Multiple Antennas in Wireless Communications: Array Signal Processing and Channel Capacity by Mahesh Godavarti A dissertation submitted in partial fulflllment of the requirements for the degree of Doctor of Philosophy (Electrical Engineering: Systems) in The University of Michigan 2001 Doctoral Committee: Professor Alfred O. Hero, III, Chair Associate Professor Kamal Sarabandi Professor Wayne E. Stark Associate Professor Kim Winick ABSTRACT Multiple Antennas in Wireless Communications: Array Signal Processing and Channel Capacity by Mahesh Godavarti Chair: Alfred O. Hero, III We investigate two aspects of multiple-antenna wireless communication systems in this thesis: 1) deployment of an adaptive beamformer array at the receiver; and 2) space-time coding for arrays at the transmitter and the receiver. In the flrst part of the thesis, we establish su–cient conditions for the convergence of a popular least mean squares (LMS) algorithm known as the sequential Partial Update LMS Algorithm for adaptive beamforming. Partial update LMS (PU-LMS) algorithms are reduced complexity versions of the full update LMS that update a subset of fllter coe–cients at each iteration. We introduce a new improved algorithm, called Stochastic PU-LMS, which selects the subsets at random at each iteration. We show that the new algorithm converges for a wider class of signals than the existing PU-LMS algorithms. The second part of this thesis deals with the multiple-input multiple-output (MIMO) Shannon capacity of multiple antenna wireless communication systems un- der the average energy constraint on the input signal. Previous work on this problem has concentrated on capacity for Rayleigh fading channels. We investigate the more general case of Rician fading. We derive capacity expressions, optimum transmit sig- nals as well as upper and lower bounds on capacity for three Rician fading models. In theflrstmodelthespecularcomponentisadynamicisotropicallydistributedrandom process. In this case, the optimum transmit signal structure is the same as that for Rayleigh fading. In the second model the specular component is a static isotropically distributed random process unknown to the transmitter, but known to the receiver. In this case the transmitter has to design the transmit signal to guarantee a cer- tain rate independent of the specular component. Here also, the optimum transmit signal structure, under the constant magnitude constraint, is the same as that for Rayleigh fading. In the third model the specular component is deterministic and known to both the transmitter and the receiver. In this case the optimum transmit signal and capacity both depend on the specular component. We show that for low signal to noise ratio (SNR) the specular component completely determines the the signal structure whereas for high SNR the specular component has no efiect. We also show that training is not efiective at low SNR and give expressions for rate-optimal allocation of training versus communication. Mahesh Godavarti 2001 c (cid:176) All Rights Reserved To my family and friends ii ACKNOWLEDGEMENTS I would like to extend my sincere thanks to my advisor Prof. Alfred O. Hero-III for letting me dictate the pace of my research, giving me freedom to a large extent on the choice of topics, his invaluable guidance and encouragement, and for giving me invaluable insight into my research. I would also like to extend my thanks to Dr. Thomas Marzetta at Bell Labs, Murray Hill, NJ for supervising my summer internship and helping me develop a signiflcant part of my thesis. Iamgratefultomycommitteemembers,ProfessorWayneStark,AssociateProfes- sor Kim Winick and Associate Professor Kamal Sarabandi for their valuable inputs. I am also thankful to them, especially Dr. Sarabandi, for being gracious enough to accommodate me and making the flnal oral defense possible on the day of my choice. I would like to thank my friends, Olgica Milenkovic, Dejan Filipovic, Tara Javidi, Victoria Yee, Riten Gupta, Robinson Piramuthu, Bing Ma, Tingfang Ji, John Choi, Ketan Patel, Sungill Kim, Selin Aviyente, Jia Li, Ali Ozgur and Rajiv Vijayakumar for making my experiences in the department pleasant; Zoya Khan and Madhumati Ramesh for being great neighbours; Sivakumar Santhanakrishnan for being an un- derstanding roommate; and Bhavani Raman and Muralikrishna Datla for making my experience in SPICMACAY rewarding. A special thanks to Navin Kashyap for being a sounding board. My sincere thanks to Department of Defense Research & Engineering (DDR&E) iii Multidisciplinary University Research Initiative (MURI) on \Low Energy Electron- ics Design for Mobile Platform" managed by the Army Research O–ce (ARO) for supporting this research through ARO grant DAAH04-96-1-0337. My thanks to the Department of Electrical Engineering as well for supporting this research through various fellowships and Assistantships. Finally, I would like to thank my parents, brother and sister who have always encouraged me in my quest for higher education and especially my wife and friend of many years Kavita Raman for encouraging me and listening to my occasional laments and for supporting my many decisions. iv TABLE OF CONTENTS DEDICATION : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : ii ACKNOWLEDGEMENTS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : iii LIST OF FIGURES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : vii LIST OF APPENDICES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : ix CHAPTER 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Partial Update LMS Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Multiple-Antenna Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Organization of the Dissertation and Signiflcant Contributions . . . . . . . . 12 2. Sequential Partial Update LMS Algorithm . . . . . . . . . . . . . . . . . . . . 16 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Algorithm Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Analysis: Stationary Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4 Analysis: Cyclo-stationary Signals . . . . . . . . . . . . . . . . . . . . . . . . 23 2.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3. Stochastic Partial Update LMS Algorithm . . . . . . . . . . . . . . . . . . . . 30 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2 Algorithm Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3 Analysis of SPU-LMS: Stationary Stochastic Signals . . . . . . . . . . . . . . 32 3.4 Analysis SPU-LMS: Deterministic Signals. . . . . . . . . . . . . . . . . . . . 35 3.5 General Analysis of SPU-LMS . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.6 Periodic and Sequential LMS Algorithms . . . . . . . . . . . . . . . . . . . . 43 3.7 Simulation of an Array Examples to Illustrate the advantage of SPU-LMS . 44 3.8 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.9 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4. Capacity: Isotropically Random Rician Fading . . . . . . . . . . . . . . . . . 53 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.3 Properties of Capacity Achieving Signals . . . . . . . . . . . . . . . . . . . . 57 4.4 Capacity Upper and Lower Bounds . . . . . . . . . . . . . . . . . . . . . . . 59 4.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 v