Foundations and TrendsTM in ∩Ow Communications and Information Theory the essence of knowledge Vol1,No1(2004)1-182 C 2004 A.M.Tulino and S.Verdui Random Matrix Theory and Wireless Communications Antonia M.Tulinol,Sergio Verdu2 1 Dept.Ingegneria Elettronica e delle Telecomunicazion,i Universita degli Studi di Napoli "Federico II".Naples 80125,Italy 2 Dept.Electrical Engineering,Princeton University,Princeton,New Jersey 08544, USA Abstract Random matrix theory has found many applications in physics,statis- tics and engineering since its inception.Although early developments were motivated by practical experimental problems,random matrices are now used in fields as diverse as Riemann hypothesis,stochastic differential equations,condensed matter physics,statistical physics, chaotic systems,numerical linear algebra,neural networks,multivari- ate statistics,information theory,signal processing and small-world networks.This article provides a tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained.Furthermore,the appli- cation of random matrix theory to the fundamental limits of wireless communication channels is described in depth.Random Matrix Theory and Wireless Communications Antonia M. Tulino1, Sergio Verd´u2 Abstract Random matrix theory has found many applications in physics, statis￾tics and engineering since its inception. Although early developments were motivated by practical experimental problems, random matrices are now used in fields as diverse as Riemann hypothesis, stochastic differential equations, condensed matter physics, statistical physics, chaotic systems, numerical linear algebra, neural networks, multivari￾ate statistics, information theory, signal processing and small-world networks. This article provides a tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained. Furthermore, the appli￾cation of random matrix theory to the fundamental limits of wireless communication channels is described in depth. 1 Dept. Ingegneria Elettronica e delle Telecomunicazion, i Universita degli Studi di Napoli “Federico II”, Naples 80125, Italy 2 Dept. Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA Foundations and Trends™ in Communications and Information Theory Vol 1, No 1 (2004) 1-182 © 2004 A.M. Tulino and S. Verd´u