Table of Contents Section 1 Introduction 5 1.1 Wireless Channels 6 1.2 The Role of the Singular Values 6 1.3 Random Matrices:A Brief Historical Account 1 Section 2 Random Matrix Theory 21 2.1 Types of Matrices and Non-Asymptotic Results 21 2.2 Transforms 38 2.3 Asymptotic Spectrum Theorems 52 2.4 Free Probability 4 2.5 Convergence Rates and Asymptotic Normality 91 Section 3 Applications to Wireless Communications 96 3.1 Direct-Sequence CDMA 96 3.2 Multi-Carrier CDMA 117 3.3 Single-User Multi-Antenna Channels 129 3.4 Other Applications 152 Section 4 Appendices 153 4.1 Proof of Theorem 2.39 153 4.2 Proof of Theorem 2.42 154 4.3 Proof of Theorem 2.44 156 4.4 Proof of Theorem 2.49 158 4.5 Proof of Theorem 2.53 159 References 163 2Table of Contents Section 1 Introduction 3 1.1 Wireless Channels 5 1.2 The Role of the Singular Values 6 1.3 Random Matrices: A Brief Historical Account 13 Section 2 Random Matrix Theory 21 2.1 Types of Matrices and Non-Asymptotic Results 21 2.2 Transforms 38 2.3 Asymptotic Spectrum Theorems 52 2.4 Free Probability 74 2.5 Convergence Rates and Asymptotic Normality 91 Section 3 Applications to Wireless Communications 96 3.1 Direct-Sequence CDMA 96 3.2 Multi-Carrier CDMA 117 3.3 Single-User Multi-Antenna Channels 129 3.4 Other Applications 152 Section 4 Appendices 153 4.1 Proof of Theorem 2.39 153 4.2 Proof of Theorem 2.42 154 4.3 Proof of Theorem 2.44 156 4.4 Proof of Theorem 2.49 158 4.5 Proof of Theorem 2.53 159 References 163 2