Adaptive Beamforming for High-Data-Rate Wireless Systems Brian Lawrence Department of Electrical & Computer Engineering McGill University Montr´eal, Canada May 2010 A thesis submitted to McGill University in partial fulfillment of the requirements for the degree of M.Eng. c 2010 Brian Lawrence ii Abstract Single-port beamforming, otherwise known as microwave or radio-frequency (RF) beam- forming, is advantageous over digital beamforming in terms of cost and power consumption, as the former only requires one downconversion receiver and analog-to-digital converter (ADC) in total, while the latter requires one downconversion receiver and ADC per an- tenna. We develop a novel, single-port beamforming algorithm based on the minimum mean-square error (MMSE) criterion. This new method is designed to minimize the num- ber of weight changes required to estimate the optimal weights, thereby making it easier to implement in practice, and more suitable for high-data-rate applications than the popular perturbation algorithms, which require their weights be continuously switched. Numerical simulations reveal that the proposed algorithm demonstrates promising performance in the presence of multiple interfering signals, and is less susceptible to performance degrada- tion than the perturbation algorithm when subjected to finite-resolution phase shifters and amplitude-control devices. iii Sommaire La formation de faisceauxa ` acc`es simple, ´egalement appel´e formation de faisceaux micro- ondes ou radiofr´equences (RF), a l’avantage sur la formation de faisceaux num´erique au niveau du coˆut et de la consommation d’´energie puisqu’elle ne requiert qu’un r´ecepteur in- fradyne et convertisseur analogique-num´erique (ADC) plutˆot qu’un par antenne. Nous d´eveloppons un nouvel algorithme de formation de faisceauxa ` acc`es simple bas´esur le crit`ere d’erreur quadratique moyenne minimale (MMSE). Cette nouvelle m´ethode est con¸cue afin de minimiser le nombre de r´eglages servant `a estimer les pond´erations opti- males. Ceci facilite la mise en œuvre pratique et rend plus convenable les applications `a haut d´ebit, l`ao`u les algorithmes de perturbation populaires n´ecessite un ajustement continu. Les simulations num´eriques r´ev`elent que l’algorithme propos´ed´emontre une per- formance prometteuse en pr´esence de multiples signaux d’interf´erences et est moins sujet que les algorithmes de perturbation aux pertes de performance caus´ees par la r´esolution finie des d´ephaseurs et contrˆoles d’amplitude. iv Acknowledgments Firstly, I would like to thank my supervisor, Professor Ioannis Psaromiligkos, for his in- valuable guidance, assistance, and encouragement. Moreover, I would also like to express my gratitude for the financial support I received from both the Natural Sciences and En- gineering Research Council of Canada, and McGill University. I am greatly indebted to my colleagues and friends, Saeed Abdallah, Fran¸cois Cˆot´e , and Mohammad Chakroun, for providing helpful advice, insight, and stimulating discussions. Moreover, I am particularly grateful to Fran¸cois Cˆot´e for translating the thesis abstract. Finally, thank you to my parents, my sister, and to all my family and friends for their unconditional moral support and encouragement. v Contents 1 Introduction 1 2 Background 3 2.1 Array Processing Fundamentals ........................ 3 2.1.1 Narrowband Beamforming ....................... 6 2.1.2 Broadband Beamforming . ....................... 11 2.2 Adaptive Beamforming Architectures . .................... 12 2.2.1 Digital Beamforming .......................... 13 2.2.2 Single-Port Beamforming ........................ 14 2.3 System Model .................................. 15 2.3.1 Eigenvalue Decomposition of R and R−1 ............... 18 2.4 Optimal Beamformers ............................. 19 2.4.1 Conventional (Delay-and-Sum) Beamformer ............. 19 2.4.2 MVDR Beamformer . ....................... 21 2.4.3 MMSE Beamformer ........................... 23 2.5 Adaptive Digital Beamforming ......................... 24 2.5.1 Sample Matrix Inversion (SMI) .................... 25 2.5.2 Least-Mean-Squares (LMS) ...................... 26 2.6 Adaptive Single-Port Beamforming ...................... 27 2.6.1 Null Steering .............................. 27 2.6.2 Aerial Beamforming .......................... 28 2.6.3 Phased-Array .............................. 28 2.6.4 Perturbation Algorithms ........................ 28 2.6.5 Proposed Single-Port Algorithm .................... 30 vi Contents 3 Adaptive Beamforming for 60-GHz Receivers 31 3.1 Design Considerations of 60-GHz Receiver . ............... 32 3.1.1 Narrowband Beamforming for 60-GHz Receivers ........... 32 3.1.2 Single-Port Architecture ........................ 33 3.1.3 Interference Mitigation . ....................... 34 3.1.4 Exploiting the High Data Rates of 60-GHz Communications .... 34 3.2 60-GHz Channel Model ............................. 35 4 Proposed Beamforming Algorithm 37 4.1 Proposed Algorithm .............................. 37 4.2 Estimation of R ................................. 38 4.2.1 Expected Value of ˜ˆr and R˜ˆ ...................... 41 4.2.2 Covariance Matrix of ˜ˆr ......................... 41 4.2.3 Hermitian Structure of R˜ˆ ....................... 44 4.3 Estimation of z ................................. 46 4.3.1 Expected Value of z˜ˆ .......................... 47 4.3.2 Covariance Matrix of z˜ˆ ......................... 48 4.4 Selection of W and W˜ ............................. 49 4.4.1 Effect of Weights on Error of ˜ˆr .................... 50 4.4.2 Effect of Weights on Error of z˜ˆ .................... 52 4.5 Computationally-Efficient Algorithm to Estimate r and z .......... 53 4.6 Estimation of wmmse .............................. 56 4.6.1 Estimation of wmmse By Means Of Diagonal Loading ........ 60 4.6.2 Estimation of wmmse Using Truncated Singular Value Decomposition (TSVD) ................................. 61 4.6.3 Estimation of wmmse Based on Dominant-Mode Rejection (DMR) . 63 4.7 Discussion of Proposed Algorithm ....................... 64 5 Numerical Simulations 67 5.1 Simulation Models . ............................. 67 5.1.1 AWGN Model .............................. 68 5.1.2 Multipath Model ............................ 69 5.1.3 MSE vs. Parameter Settings ...................... 70 5.1.4 MSE vs. Sample Size .......................... 73 Contents vii 5.1.5 Power Patterns ............................. 77 5.1.6 Effects of Phase and Amplitude Quantization ............ 77 6 Conclusions and Future Research 83 A Proof of Proposition 2 87 −1 B Weight Matrices ΨH and Ψ˜ H 93 C Details Concerning Implementation of Multipath Model 95 D Perturbation Algorithm Implementation 97 References 99 viii ix List of Figures 2.1 Antenna array receiving plane-wave front. .................. 4 2.2 Uniform linear array (ULA). .......................... 5 2.3 Narrowband beamformer. ........................... 9 2.4 Beam pattern of uniformly weighted, 10-element array. ........... 10 2.5 TDL broadband beamformer. ......................... 12 2.6 Digital beamforming architecture. ....................... 13 2.7 Single-port beamforming architecture. ................... 14 4.1 Eigenvalues of R˜ˆ calculated using (4.16) by single-port beamformer with (a) No interference; (b) One interfering signal. .................. 58 4.2 Eigenvalues of Rˆ calculated using (2.73) by digital beamformer with (a) No interference; (b) One interfering signal. .................... 59 4.3 MSE of beamformer implementing w˜ˆ mmse. .................. 59 4.4 MSE of beamformer implementing wˆ mmse. .................. 60 5.1 MSE of w˜ˆ dl as a function of υ in (a) AWGN model; (b) Multipath model. 72 5.2 MSE of w˜ˆ tsvd as a function of σ˜ˆth in (a) AWGN model; (b) Multipath model. 72 ˆ 5.3 MSE of w˜ˆ dmr as a function of λ˜th in (a) AWGN model; (b) Multipath model. 73 5.4 MSE as a function of sample size in Scenario A in (a) AWGN model; (b) Multipath model. ................................ 74 5.5 MSE as a function of sample size in Scenario B in (a) AWGN model; (b) Multipath model. ................................ 75 5.6 MSE as a function of sample size in Scenario C in (a) AWGN model; (b) Multipath model. ................................ 75 x List of Figures 5.7 MSE as a function of sample size in Scenario D in (a) AWGN model; (b) Multipath model. ................................ 76 5.8 Power patterns pertaining to Scenario A in (a) AWGN model; (b) Multipath model. ...................................... 78 5.9 Power patterns pertaining to Scenario B in (a) AWGN model; (b) Multipath model. ...................................... 78 5.10 Power patterns pertaining to Scenario C in (a) AWGN model; (b) Multipath model. ...................................... 79 5.11 Power patterns pertaining to Scenario D in (a) AWGN model; (b) Multipath model. ...................................... 79 5.12 Effects of quantization on w˜ˆ tsvd in (a) AWGN model; (b) Multipath model. 81 5.13 Effects of quantization on w˜ˆ dmr in (a) AWGN model; (b) Multipath model. 81 5.14 Effects of quantization on wpert in (a) AWGN model; (b) Multipath model. 82 5.15 Comparison of w˜ˆ tsvd, w˜ˆ dmr, and wpert when quantized to 3 bits in (a) AWGN model; (b) Multipath model. .......................... 82 C.1 Block diagram of the TDLs used to model the channel between the qth transmitter and each of the M antennas at the receiver. ........... 96 xi List of Acronyms ADC Analog-to-Digital Converter AIC Akaike Information Criterion AOA Angle-Of-Arrival AWGN Additive