Precoding and Beamforming for Multi-Input Multi-Output Downlink Channels by Roya Doostnejad A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto °c Copyright by Roya Doostnejad, 2005 Precoding and Beamforming for Multi-Input Multi-Output Downlink Channels Roya Doostnejad Doctor of Philosophy, 2005 The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto Abstract This dissertation presents precoding and beamforming schemes for multi-user wireless downlink channels when multiple antennas are employed at both the transmitter and the receivers. In the first part of the thesis, we will discuss transmitter processing with- out channel information which is applicable in both flat and frequency selective (when orthogonal frequency-division multiplexing (OFDM) is applied) fading channels. This leads to methods for designing signature matrices for transmitters that use any combina- tion of the spatial, temporal and frequency dimensions, with good performance provided by low-complexity receivers. In the rest of the thesis, we pose the problem when the channels between the base station and each user are known perfectly at the base station. A non-linear precoding scheme is designed to minimize the mean-squared error between the transmitted and received data with a per-user power constraint. We also develop methods that are able to provide user-specific signal-to-interference-noise ratios (SINRs) with minimal total transmit power, through the extension of a so-called uplink-downlink duality result. Our study indicates that channel knowledge at the transmitter leads to substantial reductions in required power for providing given levels of SINRs to users. ii Acknowledgements I would like to express my sincere gratitude to my supervisors Prof. Teng Joon Lim, and Prof. Elvino S. Sousa for their guidance, advice, and continued support throughout my thesis research. Prof. Lim has provided the key technical insights and contributed tireless editorial effort which has vastly improved the quality of this dissertation. Prof. Sousa has provided me a gentle encouragement and a far-reaching vision of the work. I wish to thank my entire committee: Prof. Frank Kschischang, Prof. Ravi Adve, Prof. Dimitris Hatzinakos, Prof. Bruce A. Francis, and Prof. Murat Uysal of the Univer- sity of Waterloo for their effort, discussions and constructive comments. In particular, I would like to thank Prof. Kschischang for his invaluable inputs and constant encourage- ment throughout the course of this research. I also acknowledge the administrative support of Diane B. Silva during these years. I am appreciative of my colleagues in the communication group as well as my friends in Toronto who made this period of my life most enjoyable and beneficial. The financial support of the University of Toronto and Ontario Graduate Scholarships in Science and Technology (OGSST) is also greatly appreciated. I would like to extend my appreciation to the professors from whom I learned a great deal in earlier stages of my studies in Isfahan University of Technology, in particular, Dr. H. Alavi, Dr. A. Doosthoseini, Dr. S. Sadri and Dr. V. Tahani. It is impossible to express the debt that I owe to my late parents. My father who shaped the first stages of my education and has been always a role model for me, and my mother, that if it was not because of her intense care and compassionate support, I would have never been able to come this far. I would also like to thank my siblings, Rezvan, Mehdi and Ahmad, and my in-laws Akbar Abdollahi and Shahla Dardashti who have always been a source of encouragement and drive behind my achievements. At last, my most special thanks goes to my husband, Kambiz Bayat for infinite love, support, patience and devotion, and to my little one for inspiration at the end of this journey. iii To my husband, Kambiz and In memory of my parents. iv Contents Abstract ii Acknowledgements . iii List of Tables ix List of Figures xii 1 Introduction 1 1.1 Multipath Fading Channels . 4 1.2 Space-Time Coding . 8 1.2.1 System Model . 8 1.2.2 Design Criteria . 9 1.2.3 Space-time Coding Schemes . 10 1.2.4 Space-Time Coding in a Multiuser System . 15 1.3 Precoding . 17 1.3.1 MIMO Single-user Systems . 17 1.3.2 MIMO Multiuser Systems . 20 1.4 Overview of the Thesis . 21 1.5 Notations . 24 v 2 Space-Time Multiplexing for MIMO Multiuser Downlink Channels 25 2.1 System Model . 27 2.2 Transmitted Signal Design . 29 2.2.1 Assumptions and Goals . 29 2.2.2 Spreading Matrix Design . 31 2.2.3 Constellation and Power Allocation . 35 2.3 Receiver Structures . 39 2.3.1 Joint ML Detection . 39 2.3.2 Multi-Stage Successive Interference Cancellation . 40 2.4 Comparison With Other STC-CDMA Transceivers . 42 2.5 Simulations . 43 2.6 Summary . 53 3 Precoding and Beamforming for MIMO Downlink Channels with Per- User Power Constraints 54 3.1 Problem Formulation . 57 3.1.1 Signal Model . 57 3.1.2 Precoding . 58 3.2 MMSE Beamforming/Precoding . 61 3.2.1 Precoding Matrix Design . 62 3.2.2 Optimum Receive Matrix . 64 3.2.3 Optimum Transmit Matrix . 65 3.2.4 Precoding Ordering . 67 3.3 Space-Time Spreading . 69 3.4 Simulation Results . 71 3.5 Summary . 75 vi 4 Precoding and Beamforming for MIMO Downlink Channels to Mini- mize Total Transmit Power 76 4.1 Problem Formulation . 78 4.1.1 Signal Model . 78 4.1.2 Background . 80 4.2 Joint Power Allocation and MMSE Beamforming Using Uplink/Downlink Duality . 83 4.2.1 Uplink-Downlink Duality for MIMO channels . 83 4.2.2 Proposed Algorithm . 85 4.3 Space-Time Spreading . 89 4.4 Multiple Symbol Transmission to each user . 91 4.5 Simulation Results . 92 4.6 Summary . 99 5 Precoding and Beamforming for the Down-link in a MIMO/OFDM System 100 5.1 Single User MIMO/OFDM Systems . 102 5.2 Signal Model . 103 5.2.1 Transmit Signal . 103 5.2.2 Received Signal . 106 5.3 SFS Matrix Design with no Channel Information at the Transmitter . 107 5.4 Comparison With MIMO Multi-Carrier CDMA Schemes . 111 5.5 SFS Matrix Design with Perfect Channel Knowledge at the Transmitter . 115 5.6 Simulation Results . 116 5.7 Summary . 124 vii 6 Conclusion 125 6.1 Summary of Contributions . 125 6.2 Future Work . 126 A Spreading Matrix Design Examples 129 B Proof of Uplink-Downlink Duality in MIMO Multiuser Systems 131 C The Algorithms for Multiple Symbol Transmission to each user 134 Bibliography 137 viii List of Tables 2.1 Comparison between different STC schemes for the downlink in a MIMO multiuser channel . 43 3.1 The algorithm for precoding and MMSE beamforming . 68 4.1 The precoding/beamforming algorithm for MIMO-BC channels minimiz- ing total transmit power. 88 4.2 The error rate performance of TTPC versus PUPC algorithm for t = r = 4, K = 4, SINR = 10(dB)........................... 98 4.3 The error rate performance of TTPC versus PUPC algorithm for t = r = 4, G = 4, K = 16, SINR = 10(dB)...................... 98 C.1 The precoding/beamforming for multiple symbol transmission. 135 C.2 The space-time precoding/beamforming for multiple symbol transmission. 136 ix List of Figures 1.1 Multiple Access Channel . 2 1.2 Broadcast Channel . 3 1.3 Matrix DFE . 18 2.1 Transmission system model . 28 2.2 Structure of two-stage SIC. 40 2.3 Performance of 2-D STSC for different receivers, t = r = 2, G = 2, U = 4. 44 2.4 The effect of MAI (number of users) on the achieved diversity with MMSE for t = r = 4, G =4. ............................. 45 2.5 The impact of power allocation on the performance of 2-D STSC for t = r = 2, U =8. ................................. 47 2.6 The impact of power allocation on the performance of SIC for t = r = 4, G = 4, U =16. ............................... 48 2.7 Performance of 2-D STSC in correlated fading channels for t = r = 2. 49 2.8 Performance comparison of various schemes for multiuser channel in the downlink for t = r = 2, G =2......................... 50 x 2.9 1214.5=13.613.6Performance of proposed 2D-STSC versus randomly gen- erated ST spreading codes which do not have the zero average MAI prop- erty, and Hadamard codes which give zero average MAI but do not satisfy the full-diversity criterion. 51 2.10 Performance comparison of the proposed space-time coding scheme and rotated constellation (TAST) in a single user system for t = r = 2, G = 2. 52 3.1 Block diagram of the matrix DFE. 59 3.2 Matrix form of the Tomlinson-Harashima precoder. 60 3.3 The average Pe for different number of receive antennas and t = 4;K = 2; z =2. .................................... 72 3.4 The performance of space-time spreading for different number of receive antennas, t = 4;G = 4;K = 8; z = 2: .................... 73 3.5 Average Pe compared with Pe for each individual user, t = 2; r = 2;K = 2; z =1. .................................... 74 4.1 Uplink-downlink duality – these two multi-user channels have the same achievable SINR region for a given sum power constraint. 84 4.2 Performance of the iterative linear beamforming and the proposed algo- rithm with MMSE and random initializations, for t = r = 4, K = 4, SINR = 10 dB. 93 4.3 Total transmit power versus the required SINR for different number of transmit/receive antennas for K =4....................