯. A,(1) D,(1) A,(1) 1: Compute uˆ U2R,i (i = 1, 2, 3) according to Chap. 3, obtain uˆ U2R,i = −uˆ U2R,i and compute ) ( c uD U2R,i according to (6.18).

2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14:

(2)* Acquire optimal solutions to (P4-a' ), i.e., w(2)* , via (6.40) and (6.41), respectively. BS and ξ Compute κ, ε1 and ηi , according to (6.45) and (6.47). Compute Pi (i = 1, 2, 3) and Pκ according to (6.49) and (6.51), respectively. (2) Obtain WUE by solving problem (P10) with CVX. (2) Obtain U and Σ by applying eigenvalue decomposition to WUE . ¯ initialize the value of f . repeat ) ( (1/2) r. ˜ (2) Randomly generate r ∈ CN 0, INUE and set w UE = UΣ ˜ (2) Compute the value of the objective function ˜f corresponding to w UE via (6.46a). if ˜f ≥ ¯f then ˜ (2) ¯ (2) Let ¯f = ˜f and set w UE = w UE . end if until The number of iterations reaches lGR . (2)*

15: Set wUE =

¯ (2) w || UE || . || (2) || w || ¯ UE ||

(2)*

(2)*

Output: wBS , ξ (2)* and wUE .

problem (P7) by maneuvering multiple beams of the UE. Its main idea is that a suboptimal solution to the problem (P7) can be obtained as the weighted sum of three basic beams respectively steering into the directions of the reflecting subsurface and the two sensing sub-surfaces. Specifically, )the beamforming vector ( (2) 1 D steering to the i-th sub-surface is .wi = √N c uU2R,i . As such, a suboptimal UE solution to the problem (P7) can be expressed in the following form (2) .w UE

Σ (2) i=1,2,3 ψi wi || , = ||Σ || (2) || || i=1,2,3 ψi wi ||

(6.55)

where .ψi ∈ [0, 1] (i = 1, 2, 3) is the weight factor. Let .ψ = [ψ1 , ψ2 , ψ3 ]T . Then, by substituting (6.55) into the problem (P7), we optimize the weight vector (2) .ψ instead of the UE beamforming vector .w UE , and transform the problem (P7) into (P11) : max q

Σ

.

ψ

ηi Fi + (1 − q)F1 , .

(6.56a)

i=2,3

s.t. |F2 − κF3 | < ε1 , . || || || (2) || ||wUE || = 1,

(6.56b) (6.56c)

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6 Beamforming for Simultaneous Communication and Sensing Enhancement

| | | (2) |2 where .Fi A |cH (uD U2R,i )wUE | , i = 1, 2, 3. To solve (P11), we incorporate the constraint (6.56b) by exploiting the penalty function method with the penalty function .P (x) = −μx, where .μ > 0 is the penalty parameter which is used to scale the penalty function and x is the variable. As such, we reformulate the problem (P11) as (P12) : max q

Σ

.

ψ

ηi Fi + (1 − q)F1 − μ (|F2 − κF3 | − ε1 ) , .

(6.57a)

i=2,3

|| || || || s.t. ||w(2) UE || = 1.

(6.57b)

In the above objective function, since the penalty part corresponds to the sensing performance weighted by .q, we deliberately set the penalty parameter as .μ = 2q such that the sensing performance, which is determined by the first and third terms, improves with the increase of the trade-off factor .q. To solve (P12), we adopt the method of particle swarm optimization (PSO). First, we generate .Np particles, and each particle has two properties, i.e., the position and the velocity, which respectively represent a possible vector of the weight factor, i.e. .ψ, and the corresponding search direction. For the k-th particle in the l-th iteration of the algorithm, we define its position and velocity as .ψ k,l and .v k,l , respectively, where .[ψ k,l ]j ∈ [0, 1] and .[v k,l ]j ∈ [vmin , vmax ] .(j = 1, 2, 3). Let the value of (6.57a) be the fitness value in the PSO process and denote it as .f itness(ψ k,l ) for given .ψ k,l . We evaluate the corresponding fitness value for each particle in each iteration, and record the best fitted position .ψ˜ k for the k-th particle and the globally best fitted position .ψ Best for all particles. For the l-th iteration, the k-th particle updates its velocity .v k,l via v k,l = c1 v k,l−1 + c2 χ (ψ Best − ψ k,l−1 ) + c3 χ (ψ˜ k − ψ k,l−1 ),

.

(6.58)

where .ci (i = 1, 2, 3) is the weight factor for each term, which represents the learning rate in the PSO process, and .χ is the random values which is generated via .χ ∼ U (0, 1). Noticing that .vmin < [v k,l ]j < vmax .(j = 1, 2, 3), we have [v k,l ]j = max(vmin , [v k,l ]j ), [v k,l ]j = min(vmax , [v k,l ]j ),

.

(6.59)

and then we update the position .ψ k,l via ψ k,l = ψ k,l−1 + v k,l ,

.

(6.60)

where we deliberately limit every element of .ψ k,l in .[0, 1]. Moreover, .ψ k,0 and v k,0 respectively represent the initial position and velocity of the k-th particle. In the initialization, the velocity and position of each particle are set randomly within

.

6.2 Beamforming for Joint Performance Enhancement of Device-Based RIS-. . .

151

the search space. The detailed process of solving the problem (P1) via the S-MBS beamforming scheme is summarized in Algorithm 8. Algorithm 8 Proposed S-MBS beamforming algorithm (1) Require: q, qBS , qi , qˆ UE , the number of particles Np and the number of iterations lp . A,(1) D,(1) A,(1) 1: Compute uˆ U2R,i (i = 1, 2, 3) according to Chap. 3, obtain uˆ U2R,i = −uˆ U2R,i and compute c(uD U2R,i ) according to (6.18). (2)* Acquire optimal solutions to (P4-a' ), i.e., w(2)* , via (6.40) and (6.41), respectively. BS and ξ Compute κ and ηi according to (6.45) and (6.47), and let μ = 2q. for k-th particle do Initialize the velocity v k,0 and the position ψ k,0 randomly. Evaluate the fitness via (6.57a) and set ψ˜ k = ψ k,0 . end for Set ψ Best = ψ˜ 1 as the initial value. for l-th iteration do for k-th particle do Update the velocity v k,l and the position ψ k,l via (6.58)–(6.60). Evaluate the fitness via (6.57a). if f itness(ψ k,l ) > f itness(ψ˜ k ) then ψ˜ k = ψ k,l . end if if f itness(ψ˜ k ) > f itness(ψ Best ) then ψ Best = ψ˜ k . end if end for end for Σ ¯ (2) w (2)* (2) || , where w ¯ (2) 21: Set wUE = |||| UE j =1,2,3 [ψ Best ]j wi . (2) || UE =

2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20:

¯ UE || ||w

(2)* and w(2)* Ensure: w(2)* BS , ξ UE .

Additionally, the complexity and the convergence analysis of the proposed two sensing-based beamforming schemes in phase 2 are provided as follows. Complexity Analysis The common part of the proposed two beamforming schemes in phase 2 deals with the problem of optimizing the active beamforming (2) vector of the BS .wBS and the passive beamforming vector of the reflecting sub(2)* surface .ξ (2) . The optimal beamforming vectors .wBS and .ξ (2)* are acquired via (6.40) and (6.41), respectively. Hence, the complexity of the common part is mainly determined by calculating (6.40) and (6.41), and the corresponding complexity is .O(NBS + M1 ). Additionally, in order to solve the non-convex QCQP problem (P7), Algorithm 7 adopts the SDR method and solves the follow-up SDP problem (P10) via CVX. By using the interior point method, the worst-case complexity 4.5 log( 1 )), where .ι > 0 is the solution of solving the SDP problem (P10) is .O(NUE ι accuracy [6, 7]. The subsequent GR procedure is applied to meet the rank-one constraint, the complexity of which is .O(lGR NUE ). Therefore, the complexity of 4.5 log( 1 ) + l N ). While for Algorithm 8, Algorithm 7 is .O(NBS + M1 + NUE GR UE ι

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6 Beamforming for Simultaneous Communication and Sensing Enhancement

due to the transformation in (6.55), the complexity of Algorithm 8 is mainly determined by the computation of (6.57a) in each iteration, and thus reduced to .O(NBS + M1 + Np lp NUE ). Convergence Analysis For Algorithm 7, its convergence is guaranteed since the value of the objective function of (P7) in each iteration of the GR procedure is updated non-decreasingly and the optimal value is bounded from above owing to the SNR constraint. Similarly, for Algorithm 8, the value of its objective function, i.e. the optimal fitness of all particles, is updated increasingly over iterations and the SNR constraint bounds its value from above.

6.2.3 Numerical Results and Discussions In this section, we provide numerical results to demonstrate the effectiveness of the proposed beamforming schemes for achieving a favorable communicationsensing trade-off. The simulation setup is shown in Fig. 6.4, where the UE is on the horizontal floor, the RIS is 3 meters (m) above the horizontal floor, and the BS is 20 m above the horizontal floor. The distances from the UE and the BS to the first sub-surface are set to be .dU2R,1 = 5 m and .dB2R,1 = 50 m, respectively. The path loss exponents from the RIS to the BS, from the UE to the RIS, and from one sub-surface to other sub-surfaces are set as .2.3, .2.2 and .2.1, respectively. The path loss at the reference distance of .1 m is set as 30 dB. Unless otherwise specified, the following setup is used: .NBS = 16, .M1 = 20×20, .M2 = M3 = Ms = 6×6, .τ1 = 5, 2 .τ2 = 95, .T = 100, .ρ = 20 dBm, noise power .σ = −80 dBm, simulation setup in 0 Fig. 6.4 and the proposed S-SDR beamforming algorithm are adopted. Besides, the root mean square error (RMSE) is adopted to measure the performance of location sensing. Let .RMSEn represent the RMSE in phase n and define it as RMSEn =

.

Fig. 6.4 Simulation setup (top view)

/ (n) qˆ U − qU , n = 1, 2.

(6.61)

6.2 Beamforming for Joint Performance Enhancement of Device-Based RIS-. . .

6.2.3.1

153

Proposed RIS-Enabled ISAC System vs. RIS-Enabled Communication System

In this subsection, we focus on the comparison of the proposed RIS-enabled ISAC system and the RIS-enabled communication system. In the RIS-enabled communication system, the alternating optimization (AO) scheme assuming perfect CSI [8] is adopted. We use the average communication rate over the whole coherence block .R¯ as the metric for measuring the communication performance and define it as T 1 Σ R (t). R¯ = T

(6.62)

.

t=1

Moreover, to characterize the JC&S performance of the RIS-enabled ISAC system, we adopt the rate-distortion metric, i.e., .R¯ − RMSE2 , which indicates the average communication rate achieved under a given RMSE in phase 2. Figure 6.5 compares the performance of the proposed RIS-enabled ISAC system and the RIS-enabled communication system under different numbers of sensing elements. The .R¯ − RMSE2 curves represent the JC&S performance of the proposed system, as the trade-off factor .q ranges from 0 (i.e., communication SNR maximization) to 1 (i.e., sensing SNR maximization). First, we can see that the communication performance of the proposed RIS-enabled ISAC system is worse than that of the RIS-enabled communication system, since the latter one assumes the perfect CSI is known and spends all its spatial resources on communication. However, despite worse communication performance, the RISenabled ISAC system realizes the new function of location sensing, and can achieve comparable communication performance to the RIS-enabled communication system by adjusting the trade-off factor .q. Moreover, their communication performance gap decreases with the number of sensing elements .Ms , because more accurate sensing information is obtained and used for beamforming design in the RIS-enabled ISAC system. Additionally, we can observe that the proposed beamforming scheme can flexibly balance the communication and sensing performance by adjusting the tradeoff factor .q. By sacrificing the performance of communication, the performance of Fig. 6.5 Impact of the sensing elements on the proposed RIS-enabled ISAC system

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6 Beamforming for Simultaneous Communication and Sensing Enhancement 15 17 16

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location sensing can be improved and vice versa. For instance, when .Ms = 16, the RMSE2 ameliorates from 0.06 to 0.01 m as the communication rate decreases from 12.3 to 6.4 bps/Hz. Figure 6.6 compares the performance of the proposed RIS-enabled ISAC system and the RIS-enabled communication system when different time ratios of phase 1 in the RIS-enabled ISAC system are considered. In Fig. 6.6a, for all configurations of .τ1 /T and .Ms , the average communication rate of the proposed RIS-enabled system is lower than that of the RIS-enabled communication system. This communication performance gap can be narrowed by increasing the number of sensing elements or properly designing the time ratio .τ1 /T . In addition, there exists an optimal ratio that maximizes the average communication rate. For example, with .Ms = 16, .R¯ increases to its highest point when .τ1 /T changes from 0.01 to 0.05 and then drops when .τ1 /T keeps increasing. This is because when the number of sensing elements .Ms and the ratio of phase 1 .τ1 /T are both small, the resulting low positioning accuracy in phase 1 would affect the effectiveness of the sensing-based beamforming design in phase 2, thereby causing the drop of the average communication rate. However, by appropriately increasing the ratio of phase 1, the error of the location sensing can be ameliorated effectively and .R¯ rises correspondingly. Moreover, as the number of sensing elements .Ms increases, the optimal time ratio becomes smaller. For instance, by increasing .Ms from 16 to 36, the best time ratio decreases from 0.05 to 0.01 for the following reasons. On the one hand, when .Ms is large, the sensing accuracy is sufficiently high for effective beamforming design even with small .τ1 /T , and excessive improvement of sensing accuracy can only bring marginal benefits to the communication performance. On the other hand, increasing .τ1 /T causes fewer time slots allocated for the high-rate communication in phase 2. More specifically, in Fig. 6.6b, the number of sensing elements .Ms is set to be fixed and we focus on the comparison between two systems with different .τ1 /T . The ratio of phase 1 affects not only the average communication rate but also the location sensing accuracy. This is expected since, with the aid of the estimated UE’s .

6.2 Beamforming for Joint Performance Enhancement of Device-Based RIS-. . .

155

location in phase 1, beamforming in phase 2 is able to effectively improve both communication and sensing performances, and such improvement depends on the value of .q. Additionally, the results of communication performance in Fig. 6.6b are consistent with the results in Fig. 6.6a, where the average communication rate .R¯ drops with the increase of .τ1 /T .

6.2.3.2

How Does Beamforming Affect the Communication-Sensing Trade-Off?

In this subsection, we focus on answering the question how beamforming affects the trade-off in the RIS-enabled ISAC system by comparing the proposed two sensing-based beamforming schemes. To characterize the JC&S performance, we also adopt .R¯ 2 − RMSE2 as the metric in this subsection, where .R¯ 2 is the average communication rate in phase 2 and is defined as T 1 Σ R (t). R¯ 2 = τ2

(6.63)

.

t=τ1 +1

Figure 6.7 compares UE’s beampattern gains achieved by the proposed two sensing-based beamforming schemes with different .q, where the location of the UE is set to be (3.46 m, .−2.00 m, 0.00 m). By adjusting the trade-off factor .q, desired beam pattern can be generated by the proposed sensing-based beamforming schemes. For instance, in Fig. 6.7a, with .q = 0 which corresponds to communication SNR maximization, the main beam is steered towards the reflecting sub-surface for assisting communication, while in Fig. 6.7c, with .q = 1 which corresponds to sensing SNR maximization, the strongest two beams are respectively steered towards the two sensing sub-surface for enhancing location sensing. In Fig. 6.7b, with .q = 0.5 which means that both communication and location sensing performances are taken into account, the strongest three beams are respectively steered towards the reflecting sub-surface and the two sensing sub-surface such that 1

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6 Beamforming for Simultaneous Communication and Sensing Enhancement

both performances can be improved. Moreover, due to the consideration of avoiding the “cask effect” in estimating AOAs of both sensing sub-surfaces, in Fig. 6.7b, c, we can readily observe that the beam to the direction of the second sub-surface (the one which is far from the UE) is stronger than the third sub-surface. This helps further improve the location sensing accuracy via UE’s beamforming. Also, increasing the number of UE’s antennas improves JC&S performance due to the higher beamforming gain. In Fig. 6.9, we present the JC&S performance of the proposed two beamforming schemes with the simulation setup illustrated in Fig. 6.8, where the UE is randomly distributed in the green area in front of the RIS. Specifically, the 3D-distance from the UE to the first sub-surface .dU2R,1 is limited in .[5, 10] m and the corresponding angle ranges in .[−45, 45] degrees. The rate-RMSE curves can be divided into three regions, i.e., the communication-sensing balance region, communication saturation region and sensing saturation region. In the balance region, the performance of communication and location is well balanced. The performance of one can be effectively improved by sacrificing the performance of another. In the communication/sensing saturation region, even if the sensing/communication performance is sacrificed a lot, little improvement of the communication/sensing performance can be achieved. Generally, we hope that the ISAC system operates in the balance region such that better joint performance can be obtained. Specifically, Fig. 6.9a compares performances of the two proposed beamforming schemes under different transmission power .ρ. The JC&S performance of the S-SDR beamforming scheme outperforms that of the S-MBS beamforming scheme, especially in the communication-sensing balance region where both performances are considered to be important. However, their performance gap gradually narrows to triviality in both communication and sensing saturation regions. Also, Fig. 6.9b shows the impact of the number of UE’s antennas .NUE on the communication-sensing trade-off. In the balance region, the JC&S performance of the S-SDR beamforming scheme is superior to that of the S-MBS beamforming scheme, and their performance gap becomes more pronounced with the increase of .NUE . While such performance gap is trivial in both communication and sensing saturation regions for any configuration of .NUE . This indicates that the S-SDR beamforming scheme has a better ability to balance communication and sensing. Moreover, as has been analysed in Sect. 6.2.2, the complexity gap between the S-SDR beamforming scheme and the S-MBS beamforming scheme enlarges with the increase of .NUE , which indicates that the S-SDR beamforming scheme can achieve better joint performance in the balance Fig. 6.8 Simulation setup for Fig. 6.9 (top view)

6.2 Beamforming for Joint Performance Enhancement of Device-Based RIS-. . .

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region with the price of higher computational complexity, whereas the S-MBS beamforming scheme can achieve almost the same performance in the saturation regions as the S-SDR beamforming scheme with much lower complexity.

6.2.3.3

How Does the Sensing Accuracy Affect ISAC Beamforming?

In this subsection, we focus on answering how the sensing accuracy in phase 1 affects the performance of ISAC beamforming in phase 2. Figure 6.10 shows the impact of the sensing accuracy in phase 1 on the average communication rate in phase 2 where the trade-off factor .q is set to be 0. Figure 6.10a illustrates that the communication rate of the proposed two beamforming algorithms gradually gets close to that of the AO beamforming algorithm with perfect CSI, when .Ms increases. Additionally, as the transmit power or the number of sensing elements increases, the gap of the communication performance between

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6 Beamforming for Simultaneous Communication and Sensing Enhancement

Fig. 6.11 Impact of the UE’s mobility on proposed sensing-based beamforming schemes

the proposed sensing-based beamforming and the AO beamforming with perfect CSI gradually vanishes, due to the increased positioning accuracy in phase 1. Figure 6.10b shows that the increase of .τ1 /T is able to improve the communication performance of the proposed sensing-based beamforming schemes in phase 2. However, when the number of sensing elements .Ms is small, there still exists a communication performance gap between the proposed beamforming and the AO beamforming even with a large number of time slots allocated to phase 1. Figure 6.11 shows the performance of the proposed sensing-based beamforming schemes when taking into account UE’s mobility. In the simulation, we compare three beamforming schemes including the short-term beamforming, long-term beamforming, and beamforming with perfect CSI [8]. For the short-term scheme, the beamforming is designed according to the transmission protocol in Fig. 6.2. For the long-term scheme, we use the extended transmission protocol explained in Remark 6.2. Numerical results are given in the figure with two y-axes, where the left y-axis expresses the average communication rate .R¯ over multiple coherence blocks, and the right y-axis expresses the rate ratio of the two beamforming schemes, i.e., short-term/long-term beamforming and AO beamforming with perfect CSI. By exploiting the sensing information obtained in the previous block for beamforming in the current block, the proposed long-term scheme performs better than the shortterm beamforming scheme. Although .R¯ of the proposed long-term scheme degrades as the speed of UE increases, it only drops about 7% when the speed of the UE increases from 1 to 20 m/s.

6.3 Beamforming for Joint Performance Enhancement of Device-Free RIS-ISAC 6.3.1 System Model We consider an RIS-aided wideband ISAC system as shown in Fig. 6.12, where an RIS-based ISAC transceiver communicates with a single-antenna user, while sensing the target in specified direction. The transceiver is equipped with two horn

6.3 Beamforming for Joint Performance Enhancement of Device-Free RIS-ISAC

159

Fig. 6.12 RIS-aided wideband ISAC system

antennas and an RIS. The two horn antennas are respectively used as the transmitting (TX) antenna and the receiving (RX) antenna to transmit wideband ISAC signals and receive the echo signals from the target, while the RIS is used to reflect and manipulate the signals from the TX antenna. Specifically, the TX antenna first sends the ISAC signals, which are then processed by the RIS to form two beams pointing at the communication user and the sensing target respectively. Finally, the RX antenna receives the echo signals for acquiring sensing information of the target, while the user receives the ISAC signals for recovering communication information. The RIS consists of a uniform rectangular array (URA) with .N = Ny × Nz elements lying on the yoz plane, where .Ny and .Nz denote the numbers of reflecting elements in the horizontal and vertical directions respectively. Let .0 = diag (ξ ) [ ]T denotes the RIS reflecting coefficient matrix, where .ξ = ξ1,1 , . . . , ξNy ,Nz ∈ ( ) j θny ,nz N ×1 . .ξny ,nz = e denotes the reflecting coefficient of the . ny , nz -reflecting C element of the RIS, and .θny ,nz ∈ [0, 2π ). For ease of practical implementation, the RIS is assumed to be only phase adjustable and the reflecting coefficient of each element can only take a finite number of discrete values, which are uniformly distributed in .[0, 2π ). Thus, the set of}the reflecting coefficients can be denoted by { | 2π | B = 0, . . . , l, . . . , 2b − 1 , where .b is the bit-quantization number. .F = B b 2

6.3.1.1

Channel Model

The layout of the reflecting elements on the RIS is shown in Figs. 6.13 and 6.14. The near-field model is adopted since the size of RIS is much smaller than the distance between the TX antenna and the RIS. For wideband OFDM waveform, its

160

6 Beamforming for Simultaneous Communication and Sensing Enhancement

Fig. 6.13 Layout of RIS elements

Fig. 6.14 The n-th RIS element

number of subcarriers is denoted by K. By applying the Saleh-Valenzuela channel model, the frequency-domain channel from the TX antenna to the RIS on the k-th subcarrier can be expressed as ( ) T2I T2I T2I d , hT2I = α O 0 O a k k k k

.

(6.64)

where .O denotes the Hadamard product, .α T2I ∈ CN ×1 denotes the channel k T2I N ×1 gain, .0k ∈ C denotes the delay of the TX-RIS channel on the k-th T2I N subcarrier, .d ∈ C ×1 denotes the distance the TX antenna and ( between ) ∈ CN ×1 represents the the reflecting elements of the RIS, and .a k d T2I

6.3 Beamforming for Joint Performance Enhancement of Device-Free RIS-ISAC

161

array steering vector at the RIS in the near-field scenario. Specifically, .α T2I k ]= [ T T2I T2I [ ]T T2I T2I jϕ jϕ αk,1,1 , . . . , αk,ny ,nz , . . . , αk,Ny ,Nz , .0k = ej ϕk,1,1 , . . . , e k,ny ,nz , . . . , e k,Ny ,Nz [ ]T T2I , . . . , d T2I , . . . , d T2I and .d T2I = . d1,1 . Considering that the frequency of ny ,nz Ny ,Nz wideband signals will affect amplitude attenuation, we have αk,ny ,nz =

.

c , 4π dnT2I f y ,nz k

T2I ϕk,n = −2πfk τnT2I = −2πfk y ,nz y ,nz

.

(6.65) dnT2I y ,nz c

(6.66)

,

where c denotes the speed of light, .fk denotes the k-th subcarrier frequency, .τnT2I y ,nz ( ) denotes the time delay from the TX antenna to the . ny , nz -th reflecting element. We denote the transmission band of the wideband waveform as B, so we have ( ) K −1 B k−1− . (6.67) .fk = fc + K 2 where .fc denotes the center frequency. And the near-field array steering vector can be expressed as (

)

[

a k d T2I = e

.

d T2I −j 2πfk 1,1 c

,...,e

dnT2I,n −j 2πfk yc z

,...,e

T2I dN ,N −j 2πfk yc z

]T .

(6.68)

For the channel from the RIS to the target, far-field model is adopted since the distance between them is much larger compared with the size of the RIS. Therefore, the RIS-target channel on the k-th subcarrier can be written as I2T I2T hI2T k = α k O 0k O bk (u, v) ,

(6.69)

.

where .α I2T ∈ CN ×1 denotes the channel gain, .0I2T ∈ CN ×1 denotes k k the delay of the RIS-target channel on the k-th subcarrier, and .bk (u, v) ∈ CN ×1 represents the array steering vector at the RIS in the far-field sce]T [ I2T , . . . , α I2T I2T = αk,1,1 , .0I2T = nario. Specifically, .α I2T k k k,ny ,nz , . . . , αk,Ny ,Nz ]T [ I2T I2T I2T jϕ jϕ ej ϕk,1,1 , . . . , e k,ny ,nz , . . . , e k,Ny ,Nz , where I2T αk,n = y ,nz

.

c , 4π dnI2T f y ,nz k

I2T ϕk,n = −2πfk τnI2T = −2πfk y ,nz y ,nz

.

(6.70) dnI2T y ,nz c

,

(6.71)

162

6 Beamforming for Simultaneous Communication and Sensing Enhancement

( ) I2T dnI2T = d1,1 + d RIS ny − 1 cosγ sinψ + d RIS (nz − 1) sinγ y ,nz . ( ) I2T + ny − 1 λc u + (nz − 1) λc v, = d1,1 I2T .τn ,n y z

=

dnI2T y ,nz c

) ( ny − 1 u + (nz − 1) v + , c fc

I2T d1,1

=

(6.72)

(6.73)

I2T denotes the distance between the .(1, 1)-th reflecting element and the where .d1,1 target, and .d RIS denotes the distance between two adjacent reflecting elements, which is usually set as half the wavelength of the central subcarrier, i.e., .d RIS = λ2c . .γ and .ψ respectively represent the elevation and azimuth angle of departure (AOD) ) ) ( ( for the link from the RIS to the target, and .γ ∈ − π2 , π2 , .ψ ∈ − π2 , π2 . RIS

RIS

γ Additionally, we define .u A d cosλkγ sin ψ and .v A d λsin as the effective k elevation and azimuth AODs, respectively. Therefore, the far-field array steering vector can be written as

]T [ ]T [ f f j 2π fkc (nz −1)v j 2π fkc (ny −1)u .b k (u, v) = 1, . . . , e ⊗ 1, . . . , e .

(6.74)

Thus we can express the cascaded channel .hT2T ∈ CN ×1 from the TX antenna k to the target on the .k-th subcarrier as ]T [ hT2T = hI2T 0hT2I k k k ,

.

(6.75)

where .hT2I ∈ CN ×1 and .hI2T ∈ CN ×1 denote the baseband equivalent channels k k from the TX antenna to RIS and from RIS to the target, respectively. Similarly, the cascaded channel .hT2U ∈ CN ×1 from the TX antenna to the user k on the .k-th subcarrier can be written as ]T [ hT2U = hI2U 0hT2I k , k k

.

(6.76)

where .hI2U ∈ CN ×1 denotes the baseband equivalent channel from RIS to the user k on the k-th subcarrier.

6.3.1.2

Signal Model

The received echo signals on the k-th subcarrier can be written as rk =

.

√

[ ]H pk hT2T 0hT2T k k sk + nk ,

(6.77)

6.3 Beamforming for Joint Performance Enhancement of Device-Free RIS-ISAC

163

where .pk represents the signal transmission power assigned to(the k-th ) subcarrier, .sk denotes the transmit symbol of each subcarrier, and .nk ∼ N 0, σ 2 is the additive white Gaussian noise (AWGN) on the k-th subcarrier with zero mean and variance 2 .σ . We define .ck (u, v) as the equivalent array steering vector, which can be written as ck (u, v) = a k O bk (u, v) .

.

(6.78)

Now we can denote .r (fk , u, v, ξ ) as the beamforming gain in the direction (u, v) on the k-th subcarrier, which can be written as | | | T | .r (fk , u, v, ξ ) = |c k (u, v) ξ | . (6.79)

.

The received signal at the user on the k-th subcarrier can be written as yk =

.

√ [ I2U ]T pk hk 0hT2I k sk + nk ,

(6.80)

Thus, the achievable rate R over all subcarriers at the user can be written as ⎛

|[ |2 ⎞ | I2U ]T | T2I | | h p 0h K k| k ⎜ k | ⎟ Σ ⎜ ⎟ .R = log2 ⎜1 + ⎟. 2 ⎝ ⎠ σ

(6.81)

k=1

6.3.2 Wideband Beamforming for Simultaneous Communication and Sensing Enhancement For wideband systems, there exists beam squint problem by using traditional narrowband beamforming method, namely the serious beamforming gain loss on some subcarriers, which would degrade the sensing accuracy and communication performance severely. In this section, we aim to optimize the reflecting coefficients of the RIS to enhance both the communication and sensing performance. As shown in Fig. 6.15, we first divide the RIS into two parts, the sensing subarray and the communication subarray with reflecting coefficient vectors .ξ 1 and .ξ 2 respectively. Then, we alternatively optimize .ξ 1 and .ξ 2 .

164

6 Beamforming for Simultaneous Communication and Sensing Enhancement

Fig. 6.15 Subarray partition

6.3.2.1

Optimization of the Sensing Subarray

For given .ξ 1 , we optimize the reflecting coefficients of the sensing subarray .ξ 2 to ensure sensing performance. Sensing resolution is determined by the system bandwidth. Hence, to avoid bandwidth loss, we maximize the minimum beamforming gain among all sub-carriers at the target’s direction by optimizing the reflecting coefficients of the sensing sub-array. As such, the subproblem with respect to .ξ 1 is formulated as max min

.

ξ 1 k=1,...,.K

r (fk , u, v, ξ ) .

| | s.t. |ξ1,n | = 1,

(6.82a) (6.82b)

]T [ where .ξ 1 = ξ1,1 , . . . , ξ1,n , . . . , ξ1,N1 . We solve the above problem by applying an estimation of distribution algorithm (EDA) method. First, we set the probability matrix corresponding to .ξ 1 as ] [ b P 1 = p 1,1 , . . . , p 1,n , . . . , p 1,N 1 ∈ C2 ×N1 ,

.

(6.83)

]T [ b where .p 1,n = p1,n,1 , . . . , p1,n,l , . . . , p1,n,2b ∈ C2 ×1 denotes the probability parameter for .ξ1,n with its entry .p1,n,l satisfying the probability constraints b

0 < p1,n,l