Multiple Antennas in Wireless Communications: Array Signal

197 Pages·2002·0.92 MB·English

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)
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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.
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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
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