随机矩阵理论在无线通信中的应用详解

随机矩阵

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xiv Preface

the theory has been shown to be an eﬃcient tool to predict the behavior of

wireless systems with only few meaningful parameters. Random matrix theory

is also increasingly making its way into the statistical signal processing ﬁeld

with the generalization of detection and inference methods, e.g. array processing,

hypothesis tests, parameter estimation, etc., to the multi-variate case. This comes

as a small revolution in modern signal processing as legacy estimators, such as the

MUSIC method, become increasingly obsolete and unadapted to large sensing

arrays with few observations.

The authors are conﬁdent and have no doubt on the usefulness of the tool for

the engineering community in the upcoming years, especially as networks become

denser. They also think that random matrix theory should become sooner or later

a major tool for electrical engineers, taught at the graduate level in universities.

Indeed, engineering education programs of the twentieth century were mostly

focused on the Fourier transform theory due to the omnipresence of frequency

spectrum. The twenty-ﬁrst century engineers know by now that space is the next

frontier due to the omnipresence of spatial spectrum modes, which refocuses the

programs towards a Stieltjes transform theory.

We sincerely hope that this book will inspire students, teachers, and engineers,

and answer their present and future problems.

Romain Couillet and M´erouane Debbah

Acknowledgments

This book is the fruit of many years of the authors’ involvement in the ﬁeld

of random matrix theory for wireless communications. This topic, which has

gained increasing interest in the last decade, was brought to light in the

telecommunication community in particular through the work of Stephen Hanly,

Ralf M¨uller, Shlomo Shamai, Emre Telatar, David Tse, Antonia Tulino, and

Sergio Verd´u, among others. It then rapidly grew into a joint research framework

gathering both telecommunication engineers and mathematicians, among which

Zhidong Bai, Vyacheslav L. Girko, Leonid Pastur, and Jack W. Silverstein.

The authors are especially indebted to Prof. Silverstein for the agreeable

time spent discussing random matrix matters. Prof. Silverstein has a very

insightful approach to random matrices, which it was a delight to share with

him. The general point of view taken in this book is mostly inﬂuenced by Prof.

Silverstein’s methodology. The authors are also grateful to the many colleagues

working in this ﬁeld whose knowledge and wisdom about applied random matrix

theory contributed signiﬁcantly to its current popularity and elegance. This book

gathers many of their results and intends above all to deliver to the readers this

simpliﬁed approach to applied random matrix theory. The colleagues involved in

long and exciting discussions as well as collaborative works are Florent Benaych-

Georges, Pascal Bianchi, Laura Cottatellucci, Maxime Guillaud, Walid Hachem,

Philippe Loubaton, Myl`ene Ma¨ıda, Xavier Mestre, Aris Moustakas, Ralf M¨uller,

Jamal Najim, and Øyvind Ryan.

Regarding the book manuscript itself, the authors would also like to sincerely

thank the anonymous reviewers for their wise comments which contributed to

improve substantially the overall quality of the ﬁnal book and more importantly

the few people who dedicated a long time to thoroughly review the successive

drafts and who often came up with inspiring remarks. Among the latter are

David Gregoratti, Jakob Hoydis, Xavier Mestre, and Sebastian Wagner.

The success of this book relies in a large part on these people.

Romain Couillet and M´erouane Debbah

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随机矩阵理论在无线通信中的应用详解

Random Matrix Theory and Wireless Communications.pdf

经典随机矩阵理论入门书：Random Matrices (Mehta,

Random Matrix Methods for Wireless Communications

random matrix theory and wireless communications pdf

random matirx methods for wireless communication

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j1 = random.uniform(360, -360)

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X(n,:)=1+rand(size(xo)).*(u-1)

利用Random类产生5个20-30之间的随机整数

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