Linear Estimation and Detection in Krylov Subspaces (eBook)

Preface 7
Contents 9
List of Algorithms 12
List of Figures 13
List of Tables 16
1 Introduction 17
1.1 Overview and Contributions 20
1.2 Notation 23
Theory: Linear Estimation in Krylov Subspaces 27
2 Efficient Matrix Wiener Filter Implementations 28
2.1 Matrix Wiener Filter 29
2.2 Reduced-Complexity Matrix Wiener Filters 32
2.3 Reduced-Rank Matrix Wiener Filters 41
3 Block Krylov Methods 47
3.1 Principles and Application Areas 49
3.2 Block Arnoldi Algorithm 52
3.3 Block Lanczos Algorithm 55
3.4 Block Conjugate Gradient Algorithm 60
4 Reduced-Rank Matrix Wiener Filters in Krylov Subspaces 84
4.1 Multistage Matrix Wiener Filter 86
4.2 Relationship Between Multistage Matrix Wiener Filter and Krylov Subspace Methods 104
4.3 Krylov Subspace Based Multistage Matrix Wiener Filter Implementations 111
4.4 Computational Complexity Considerations 116
Application: Iterative Multiuser Detection 123
5 System Model for Iterative Multiuser Detection 124
5.1 Transmitter Structure 126
5.2 Channel Model 135
5.3 Iterative Receiver Structure 137
6 System Performance 151
6.1 Extrinsic Information Transfer Charts 152
6.2 Analysis Based on Extrinsic Information Transfer Charts 162
6.3 Bit Error Rate Performance Analysis 175
7 Conclusions 184
A Mathematical Basics 186
A.1 Inverses of Structured Matrices 186
A.2 Matrix Norms 187
A.3 Chebyshev Polynomials 188
A.4 Regularization 189
A.5 Vector Valued Function of a Matrix and Kronecker Product 192
A.6 Square Root Matrices 193
A.7 Binary Galois Field 194
B Derivations and Proofs 195
B.1 Inversion of Hermitian and Positive Definite Matrices 195
B.2 Real-Valued Coefficients of Krylov Subspace Polynomials 198
B.3 QR Factorization 199
B.4 Proof of Proposition 3.3 200
B.5 Correlated Subspace 203
C Abbreviations and Acronyms 208
References 211
Index 229