Random Matrix Methods for Wireless Communications -Cambridge University Press

【实例简介】
这是一本论述在随机矩阵在无线通信中使用的专业书籍，可以帮助相关的研究人员深入理解如何借助随机矩阵方法研究大数据技术在无线通信中的作用。
Random matrix methods for wireless communications Blending theoretical results with practical applications, 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 Supelec, France. Previously he was an Algorithm Development Engineer for ST-Ericsson, and he received his PhD from Supelec in 2010 Merouane Debbah is a Professor at Supelec, 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 merouane debbah Ecole Superieure d Electricite, Gif sur Yvette, France CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo, Delhi, Tokyo, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 &RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Informationonthistitlewww.cambridge.org/9781107011632 C Cambridge University Press 2011 This publication is in copyright. Subject to statutory exception 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 llet ro Random matrix methods for wireless communications/ Romain Couillet Merouane debbah p. cm. Includes bibliographical references and index ISBN978-1-107-01163-2( hardback 1. Wireless communication systems- Mathematics. 2. Matrix analytic methods I. Debbah Merouane 1975-I. Title TK5103.2C682011 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. To my family, Romain Couillet To my parents, merouane debbah Contents P reface page xll Acknowledgments cRonyn XVI Notation Introduction 1.1 Motivation 1.2 History and book outline 116 Part I Theoretical aspects 2 Random matrices 17 2.1 Small dimensional random matrices 17 2.1.1 Definitions and notations 17 2.1.2 Wishart matrices 19 2.2 Large dimensional random matrices 29 2.2.1 Why go to infinity? 29 2.2.2 Limit spectral distributions 30 The Stieltjes transform method 35 3.1 Definitions and overview 35 3.2 The marcenko-Pastur law 42 3.2.1 Proof of the marcenko- Pastur law 44 3.2.2 Truncation, centralization, and rescaling 54 3.3 Stieltjes transform for advanced models 57 3.4 Tonelli theorem 61 3.5 Central limit theorems 63 Free probability theory 4.1 Introduction to free probability theory 72 4.2 R- and s-transforms 75 4.3 Free probability and random matrices 77 4.4 Free probability for Gaussian matrices 84 Contents 4.5 Free probability for Haar matrices Combinatoric approaches 95 5.1 The method of moments 5.2 Free moments and cumulants 5.3 Generalization to more structured matrices 105 5.4 Free moments in small dimensional matrices 5.5 Rectangular free probability 10 5.6 Methodology 111 Deterministic equivalents 113 6.1 Introduction to deterministic equivalents 113 6.2 Techniques for deterministic equivalents 115 6.2.1 Bai and silverstein method 115 6.2.2 Gaussian method 139 6.2.3 Information plus noise models 145 6.2.4 Models involving Haar matrices 153 6.3 a central limit the 175 Spectrum analysis 7. 1 Sample covariance matrix 180 7. 1.1 No eigenvalues outside the support 180 7.1.2 Exact spectrum separation 183 7. 1.3 Asymptotic spectrum analysis 186 7.2 Information plus noise model 192 7.2.1 Exact separation 192 7.2.2 Asymptotic spectrum analysis 195 Eigen-inference 8. 1 G-estimation 8.1.1 Girko G-estimators 199 8.1.2 G-estimation of population eigenvalues and eigenvectors 201 8.1.3 Central limit for G-estimators 213 8.2 Moment deconvolution approach 218 Extreme eigenvalues 223 9.1 Spiked models 223 9.1.1 Perturbed sample covariance matrix 224 9.1.2 Perturbed random matrices with invariance properties 228 9.2 Distribution of extreme eigenvalues 230 9.2.1 Introduction to the method of orthogonal polynomials 230 9.2.2 Limiting laws of the extreme eigenvalues 233 9.3 Random matrix theory and eigenvectors 237 【实例截图】
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