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随机矩阵 Random.Matrix.Methods.for.Wireless.Communications.pdf

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    Cover
    Title
    Copyright
    Dedication
    Contents
    Preface
    Acknowledgments
    Acronyms
    Notation
    1 Introduction
    1.1 Motivation
    1.2 History and book outline
    Part I Theoretical aspects
    2 Random matrices
    2.1 Small dimensional random matrices
    2.1.1 Definitions and notations
    2.1.2 Wishart matrices
    2.2 Large dimensional random matrices
    2.2.1 Why go to infinity?
    2.2.2 Limit spectral distributions
    3 The Stieltjes transform method
    3.1 Definitions and overview
    3.2 The MarĊenko–Pastur law
    3.2.1 Proof of the MarĊenko–Pastur law
    3.2.2 Truncation, centralization, and rescaling
    3.3 Stieltjes transform for advanced models
    3.4 Tonelli theorem
    3.5 Central limit theorems
    4 Free probability theory
    4.1 Introduction to free probability theory
    4.2 R- and S-transforms
    4.3 Free probability and random matrices
    4.4 Free probability for Gaussian matrices
    4.5 Free probability for Haar matrices
    5 Combinatoric approaches
    5.1 The method of moments
    5.2 Free moments and cumulants
    5.3 Generalization to more structured matrices
    5.4 Free moments in small dimensional matrices
    5.5 Rectangular free probability
    5.6 Methodology
    6 Deterministic equivalents
    6.1 Introduction to deterministic equivalents
    6.2 Techniques for deterministic equivalents
    6.2.1 Bai and Silverstein method
    6.2.2 Gaussian method
    6.2.3 Information plus noise models
    6.2.4 Models involving Haar matrices
    6.3 A central limit theorem
    7 Spectrum analysis
    7.1 Sample covariance matrix
    7.1.1 No eigenvalues outside the support
    7.1.2 Exact spectrum separation
    7.1.3 Asymptotic spectrum analysis
    7.2 Information plus noise model
    7.2.1 Exact separation
    7.2.2 Asymptotic spectrum analysis
    8 Eigen-inference
    8.1 G-estimation
    8.1.1 Girko G-estimators
    8.1.2 G-estimation of population eigenvalues and eigenvectors
    8.1.3 Central limit for G-estimators
    8.2 Moment deconvolution approach
    9 Extreme eigenvalues
    9.1 Spiked models
    9.1.1 Perturbed sample covariance matrix
    9.1.2 Perturbed random matrices with invariance properties
    9.2 Distribution of extreme eigenvalues
    9.2.1 Introduction to the method of orthogonal polynomials
    9.2.2 Limiting laws of the extreme eigenvalues
    9.3 Random matrix theory and eigenvectors
    10 Summary and partial conclusions
    Part II Applications to wireless communications
    11 Introduction to applications in telecommunications
    11.1 Historical account of major results
    11.1.1 Rate performance of multi-dimensional systems
    11.1.2 Detection and estimation in large dimensional systems
    11.1.3 Random matrices and flexible radio
    12 System performance of CDMA technologies
    12.1 Introduction
    12.2 Performance of random CDMA technologies
    12.2.1 Random CDMA in uplink frequency flat channels
    12.2.2 Random CDMA in uplink frequency selective channels
    12.2.3 Random CDMA in downlink frequency selective channels
    12.3 Performance of orthogonal CDMA technologies
    12.3.1 Orthogonal CDMA in uplink frequency flat channels
    12.3.2 Orthogonal CDMA in uplink frequency selective channels
    12.3.2.1 Matched-flter
    12.3.3 Orthogonal CDMA in downlink frequency selective channels
    12.3.3.1 Matched-flter
    12.3.3.2 MMSE decoder
    13 Performance of multiple antenna systems
    13.1 Quasi-static MIMO fading channels
    13.2 Time-varying Rayleigh channels
    13.2.1 Small dimensional analysis
    13.2.2 Large dimensional analysis
    13.2.3 Outage capacity
    13.3 Correlated frequency flat fading channels
    13.3.1 Communication in strongly correlated channels
    13.3.2 Ergodic capacity in strongly correlated channels
    13.3.3 Ergodic capacity in weakly correlated channels
    13.3.4 Capacity maximizing precoder
    13.4 Rician flat fading channels
    13.4.1 Quasi-static mutual information and ergodic capacity
    13.4.2 Capacity maximizing power allocation
    13.4.3 Outage mutual information
    13.5 Frequency selective channels
    13.5.1 Ergodic capacity
    13.5.2 Capacity maximizing power allocation
    13.6 Transceiver design
    13.6.1 Channel matrix model with i.i.d. entries
    13.6.2 Channel matrix model with generalized variance profile
    14 Rate performance in multiple access and broadcast channels
    14.1 Broadcast channels with linear precoders
    14.1.1 System model
    14.1.2 Deterministic equivalent of the SINR
    14.1.3 Optimal regularized zero-forcing precoding
    14.1.4 Zero-forcing precoding
    14.1.5 Applications
    14.2 Rate region of MIMO multiple access channels
    14.2.1 MAC rate region in quasi-static channels
    14.2.2 Ergodic MAC rate region
    14.2.3 Multi-user uplink sum rate capacity
    15 Performance of multi-cellular and relay networks
    15.1 Performance of multi-cell networks
    15.1.1 Two-cell network
    15.1.2 Wyner model
    15.2 Multi-hop communications
    15.2.1 Multi-hop model
    15.2.2 Mutual information
    15.2.3 Large dimensional analysis
    15.2.4 Optimal transmission strategy
    16 Detection
    16.1 Cognitive radios and sensor networks
    16.2 System model
    16.3 Neyman–Pearson criterion
    16.3.1 Known signal and noise variances
    16.3.1.1 Derivation of PY│Hi in the SIMO case
    16.3.1.2 Multi-source case
    16.3.2 Unknown signal and noise variances
    16.3.3 Unknown number of sources
    16.4 Alternative signal sensing approaches
    16.4.1 Condition number method
    16.4.2 Generalized likelihood ratio test
    16.4.3 Test power and error exponents
    17 Estimation
    17.1 Directions of arrival
    17.1.1 System model
    17.1.2 The MUSIC approach
    17.1.3 Large dimensional eigen-inference
    17.1.4 The correlated signal case
    17.2 Blind multi-source localization
    17.2.1 System model
    17.2.2 Small dimensional inference
    17.2.3 Conventional large dimensional approach
    17.2.4 Free deconvolution approach
    17.2.5 Analytic method
    17.2.6 Joint estimation of number of users, antennas and powers
    17.2.7 Performance analysis
    17.2.7.1 Method comparison
    17.2.7.2 Joint estimation of K, nk, Pk
    18 System modeling
    18.1 Introduction to Bayesian channel modeling
    18.2 Channel modeling under environmental uncertainty
    18.2.1 Channel energy constraints
    18.2.1.1 Average channel energy constraint
    18.2.1.2 Probabilistic average channel energy constraint
    18.2.1.3 Application to the single antenna channel
    18.2.2 Spatial correlation models
    18.2.2.1 Deterministic knowledge of the correlation matrix
    18.2.2.2 Knowledge of the existence of a correlation matrix
    18.2.2.3 Limited-rank covariance matrix
    18.2.2.4 Discussion
    19 Perspectives
    19.1 From asymptotic results to finite dimensional studies
    19.2 The replica method
    19.3 Towards time-varying random matrices
    20 Conclusion
    References
    Index
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    Random Matrix Methods for Wireless Communications results with practical applications, Blending theoretical this book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications. The Stieltjes transform method, free probabil- ity theory, combinatoric approaches, deterministic equivalents, and spectral analysis methods for statistical inference are all covered from a unique engineering perspective. Detailed mathematical derivations are presented throughout, with thorough explana- tions of the key results and all fundamental lemmas required for the readers to derive similar calculus on their own. These core theoretical concepts are then applied to a wide range of real-world problems in signal processing and wireless communications, includ- ing performance analysis of CDMA, MIMO, and multi-cell networks, as well as signal detection and estimation in cognitive radio networks. The rigorous yet intuitive style helps demonstrate to students and researchers alike how to choose the correct approach for obtaining mathematically accurate results. Romain Couillet is an Assistant Professor at the Chair on System Sciences and the Energy Challenge at Sup´elec, France. Previously he was an Algorithm Development Engineer for ST-Ericsson, and he received his PhD from Sup´elec in 2010. M ´erouane Debbah is a Professor at Sup´elec, where he holds the Alcatel-Lucent Chair on Flexible Radio. He is the recipient of several awards, including the 2007 General Symposium IEEE Globecom best paper award and the Wi-Opt 2009 best paper award.
    Random Matrix Methods for Wireless Communications Romain Couillet and M ´erouane Debbah ´Ecole Sup ´erieure d’ ´Electricit ´e, Gif sur Yvette, France
    C A M B R I D G E U N I V E R S I T Y P R E S S Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S˜ao Paulo, Delhi, Tokyo, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9781107011632 c Cambridge University Press 2011 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2011 Printed in the United Kingdom at the University Press, Cambridge A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Couillet, Romain, 1983– Random matrix methods for wireless communications / Romain Couillet, Merouane Debbah. p. cm. Includes bibliographical references and index. ISBN 978-1-107-01163-2 (hardback) 1. Wireless communication systems – Mathematics. 2. Matrix analytic methods. I. Debbah, Merouane, 1975– II. Title. TK5103.2.C68 2011 621.3840151–dc23 2011013189 ISBN 978-1-107-01163-2 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
    v To my family, – Romain Couillet To my parents, – M´erouane Debbah
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