Parameter Estimation for Multi-Sensor Signal Processing（博士论文）

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Parameter Estimation for Multi-Sensor SignalProcessing: Reduced Rank Regression, Array Processing, and MIMO Communications


KARL WERNER

Doctoral Thesis in Signal Processing
Stockholm, Sweden, 2007


Contents vi
1 Introduction 1
1.1 The topics of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Outline and contributions . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.6 Some useful matrix results . . . . . . . . . . . . . . . . . . . . . . . . 16
1.7 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.A The tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
I Optimal utilization of signal-free samples for array processing
in unknown colored noise-fields 23
2 Introduction to DOA estimation in colored noise 25
2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2 Organization of Part I . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3 Data model and problem statement . . . . . . . . . . . . . . . . . . . 28
2.4 The maximum likelihood approach . . . . . . . . . . . . . . . . . . . 29
2.5 The Cramér-Rao lower bound . . . . . . . . . . . . . . . . . . . . . . 30
2.A Proof of Theorem 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 DOA estimation in colored noise - novel algorithms and their
performance 41
3.1 Weighted subspace fitting . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 An approximative maximum likelihood approach . . . . . . . . . . . 46
3.3 Numerical study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.A Proof of Theorem 3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.B Proof of Lemma 3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
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vii
4 Fast algorithms for uniform linear arrays 65
4.1 MODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2 C-MODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3 W-MODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.4 Complexity comparison . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.5 Implementation and numerical results . . . . . . . . . . . . . . . . . 70
5 Source detection 79
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.2 The WSF criterion function . . . . . . . . . . . . . . . . . . . . . . . 80
5.3 The AML criterion function . . . . . . . . . . . . . . . . . . . . . . . 82
5.4 Generalized likelihood ratio test . . . . . . . . . . . . . . . . . . . . . 84
5.5 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.A Proof of Lemma 5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
II Reduced rank linear regression and weighted low rank
approximations 91
6 Introduction to reduced rank linear regression 93
6.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2 Organization of Part II . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.3 Data model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7 An instrumental variable method for the reduced rank linear
regression 97
7.1 The proposed method . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.2 Estimation of the weighting matrix . . . . . . . . . . . . . . . . . . . 99
7.3 Weighted low rank approximation . . . . . . . . . . . . . . . . . . . 100
7.4 Detecting the rank of the regression . . . . . . . . . . . . . . . . . . 104
7.5 The proposed algorithm step-by-step . . . . . . . . . . . . . . . . . . 106
7.A Useful gradients and Hessians . . . . . . . . . . . . . . . . . . . . . . 109
8 Performance of the proposed algorithm 113
8.1 Asymptotical covariance of the estimate . . . . . . . . . . . . . . . . 113
8.2 The Cramér-Rao lower bound . . . . . . . . . . . . . . . . . . . . . . 115
8.3 Relation to previous methods . . . . . . . . . . . . . . . . . . . . . . 119
8.4 Numerical study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
8.A Equivalence of the proposed estimator to maximum likelihood . . . . 128
III Estimation of covariance matrices with Kronecker product
structure 131
9 Introduction to Kronecker product structured covariance matrices 133
viii CONTENTS
9.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
9.2 Organization of Part III . . . . . . . . . . . . . . . . . . . . . . . . . 135
9.3 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
10 Estimation based on exact channel knowledge 139
10.1 Maximum likelihood estimation . . . . . . . . . . . . . . . . . . . . . 139
10.2 The Cramér-Rao lower bound . . . . . . . . . . . . . . . . . . . . . . 142
10.3 A non-iterative flipflop approach . . . . . . . . . . . . . . . . . . . . 144
10.4 A covariance matching approach . . . . . . . . . . . . . . . . . . . . 145
10.5 Asymptotic performance of the covariance matching estimator . . . . 148
10.6 Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
10.7 Numerical study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
10.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
10.A Proof of Theorem 10.2 . . . . . . . . . . . . . . . . . . . . . . . . . . 160
10.B Proof of Theorem 10.3 . . . . . . . . . . . . . . . . . . . . . . . . . . 163
11 Estimation based on pilots 165
11.1 Data model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
11.2 Heuristic approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
11.3 The Cramér-Rao lower bound . . . . . . . . . . . . . . . . . . . . . . 167
11.4 A covariance matching approach . . . . . . . . . . . . . . . . . . . . 168
11.5 Weighted low rank approximation . . . . . . . . . . . . . . . . . . . 171
11.6 Performance of the covariance matching approach . . . . . . . . . . . 172
11.7 An alternative approach . . . . . . . . . . . . . . . . . . . . . . . . . 174
11.8 Practical considerations . . . . . . . . . . . . . . . . . . . . . . . . . 176
11.9 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
11.10Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
11.11Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
11.A Proof of Theorem 11.1 . . . . . . . . . . . . . . . . . . . . . . . . . . 187
11.B Proof of Lemma 11.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Bibliography

randomheart

收下了，不知道是哪年的啊？