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A problem-solving approach to statistical signal processing for practicing engineers, technicians, and graduate students
This book takes a pragmatic approach in solving a set of common problems engineers and technicians encounter when processing signals. In writing it, the author drew on his vast theoretical and practical experience in the field to provide a quick-solution manual for technicians and engineers, offering field-tested solutions to most problems engineers can encounter. At the same time, the book delineates the basic concepts and applied mathematics underlying each solution so that readers can go deeper into the theory to gain a better idea of the solution's limitations and potential pitfalls, and thus tailor the best solution for the specific engineering application.
Uniquely, Statistical Signal Processing in Engineering can also function as a textbook for engineering graduates and post-graduates. Dr. Spagnolini, who has had a quarter of a century of experience teaching graduate-level courses in digital and statistical signal processing methods, provides a detailed axiomatic presentation of the conceptual and mathematical foundations of statistical signal processing that will challenge students' analytical skills and motivate them to develop new applications on their own, or better understand the motivation underlining the existing solutions.
Throughout the book, some real-world examples demonstrate how powerful a tool statistical signal processing is in practice across a wide range of applications.
* Takes an interdisciplinary approach, integrating basic concepts and tools for statistical signal processing
* Informed by its author's vast experience as both a practitioner and teacher
* Offers a hands-on approach to solving problems in statistical signal processing
* Covers a broad range of applications, including communication systems, machine learning, wavefield and array processing, remote sensing, image filtering and distributed computations
* Features numerous real-world examples from a wide range of applications showing the mathematical concepts involved in practice
* Includes MATLAB code of many of the experiments in the book
Statistical Signal Processing in Engineering is an indispensable working resource for electrical engineers, especially those working in the information and communication technology (ICT) industry. It is also an ideal text for engineering students at large, applied mathematics post-graduates and advanced undergraduates in electrical engineering, applied statistics, and pure mathematics, studying statistical signal processing.
This book takes a pragmatic approach in solving a set of common problems engineers and technicians encounter when processing signals. In writing it, the author drew on his vast theoretical and practical experience in the field to provide a quick-solution manual for technicians and engineers, offering field-tested solutions to most problems engineers can encounter. At the same time, the book delineates the basic concepts and applied mathematics underlying each solution so that readers can go deeper into the theory to gain a better idea of the solution's limitations and potential pitfalls, and thus tailor the best solution for the specific engineering application.
Uniquely, Statistical Signal Processing in Engineering can also function as a textbook for engineering graduates and post-graduates. Dr. Spagnolini, who has had a quarter of a century of experience teaching graduate-level courses in digital and statistical signal processing methods, provides a detailed axiomatic presentation of the conceptual and mathematical foundations of statistical signal processing that will challenge students' analytical skills and motivate them to develop new applications on their own, or better understand the motivation underlining the existing solutions.
Throughout the book, some real-world examples demonstrate how powerful a tool statistical signal processing is in practice across a wide range of applications.
* Takes an interdisciplinary approach, integrating basic concepts and tools for statistical signal processing
* Informed by its author's vast experience as both a practitioner and teacher
* Offers a hands-on approach to solving problems in statistical signal processing
* Covers a broad range of applications, including communication systems, machine learning, wavefield and array processing, remote sensing, image filtering and distributed computations
* Features numerous real-world examples from a wide range of applications showing the mathematical concepts involved in practice
* Includes MATLAB code of many of the experiments in the book
Statistical Signal Processing in Engineering is an indispensable working resource for electrical engineers, especially those working in the information and communication technology (ICT) industry. It is also an ideal text for engineering students at large, applied mathematics post-graduates and advanced undergraduates in electrical engineering, applied statistics, and pure mathematics, studying statistical signal processing.
A problem-solving approach to statistical signal processing for practicing engineers, technicians, and graduate students
This book takes a pragmatic approach in solving a set of common problems engineers and technicians encounter when processing signals. In writing it, the author drew on his vast theoretical and practical experience in the field to provide a quick-solution manual for technicians and engineers, offering field-tested solutions to most problems engineers can encounter. At the same time, the book delineates the basic concepts and applied mathematics underlying each solution so that readers can go deeper into the theory to gain a better idea of the solution's limitations and potential pitfalls, and thus tailor the best solution for the specific engineering application.
Uniquely, Statistical Signal Processing in Engineering can also function as a textbook for engineering graduates and post-graduates. Dr. Spagnolini, who has had a quarter of a century of experience teaching graduate-level courses in digital and statistical signal processing methods, provides a detailed axiomatic presentation of the conceptual and mathematical foundations of statistical signal processing that will challenge students' analytical skills and motivate them to develop new applications on their own, or better understand the motivation underlining the existing solutions.
Throughout the book, some real-world examples demonstrate how powerful a tool statistical signal processing is in practice across a wide range of applications.
* Takes an interdisciplinary approach, integrating basic concepts and tools for statistical signal processing
* Informed by its author's vast experience as both a practitioner and teacher
* Offers a hands-on approach to solving problems in statistical signal processing
* Covers a broad range of applications, including communication systems, machine learning, wavefield and array processing, remote sensing, image filtering and distributed computations
* Features numerous real-world examples from a wide range of applications showing the mathematical concepts involved in practice
* Includes MATLAB code of many of the experiments in the book
Statistical Signal Processing in Engineering is an indispensable working resource for electrical engineers, especially those working in the information and communication technology (ICT) industry. It is also an ideal text for engineering students at large, applied mathematics post-graduates and advanced undergraduates in electrical engineering, applied statistics, and pure mathematics, studying statistical signal processing.
This book takes a pragmatic approach in solving a set of common problems engineers and technicians encounter when processing signals. In writing it, the author drew on his vast theoretical and practical experience in the field to provide a quick-solution manual for technicians and engineers, offering field-tested solutions to most problems engineers can encounter. At the same time, the book delineates the basic concepts and applied mathematics underlying each solution so that readers can go deeper into the theory to gain a better idea of the solution's limitations and potential pitfalls, and thus tailor the best solution for the specific engineering application.
Uniquely, Statistical Signal Processing in Engineering can also function as a textbook for engineering graduates and post-graduates. Dr. Spagnolini, who has had a quarter of a century of experience teaching graduate-level courses in digital and statistical signal processing methods, provides a detailed axiomatic presentation of the conceptual and mathematical foundations of statistical signal processing that will challenge students' analytical skills and motivate them to develop new applications on their own, or better understand the motivation underlining the existing solutions.
Throughout the book, some real-world examples demonstrate how powerful a tool statistical signal processing is in practice across a wide range of applications.
* Takes an interdisciplinary approach, integrating basic concepts and tools for statistical signal processing
* Informed by its author's vast experience as both a practitioner and teacher
* Offers a hands-on approach to solving problems in statistical signal processing
* Covers a broad range of applications, including communication systems, machine learning, wavefield and array processing, remote sensing, image filtering and distributed computations
* Features numerous real-world examples from a wide range of applications showing the mathematical concepts involved in practice
* Includes MATLAB code of many of the experiments in the book
Statistical Signal Processing in Engineering is an indispensable working resource for electrical engineers, especially those working in the information and communication technology (ICT) industry. It is also an ideal text for engineering students at large, applied mathematics post-graduates and advanced undergraduates in electrical engineering, applied statistics, and pure mathematics, studying statistical signal processing.
Über den Autor
UMBERTO SPAGNOLINI is Professor in Signal Processing and Telecommunications at Politecnico di Milano, Italy. Prof. Spagnolini's research focuses on statistical signal processing, communication systems, and advanced topics in signal processing for remote sensing and wireless communication systems. He is a Senior Member of the IEEE, engages in editorial activity for IEEE journals and conferences, and has authored 300 patents and papers in peer reviewed journals and conferences.
Inhaltsverzeichnis
List of Figures xvii
List of Tables xxiii
Preface xxv
List of Abbreviations xxix
How to Use the Book xxxi
About the Companion Website xxxiii
Prerequisites xxxv
Why are there so many matrixes in this book? xxxvii
1 Manipulations on Matrixes 1
1.1 Matrix Properties 1
1.1.1 Elementary Operations 2
1.2 Eigen-Decomposition 6
1.3 Eigenvectors in Everyday Life 9
1.3.1 Conversations in a Noisy Restaurant 9
1.3.2 Power Control in a Cellular System 12
1.3.3 Price Equilibrium in the Economy 14
1.4 Derivative Rules 15
1.4.1 Derivative with respect to x 16
1.4.2 Derivative with respect to x 17
1.4.3 Derivative with respect to the Matrix X 18
1.5 Quadratic Forms 19
1.6 Diagonalization of a Quadratic Form 20
1.7 Rayleigh Quotient 21
1.8 Basics of Optimization 22
1.8.1 Quadratic Function with Simple Linear Constraint (M=1) 23
1.8.2 Quadratic Function with Multiple Linear Constraints 23
Appendix A: Arithmetic vs. Geometric Mean 24
2 Linear Algebraic Systems 27
2.1 Problem Definition and Vector Spaces 27
2.1.1 Vector Spaces in Tomographic Radiometric Inversion 29
2.2 Rotations 31
2.3 Projection Matrixes and Data-Filtering 33
2.3.1 Projections and Commercial FM Radio 34
2.4 Singular Value Decomposition (SVD) and Subspaces 34
2.4.1 How to Choose the Rank of Afor Gaussian Model? 35
2.5 QR and Cholesky Factorization 36
2.6 Power Method for Leading Eigenvectors 38
2.7 Least Squares Solution of Overdetermined Linear Equations 39
2.8 Efficient Implementation of the LS Solution 41
2.9 Iterative Methods 42
3 Random Variables in Brief 45
3.1 Probability Density Function (pdf), Moments, and Other Useful Properties 45
3.2 Convexity and Jensen Inequality 49
3.3 Uncorrelatedness and Statistical Independence 49
3.4 Real-Valued Gaussian Random Variables 51
3.5 Conditional pdf for Real-Valued Gaussian Random Variables 54
3.6 Conditional pdf in Additive Noise Model 56
3.7 Complex Gaussian Random Variables 56
3.7.1 Single Complex Gaussian Random Variable 56
3.7.2 Circular Complex Gaussian Random Variable 57
3.7.3 Multivariate Complex Gaussian Random Variables 58
3.8 Sum of Square of Gaussians: Chi-Square 59
3.9 Order Statistics for N rvs 60
4 Random Processes and Linear Systems 63
4.1 Moment Characterizations and Stationarity 64
4.2 Random Processes and Linear Systems 66
4.3 Complex-Valued Random Processes 68
4.4 Pole-Zero and Rational Spectra (Discrete-Time) 69
4.4.1 Stability of LTI Systems 70
4.4.2 Rational PSD 71
4.4.3 Paley-Wiener Theorem 72
4.5 Gaussian Random Process (Discrete-Time) 73
4.6 Measuring Moments in Stochastic Processes 75
Appendix A: Transforms for Continuous-Time Signals 76
Appendix B: Transforms for Discrete-Time Signals 79
5 Models and Applications 83
5.1 Linear Regression Model 84
5.2 Linear Filtering Model 86
5.2.1 Block-Wise Circular Convolution 88
5.2.2 Discrete Fourier Transform and Circular Convolution Matrixes 89
5.2.3 Identification and Deconvolution 90
5.3 MIMO systems and Interference Models 91
5.3.1 DSL System 92
5.3.2 MIMO in Wireless Communication 92
5.4 Sinusoidal Signal 97
5.5 Irregular Sampling and Interpolation 97
5.5.1 Sampling With Jitter 100
5.6 Wavefield Sensing System 101
6 Estimation Theory 105
6.1 Historical Notes 105
6.2 Non-Bayesian vs. Bayesian 106
6.3 Performance Metrics and Bounds 107
6.3.1 Bias 107
6.3.2 Mean Square Error (MSE) 108
6.3.3 Performance Bounds 109
6.4 Statistics and Sufficient Statistics 110
6.5 MVU and BLU Estimators 111
6.6 BLUE for Linear Models 112
6.7 Example: BLUE of the Mean Value of Gaussian rvs 114
7 Parameter Estimation 117
7.1 Maximum Likelihood Estimation (MLE) 117
7.2 MLE for Gaussian Model 119
7.2.1 Additive Noise Model with 119
7.2.2 Additive Noise Model with 120
7.2.3 Additive Noise Model with Multiple Observations with Known 121
7.2.3.1 Linear Model 121
7.2.3.2 Model 122
7.2.3.3 Model 123
7.2.4 Model 123
7.2.5 Additive Noise Model with Multiple Observations with Unknown 124
7.3 Other Noise Models 125
7.4 MLE and Nuisance Parameters 126
7.5 MLE for Continuous-Time Signals 128
7.5.1 Example: Amplitude Estimation 129
7.5.2 MLE for Correlated Noise 130
7.6 MLE for Circular Complex Gaussian 131
7.7 Estimation in Phase/Frequency Modulations 131
7.7.1 MLE Phase Estimation 132
7.7.2 Phase Locked Loops 133
7.8 Least Square (LS) Estimation 135
7.8.1 Weighted LS with 136
7.8.2 LS Estimation and Linear Models 137
7.8.3 Under or Over-Parameterizing? 138
7.8.4 Constrained LS Estimation 139
7.9 Robust Estimation 140
8 Cramér-Rao Bound 143
8.1 Cramér-Rao Bound and Fisher Information Matrix 143
8.1.1 CRB for Scalar Problem (P=1) 143
8.1.2 CRB and Local Curvature of Log-Likelihood 144
8.1.3 CRB for Multiple Parameters (p 1) 144
8.2 Interpretation of CRB and Remarks 146
8.2.1 Variance of Each Parameter 146
8.2.2 Compactness of the Estimates 146
8.2.3 FIM for Known Parameters 147
8.2.4 Approximation of the Inverse of FIM 148
8.2.5 Estimation Decoupled From FIM 148
8.2.6 CRB and Nuisance Parameters 149
8.2.7 CRB for Non-Gaussian rv and Gaussian Bound 149
8.3 CRB and Variable Transformations 150
8.4 FIM for Gaussian Parametric Model 151
8.4.1 FIM for with 151
8.4.2 FIM for Continuous-Time Signals in Additive White Gaussian Noise 152
8.4.3 FIM for Circular Complex Model 152
Appendix A: Proof of CRB 154
Appendix B: FIM for Gaussian Model 156
Appendix C: Some Derivatives for MLE and CRB Computations 157
9 MLE and CRB for Some Selected Cases 159
9.1 Linear Regressions 159
9.2 Frequency Estimation 162
9.3 Estimation of Complex Sinusoid 164
9.3.1 Proper, Improper, and Non-Circular Signals 165
9.4 Time of Delay Estimation 166
9.5 Estimation of Max for Uniform pdf 170
9.6 Estimation of Occurrence Probability for Binary pdf 172
9.7 How to Optimize Histograms? 173
9.8 Logistic Regression 176
10 Numerical Analysis and Montecarlo Simulations 179
10.1 System Identification and Channel Estimation 181
10.1.1 Matlab Code and Results 184
10.2 Frequency Estimation 184
10.2.1 Variable (Coarse/Fine) Sampling 187
10.2.2 Local Parabolic Regression 189
10.2.3 Matlab Code and Results 190
10.3 Time of Delay Estimation 192
10.3.1 Granularity of Sampling in ToD Estimation 193
10.3.2 Matlab Code and Results 194
10.4 Doppler-Radar System by Frequency Estimation 196
10.4.1 EM Method 197
10.4.2 Matlab Code and Results 199
11 Bayesian Estimation 201
11.1 Additive Linear Model with Gaussian Noise 203
11.1.1 Gaussian A-priori: 204
11.1.2 Non-Gaussian A-Priori 206
11.1.3 Binary Signals: MMSE vs. MAP Estimators 207
11.1.4 Example: Impulse Noise Mitigation 210
11.2 Bayesian Estimation in Gaussian Settings 212
11.2.1 MMSE Estimator 213
11.2.2 MMSE Estimator for Linear Models 213
11.3 LMMSE Estimation and Orthogonality 215
11.4 Bayesian CRB 218
11.5 Mixing Bayesian and Non-Bayesian 220
11.5.1 Linear Model with Mixed Random/Deterministic Parameters 220
11.5.2 Hybrid CRB 222
11.6 Expectation-Maximization (EM) 223
11.6.1 EM of the Sum of Signals in Gaussian Noise 224
11.6.2 EM Method for the Time of Delay Estimation of Multiple Waveforms 227
11.6.3 Remarks 228
Appendix A: Gaussian Mixture pdf 229
12 Optimal Filtering 231
12.1 Wiener Filter 231
12.2 MMSE Deconvolution (or Equalization) 233
12.3 Linear Prediction 234
12.3.1 Yule-Walker Equations 235
12.4 LS Linear Prediction 237
12.5 Linear Prediction and AR Processes 239
12.6 Levinson Recursion and Lattice Predictors 241
13 Bayesian Tracking and Kalman Filter 245
13.1 Bayesian Tracking of State in Dynamic Systems 246
13.1.1 Evolution of the A-posteriori pdf 247
13.2 Kalman Filter (KF) 249
13.2.1 KF Equations 251
13.2.2 Remarks 253
13.3 Identification of Time-Varying Filters in Wireless Communication 255
13.4 Extended Kalman Filter (EKF) for Non-Linear Dynamic Systems 257
13.5 Position Tracking by Multi-Lateration 258
13.5.1 Positioning and Noise 260
13.5.2 Example of Position Tracking 263
13.6 Non-Gaussian Pdf and Particle Filters264
14 Spectral Analysis 267
14.1 Periodogram 268
14.1.1 Bias of the Periodogram 268
14.1.2 Variance of the Periodogram 271
14.1.3 Filterbank Interpretation 273
14.1.4 Pdf of the Periodogram (White Gaussian Process) 274
14.1.5 Bias and Resolution 275
14.1.6 Variance Reduction and WOSA 278
14.1.7 Numerical Example: Bandlimited Process and (Small) Sinusoid 280
14.2 Parametric Spectral Analysis 282
14.2.1 MLE and CRB 284
14.2.2 General Model for AR, MA, ARMA Spectral Analysis 285
14.3 AR Spectral Analysis 286
14.3.1 MLE and CRB 286
14.3.2 A Good Reason to Avoid Over-Parametrization in AR 289
14.3.3 Cramér-Rao Bound of Poles in AR Spectral Analysis 291
14.3.4 Example: Frequency Estimation by AR Spectral Analysis 293
14.4 MA Spectral Analysis 296
14.5 ARMA Spectral Analysis 298
14.5.1 Cramér-Rao Bound for ARMA Spectral Analysis 300
Appendix A: Which Sample Estimate of the Autocorrelation to Use? 302
Appendix B: Eigenvectors and Eigenvalues of Correlation Matrix 303
Appendix C: Property of Monic Polynomial 306
Appendix D: Variance of Pole in AR(1) 307
15 Adaptive Filtering 309
15.1 Adaptive Interference Cancellation 311
15.2 Adaptive Equalization in Communication Systems 313
15.2.1 Wireless Communication Systems in Brief 313
15.2.2 Adaptive Equalization 315
15.3 Steepest Descent MSE Minimization 317
15.3.1 Convergence Analysis and Step-Size 318
15.3.2 An Intuitive View of Convergence Conditions 320
15.4 From Iterative to Adaptive Filters 323
15.5 LMS Algorithm and Stochastic Gradient 324
15.6 Convergence Analysis of LMS Algorithm 325
15.6.1 Convergence in the Mean 326
15.6.2 Convergence in the Mean Square 326
15.6.3 Excess MSE 329
15.7 Learning Curve of LMS 331
15.7.1 Optimization of the Step-Size 332
15.8 NLMS Updating and Non-Stationarity 333
15.9 Numerical Example: Adaptive Identification 334
15.10 RLS Algorithm 338
15.10.1 Convergence Analysis 339
15.10.2 Learning Curve of RLS 341
15.11 Exponentially-Weighted RLS...
List of Tables xxiii
Preface xxv
List of Abbreviations xxix
How to Use the Book xxxi
About the Companion Website xxxiii
Prerequisites xxxv
Why are there so many matrixes in this book? xxxvii
1 Manipulations on Matrixes 1
1.1 Matrix Properties 1
1.1.1 Elementary Operations 2
1.2 Eigen-Decomposition 6
1.3 Eigenvectors in Everyday Life 9
1.3.1 Conversations in a Noisy Restaurant 9
1.3.2 Power Control in a Cellular System 12
1.3.3 Price Equilibrium in the Economy 14
1.4 Derivative Rules 15
1.4.1 Derivative with respect to x 16
1.4.2 Derivative with respect to x 17
1.4.3 Derivative with respect to the Matrix X 18
1.5 Quadratic Forms 19
1.6 Diagonalization of a Quadratic Form 20
1.7 Rayleigh Quotient 21
1.8 Basics of Optimization 22
1.8.1 Quadratic Function with Simple Linear Constraint (M=1) 23
1.8.2 Quadratic Function with Multiple Linear Constraints 23
Appendix A: Arithmetic vs. Geometric Mean 24
2 Linear Algebraic Systems 27
2.1 Problem Definition and Vector Spaces 27
2.1.1 Vector Spaces in Tomographic Radiometric Inversion 29
2.2 Rotations 31
2.3 Projection Matrixes and Data-Filtering 33
2.3.1 Projections and Commercial FM Radio 34
2.4 Singular Value Decomposition (SVD) and Subspaces 34
2.4.1 How to Choose the Rank of Afor Gaussian Model? 35
2.5 QR and Cholesky Factorization 36
2.6 Power Method for Leading Eigenvectors 38
2.7 Least Squares Solution of Overdetermined Linear Equations 39
2.8 Efficient Implementation of the LS Solution 41
2.9 Iterative Methods 42
3 Random Variables in Brief 45
3.1 Probability Density Function (pdf), Moments, and Other Useful Properties 45
3.2 Convexity and Jensen Inequality 49
3.3 Uncorrelatedness and Statistical Independence 49
3.4 Real-Valued Gaussian Random Variables 51
3.5 Conditional pdf for Real-Valued Gaussian Random Variables 54
3.6 Conditional pdf in Additive Noise Model 56
3.7 Complex Gaussian Random Variables 56
3.7.1 Single Complex Gaussian Random Variable 56
3.7.2 Circular Complex Gaussian Random Variable 57
3.7.3 Multivariate Complex Gaussian Random Variables 58
3.8 Sum of Square of Gaussians: Chi-Square 59
3.9 Order Statistics for N rvs 60
4 Random Processes and Linear Systems 63
4.1 Moment Characterizations and Stationarity 64
4.2 Random Processes and Linear Systems 66
4.3 Complex-Valued Random Processes 68
4.4 Pole-Zero and Rational Spectra (Discrete-Time) 69
4.4.1 Stability of LTI Systems 70
4.4.2 Rational PSD 71
4.4.3 Paley-Wiener Theorem 72
4.5 Gaussian Random Process (Discrete-Time) 73
4.6 Measuring Moments in Stochastic Processes 75
Appendix A: Transforms for Continuous-Time Signals 76
Appendix B: Transforms for Discrete-Time Signals 79
5 Models and Applications 83
5.1 Linear Regression Model 84
5.2 Linear Filtering Model 86
5.2.1 Block-Wise Circular Convolution 88
5.2.2 Discrete Fourier Transform and Circular Convolution Matrixes 89
5.2.3 Identification and Deconvolution 90
5.3 MIMO systems and Interference Models 91
5.3.1 DSL System 92
5.3.2 MIMO in Wireless Communication 92
5.4 Sinusoidal Signal 97
5.5 Irregular Sampling and Interpolation 97
5.5.1 Sampling With Jitter 100
5.6 Wavefield Sensing System 101
6 Estimation Theory 105
6.1 Historical Notes 105
6.2 Non-Bayesian vs. Bayesian 106
6.3 Performance Metrics and Bounds 107
6.3.1 Bias 107
6.3.2 Mean Square Error (MSE) 108
6.3.3 Performance Bounds 109
6.4 Statistics and Sufficient Statistics 110
6.5 MVU and BLU Estimators 111
6.6 BLUE for Linear Models 112
6.7 Example: BLUE of the Mean Value of Gaussian rvs 114
7 Parameter Estimation 117
7.1 Maximum Likelihood Estimation (MLE) 117
7.2 MLE for Gaussian Model 119
7.2.1 Additive Noise Model with 119
7.2.2 Additive Noise Model with 120
7.2.3 Additive Noise Model with Multiple Observations with Known 121
7.2.3.1 Linear Model 121
7.2.3.2 Model 122
7.2.3.3 Model 123
7.2.4 Model 123
7.2.5 Additive Noise Model with Multiple Observations with Unknown 124
7.3 Other Noise Models 125
7.4 MLE and Nuisance Parameters 126
7.5 MLE for Continuous-Time Signals 128
7.5.1 Example: Amplitude Estimation 129
7.5.2 MLE for Correlated Noise 130
7.6 MLE for Circular Complex Gaussian 131
7.7 Estimation in Phase/Frequency Modulations 131
7.7.1 MLE Phase Estimation 132
7.7.2 Phase Locked Loops 133
7.8 Least Square (LS) Estimation 135
7.8.1 Weighted LS with 136
7.8.2 LS Estimation and Linear Models 137
7.8.3 Under or Over-Parameterizing? 138
7.8.4 Constrained LS Estimation 139
7.9 Robust Estimation 140
8 Cramér-Rao Bound 143
8.1 Cramér-Rao Bound and Fisher Information Matrix 143
8.1.1 CRB for Scalar Problem (P=1) 143
8.1.2 CRB and Local Curvature of Log-Likelihood 144
8.1.3 CRB for Multiple Parameters (p 1) 144
8.2 Interpretation of CRB and Remarks 146
8.2.1 Variance of Each Parameter 146
8.2.2 Compactness of the Estimates 146
8.2.3 FIM for Known Parameters 147
8.2.4 Approximation of the Inverse of FIM 148
8.2.5 Estimation Decoupled From FIM 148
8.2.6 CRB and Nuisance Parameters 149
8.2.7 CRB for Non-Gaussian rv and Gaussian Bound 149
8.3 CRB and Variable Transformations 150
8.4 FIM for Gaussian Parametric Model 151
8.4.1 FIM for with 151
8.4.2 FIM for Continuous-Time Signals in Additive White Gaussian Noise 152
8.4.3 FIM for Circular Complex Model 152
Appendix A: Proof of CRB 154
Appendix B: FIM for Gaussian Model 156
Appendix C: Some Derivatives for MLE and CRB Computations 157
9 MLE and CRB for Some Selected Cases 159
9.1 Linear Regressions 159
9.2 Frequency Estimation 162
9.3 Estimation of Complex Sinusoid 164
9.3.1 Proper, Improper, and Non-Circular Signals 165
9.4 Time of Delay Estimation 166
9.5 Estimation of Max for Uniform pdf 170
9.6 Estimation of Occurrence Probability for Binary pdf 172
9.7 How to Optimize Histograms? 173
9.8 Logistic Regression 176
10 Numerical Analysis and Montecarlo Simulations 179
10.1 System Identification and Channel Estimation 181
10.1.1 Matlab Code and Results 184
10.2 Frequency Estimation 184
10.2.1 Variable (Coarse/Fine) Sampling 187
10.2.2 Local Parabolic Regression 189
10.2.3 Matlab Code and Results 190
10.3 Time of Delay Estimation 192
10.3.1 Granularity of Sampling in ToD Estimation 193
10.3.2 Matlab Code and Results 194
10.4 Doppler-Radar System by Frequency Estimation 196
10.4.1 EM Method 197
10.4.2 Matlab Code and Results 199
11 Bayesian Estimation 201
11.1 Additive Linear Model with Gaussian Noise 203
11.1.1 Gaussian A-priori: 204
11.1.2 Non-Gaussian A-Priori 206
11.1.3 Binary Signals: MMSE vs. MAP Estimators 207
11.1.4 Example: Impulse Noise Mitigation 210
11.2 Bayesian Estimation in Gaussian Settings 212
11.2.1 MMSE Estimator 213
11.2.2 MMSE Estimator for Linear Models 213
11.3 LMMSE Estimation and Orthogonality 215
11.4 Bayesian CRB 218
11.5 Mixing Bayesian and Non-Bayesian 220
11.5.1 Linear Model with Mixed Random/Deterministic Parameters 220
11.5.2 Hybrid CRB 222
11.6 Expectation-Maximization (EM) 223
11.6.1 EM of the Sum of Signals in Gaussian Noise 224
11.6.2 EM Method for the Time of Delay Estimation of Multiple Waveforms 227
11.6.3 Remarks 228
Appendix A: Gaussian Mixture pdf 229
12 Optimal Filtering 231
12.1 Wiener Filter 231
12.2 MMSE Deconvolution (or Equalization) 233
12.3 Linear Prediction 234
12.3.1 Yule-Walker Equations 235
12.4 LS Linear Prediction 237
12.5 Linear Prediction and AR Processes 239
12.6 Levinson Recursion and Lattice Predictors 241
13 Bayesian Tracking and Kalman Filter 245
13.1 Bayesian Tracking of State in Dynamic Systems 246
13.1.1 Evolution of the A-posteriori pdf 247
13.2 Kalman Filter (KF) 249
13.2.1 KF Equations 251
13.2.2 Remarks 253
13.3 Identification of Time-Varying Filters in Wireless Communication 255
13.4 Extended Kalman Filter (EKF) for Non-Linear Dynamic Systems 257
13.5 Position Tracking by Multi-Lateration 258
13.5.1 Positioning and Noise 260
13.5.2 Example of Position Tracking 263
13.6 Non-Gaussian Pdf and Particle Filters264
14 Spectral Analysis 267
14.1 Periodogram 268
14.1.1 Bias of the Periodogram 268
14.1.2 Variance of the Periodogram 271
14.1.3 Filterbank Interpretation 273
14.1.4 Pdf of the Periodogram (White Gaussian Process) 274
14.1.5 Bias and Resolution 275
14.1.6 Variance Reduction and WOSA 278
14.1.7 Numerical Example: Bandlimited Process and (Small) Sinusoid 280
14.2 Parametric Spectral Analysis 282
14.2.1 MLE and CRB 284
14.2.2 General Model for AR, MA, ARMA Spectral Analysis 285
14.3 AR Spectral Analysis 286
14.3.1 MLE and CRB 286
14.3.2 A Good Reason to Avoid Over-Parametrization in AR 289
14.3.3 Cramér-Rao Bound of Poles in AR Spectral Analysis 291
14.3.4 Example: Frequency Estimation by AR Spectral Analysis 293
14.4 MA Spectral Analysis 296
14.5 ARMA Spectral Analysis 298
14.5.1 Cramér-Rao Bound for ARMA Spectral Analysis 300
Appendix A: Which Sample Estimate of the Autocorrelation to Use? 302
Appendix B: Eigenvectors and Eigenvalues of Correlation Matrix 303
Appendix C: Property of Monic Polynomial 306
Appendix D: Variance of Pole in AR(1) 307
15 Adaptive Filtering 309
15.1 Adaptive Interference Cancellation 311
15.2 Adaptive Equalization in Communication Systems 313
15.2.1 Wireless Communication Systems in Brief 313
15.2.2 Adaptive Equalization 315
15.3 Steepest Descent MSE Minimization 317
15.3.1 Convergence Analysis and Step-Size 318
15.3.2 An Intuitive View of Convergence Conditions 320
15.4 From Iterative to Adaptive Filters 323
15.5 LMS Algorithm and Stochastic Gradient 324
15.6 Convergence Analysis of LMS Algorithm 325
15.6.1 Convergence in the Mean 326
15.6.2 Convergence in the Mean Square 326
15.6.3 Excess MSE 329
15.7 Learning Curve of LMS 331
15.7.1 Optimization of the Step-Size 332
15.8 NLMS Updating and Non-Stationarity 333
15.9 Numerical Example: Adaptive Identification 334
15.10 RLS Algorithm 338
15.10.1 Convergence Analysis 339
15.10.2 Learning Curve of RLS 341
15.11 Exponentially-Weighted RLS...
Details
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Nachrichtentechnik |
| Genre: | Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 608 |
| Inhalt: | 608 S. |
| ISBN-13: | 9781119293972 |
| ISBN-10: | 1119293979 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Spagnolini, Umberto |
| Hersteller: |
Wiley
John Wiley & Sons |
| Maße: | 250 x 175 x 37 mm |
| Von/Mit: | Umberto Spagnolini |
| Erscheinungsdatum: | 05.02.2018 |
| Gewicht: | 1,209 kg |
Über den Autor
UMBERTO SPAGNOLINI is Professor in Signal Processing and Telecommunications at Politecnico di Milano, Italy. Prof. Spagnolini's research focuses on statistical signal processing, communication systems, and advanced topics in signal processing for remote sensing and wireless communication systems. He is a Senior Member of the IEEE, engages in editorial activity for IEEE journals and conferences, and has authored 300 patents and papers in peer reviewed journals and conferences.
Inhaltsverzeichnis
List of Figures xvii
List of Tables xxiii
Preface xxv
List of Abbreviations xxix
How to Use the Book xxxi
About the Companion Website xxxiii
Prerequisites xxxv
Why are there so many matrixes in this book? xxxvii
1 Manipulations on Matrixes 1
1.1 Matrix Properties 1
1.1.1 Elementary Operations 2
1.2 Eigen-Decomposition 6
1.3 Eigenvectors in Everyday Life 9
1.3.1 Conversations in a Noisy Restaurant 9
1.3.2 Power Control in a Cellular System 12
1.3.3 Price Equilibrium in the Economy 14
1.4 Derivative Rules 15
1.4.1 Derivative with respect to x 16
1.4.2 Derivative with respect to x 17
1.4.3 Derivative with respect to the Matrix X 18
1.5 Quadratic Forms 19
1.6 Diagonalization of a Quadratic Form 20
1.7 Rayleigh Quotient 21
1.8 Basics of Optimization 22
1.8.1 Quadratic Function with Simple Linear Constraint (M=1) 23
1.8.2 Quadratic Function with Multiple Linear Constraints 23
Appendix A: Arithmetic vs. Geometric Mean 24
2 Linear Algebraic Systems 27
2.1 Problem Definition and Vector Spaces 27
2.1.1 Vector Spaces in Tomographic Radiometric Inversion 29
2.2 Rotations 31
2.3 Projection Matrixes and Data-Filtering 33
2.3.1 Projections and Commercial FM Radio 34
2.4 Singular Value Decomposition (SVD) and Subspaces 34
2.4.1 How to Choose the Rank of Afor Gaussian Model? 35
2.5 QR and Cholesky Factorization 36
2.6 Power Method for Leading Eigenvectors 38
2.7 Least Squares Solution of Overdetermined Linear Equations 39
2.8 Efficient Implementation of the LS Solution 41
2.9 Iterative Methods 42
3 Random Variables in Brief 45
3.1 Probability Density Function (pdf), Moments, and Other Useful Properties 45
3.2 Convexity and Jensen Inequality 49
3.3 Uncorrelatedness and Statistical Independence 49
3.4 Real-Valued Gaussian Random Variables 51
3.5 Conditional pdf for Real-Valued Gaussian Random Variables 54
3.6 Conditional pdf in Additive Noise Model 56
3.7 Complex Gaussian Random Variables 56
3.7.1 Single Complex Gaussian Random Variable 56
3.7.2 Circular Complex Gaussian Random Variable 57
3.7.3 Multivariate Complex Gaussian Random Variables 58
3.8 Sum of Square of Gaussians: Chi-Square 59
3.9 Order Statistics for N rvs 60
4 Random Processes and Linear Systems 63
4.1 Moment Characterizations and Stationarity 64
4.2 Random Processes and Linear Systems 66
4.3 Complex-Valued Random Processes 68
4.4 Pole-Zero and Rational Spectra (Discrete-Time) 69
4.4.1 Stability of LTI Systems 70
4.4.2 Rational PSD 71
4.4.3 Paley-Wiener Theorem 72
4.5 Gaussian Random Process (Discrete-Time) 73
4.6 Measuring Moments in Stochastic Processes 75
Appendix A: Transforms for Continuous-Time Signals 76
Appendix B: Transforms for Discrete-Time Signals 79
5 Models and Applications 83
5.1 Linear Regression Model 84
5.2 Linear Filtering Model 86
5.2.1 Block-Wise Circular Convolution 88
5.2.2 Discrete Fourier Transform and Circular Convolution Matrixes 89
5.2.3 Identification and Deconvolution 90
5.3 MIMO systems and Interference Models 91
5.3.1 DSL System 92
5.3.2 MIMO in Wireless Communication 92
5.4 Sinusoidal Signal 97
5.5 Irregular Sampling and Interpolation 97
5.5.1 Sampling With Jitter 100
5.6 Wavefield Sensing System 101
6 Estimation Theory 105
6.1 Historical Notes 105
6.2 Non-Bayesian vs. Bayesian 106
6.3 Performance Metrics and Bounds 107
6.3.1 Bias 107
6.3.2 Mean Square Error (MSE) 108
6.3.3 Performance Bounds 109
6.4 Statistics and Sufficient Statistics 110
6.5 MVU and BLU Estimators 111
6.6 BLUE for Linear Models 112
6.7 Example: BLUE of the Mean Value of Gaussian rvs 114
7 Parameter Estimation 117
7.1 Maximum Likelihood Estimation (MLE) 117
7.2 MLE for Gaussian Model 119
7.2.1 Additive Noise Model with 119
7.2.2 Additive Noise Model with 120
7.2.3 Additive Noise Model with Multiple Observations with Known 121
7.2.3.1 Linear Model 121
7.2.3.2 Model 122
7.2.3.3 Model 123
7.2.4 Model 123
7.2.5 Additive Noise Model with Multiple Observations with Unknown 124
7.3 Other Noise Models 125
7.4 MLE and Nuisance Parameters 126
7.5 MLE for Continuous-Time Signals 128
7.5.1 Example: Amplitude Estimation 129
7.5.2 MLE for Correlated Noise 130
7.6 MLE for Circular Complex Gaussian 131
7.7 Estimation in Phase/Frequency Modulations 131
7.7.1 MLE Phase Estimation 132
7.7.2 Phase Locked Loops 133
7.8 Least Square (LS) Estimation 135
7.8.1 Weighted LS with 136
7.8.2 LS Estimation and Linear Models 137
7.8.3 Under or Over-Parameterizing? 138
7.8.4 Constrained LS Estimation 139
7.9 Robust Estimation 140
8 Cramér-Rao Bound 143
8.1 Cramér-Rao Bound and Fisher Information Matrix 143
8.1.1 CRB for Scalar Problem (P=1) 143
8.1.2 CRB and Local Curvature of Log-Likelihood 144
8.1.3 CRB for Multiple Parameters (p 1) 144
8.2 Interpretation of CRB and Remarks 146
8.2.1 Variance of Each Parameter 146
8.2.2 Compactness of the Estimates 146
8.2.3 FIM for Known Parameters 147
8.2.4 Approximation of the Inverse of FIM 148
8.2.5 Estimation Decoupled From FIM 148
8.2.6 CRB and Nuisance Parameters 149
8.2.7 CRB for Non-Gaussian rv and Gaussian Bound 149
8.3 CRB and Variable Transformations 150
8.4 FIM for Gaussian Parametric Model 151
8.4.1 FIM for with 151
8.4.2 FIM for Continuous-Time Signals in Additive White Gaussian Noise 152
8.4.3 FIM for Circular Complex Model 152
Appendix A: Proof of CRB 154
Appendix B: FIM for Gaussian Model 156
Appendix C: Some Derivatives for MLE and CRB Computations 157
9 MLE and CRB for Some Selected Cases 159
9.1 Linear Regressions 159
9.2 Frequency Estimation 162
9.3 Estimation of Complex Sinusoid 164
9.3.1 Proper, Improper, and Non-Circular Signals 165
9.4 Time of Delay Estimation 166
9.5 Estimation of Max for Uniform pdf 170
9.6 Estimation of Occurrence Probability for Binary pdf 172
9.7 How to Optimize Histograms? 173
9.8 Logistic Regression 176
10 Numerical Analysis and Montecarlo Simulations 179
10.1 System Identification and Channel Estimation 181
10.1.1 Matlab Code and Results 184
10.2 Frequency Estimation 184
10.2.1 Variable (Coarse/Fine) Sampling 187
10.2.2 Local Parabolic Regression 189
10.2.3 Matlab Code and Results 190
10.3 Time of Delay Estimation 192
10.3.1 Granularity of Sampling in ToD Estimation 193
10.3.2 Matlab Code and Results 194
10.4 Doppler-Radar System by Frequency Estimation 196
10.4.1 EM Method 197
10.4.2 Matlab Code and Results 199
11 Bayesian Estimation 201
11.1 Additive Linear Model with Gaussian Noise 203
11.1.1 Gaussian A-priori: 204
11.1.2 Non-Gaussian A-Priori 206
11.1.3 Binary Signals: MMSE vs. MAP Estimators 207
11.1.4 Example: Impulse Noise Mitigation 210
11.2 Bayesian Estimation in Gaussian Settings 212
11.2.1 MMSE Estimator 213
11.2.2 MMSE Estimator for Linear Models 213
11.3 LMMSE Estimation and Orthogonality 215
11.4 Bayesian CRB 218
11.5 Mixing Bayesian and Non-Bayesian 220
11.5.1 Linear Model with Mixed Random/Deterministic Parameters 220
11.5.2 Hybrid CRB 222
11.6 Expectation-Maximization (EM) 223
11.6.1 EM of the Sum of Signals in Gaussian Noise 224
11.6.2 EM Method for the Time of Delay Estimation of Multiple Waveforms 227
11.6.3 Remarks 228
Appendix A: Gaussian Mixture pdf 229
12 Optimal Filtering 231
12.1 Wiener Filter 231
12.2 MMSE Deconvolution (or Equalization) 233
12.3 Linear Prediction 234
12.3.1 Yule-Walker Equations 235
12.4 LS Linear Prediction 237
12.5 Linear Prediction and AR Processes 239
12.6 Levinson Recursion and Lattice Predictors 241
13 Bayesian Tracking and Kalman Filter 245
13.1 Bayesian Tracking of State in Dynamic Systems 246
13.1.1 Evolution of the A-posteriori pdf 247
13.2 Kalman Filter (KF) 249
13.2.1 KF Equations 251
13.2.2 Remarks 253
13.3 Identification of Time-Varying Filters in Wireless Communication 255
13.4 Extended Kalman Filter (EKF) for Non-Linear Dynamic Systems 257
13.5 Position Tracking by Multi-Lateration 258
13.5.1 Positioning and Noise 260
13.5.2 Example of Position Tracking 263
13.6 Non-Gaussian Pdf and Particle Filters264
14 Spectral Analysis 267
14.1 Periodogram 268
14.1.1 Bias of the Periodogram 268
14.1.2 Variance of the Periodogram 271
14.1.3 Filterbank Interpretation 273
14.1.4 Pdf of the Periodogram (White Gaussian Process) 274
14.1.5 Bias and Resolution 275
14.1.6 Variance Reduction and WOSA 278
14.1.7 Numerical Example: Bandlimited Process and (Small) Sinusoid 280
14.2 Parametric Spectral Analysis 282
14.2.1 MLE and CRB 284
14.2.2 General Model for AR, MA, ARMA Spectral Analysis 285
14.3 AR Spectral Analysis 286
14.3.1 MLE and CRB 286
14.3.2 A Good Reason to Avoid Over-Parametrization in AR 289
14.3.3 Cramér-Rao Bound of Poles in AR Spectral Analysis 291
14.3.4 Example: Frequency Estimation by AR Spectral Analysis 293
14.4 MA Spectral Analysis 296
14.5 ARMA Spectral Analysis 298
14.5.1 Cramér-Rao Bound for ARMA Spectral Analysis 300
Appendix A: Which Sample Estimate of the Autocorrelation to Use? 302
Appendix B: Eigenvectors and Eigenvalues of Correlation Matrix 303
Appendix C: Property of Monic Polynomial 306
Appendix D: Variance of Pole in AR(1) 307
15 Adaptive Filtering 309
15.1 Adaptive Interference Cancellation 311
15.2 Adaptive Equalization in Communication Systems 313
15.2.1 Wireless Communication Systems in Brief 313
15.2.2 Adaptive Equalization 315
15.3 Steepest Descent MSE Minimization 317
15.3.1 Convergence Analysis and Step-Size 318
15.3.2 An Intuitive View of Convergence Conditions 320
15.4 From Iterative to Adaptive Filters 323
15.5 LMS Algorithm and Stochastic Gradient 324
15.6 Convergence Analysis of LMS Algorithm 325
15.6.1 Convergence in the Mean 326
15.6.2 Convergence in the Mean Square 326
15.6.3 Excess MSE 329
15.7 Learning Curve of LMS 331
15.7.1 Optimization of the Step-Size 332
15.8 NLMS Updating and Non-Stationarity 333
15.9 Numerical Example: Adaptive Identification 334
15.10 RLS Algorithm 338
15.10.1 Convergence Analysis 339
15.10.2 Learning Curve of RLS 341
15.11 Exponentially-Weighted RLS...
List of Tables xxiii
Preface xxv
List of Abbreviations xxix
How to Use the Book xxxi
About the Companion Website xxxiii
Prerequisites xxxv
Why are there so many matrixes in this book? xxxvii
1 Manipulations on Matrixes 1
1.1 Matrix Properties 1
1.1.1 Elementary Operations 2
1.2 Eigen-Decomposition 6
1.3 Eigenvectors in Everyday Life 9
1.3.1 Conversations in a Noisy Restaurant 9
1.3.2 Power Control in a Cellular System 12
1.3.3 Price Equilibrium in the Economy 14
1.4 Derivative Rules 15
1.4.1 Derivative with respect to x 16
1.4.2 Derivative with respect to x 17
1.4.3 Derivative with respect to the Matrix X 18
1.5 Quadratic Forms 19
1.6 Diagonalization of a Quadratic Form 20
1.7 Rayleigh Quotient 21
1.8 Basics of Optimization 22
1.8.1 Quadratic Function with Simple Linear Constraint (M=1) 23
1.8.2 Quadratic Function with Multiple Linear Constraints 23
Appendix A: Arithmetic vs. Geometric Mean 24
2 Linear Algebraic Systems 27
2.1 Problem Definition and Vector Spaces 27
2.1.1 Vector Spaces in Tomographic Radiometric Inversion 29
2.2 Rotations 31
2.3 Projection Matrixes and Data-Filtering 33
2.3.1 Projections and Commercial FM Radio 34
2.4 Singular Value Decomposition (SVD) and Subspaces 34
2.4.1 How to Choose the Rank of Afor Gaussian Model? 35
2.5 QR and Cholesky Factorization 36
2.6 Power Method for Leading Eigenvectors 38
2.7 Least Squares Solution of Overdetermined Linear Equations 39
2.8 Efficient Implementation of the LS Solution 41
2.9 Iterative Methods 42
3 Random Variables in Brief 45
3.1 Probability Density Function (pdf), Moments, and Other Useful Properties 45
3.2 Convexity and Jensen Inequality 49
3.3 Uncorrelatedness and Statistical Independence 49
3.4 Real-Valued Gaussian Random Variables 51
3.5 Conditional pdf for Real-Valued Gaussian Random Variables 54
3.6 Conditional pdf in Additive Noise Model 56
3.7 Complex Gaussian Random Variables 56
3.7.1 Single Complex Gaussian Random Variable 56
3.7.2 Circular Complex Gaussian Random Variable 57
3.7.3 Multivariate Complex Gaussian Random Variables 58
3.8 Sum of Square of Gaussians: Chi-Square 59
3.9 Order Statistics for N rvs 60
4 Random Processes and Linear Systems 63
4.1 Moment Characterizations and Stationarity 64
4.2 Random Processes and Linear Systems 66
4.3 Complex-Valued Random Processes 68
4.4 Pole-Zero and Rational Spectra (Discrete-Time) 69
4.4.1 Stability of LTI Systems 70
4.4.2 Rational PSD 71
4.4.3 Paley-Wiener Theorem 72
4.5 Gaussian Random Process (Discrete-Time) 73
4.6 Measuring Moments in Stochastic Processes 75
Appendix A: Transforms for Continuous-Time Signals 76
Appendix B: Transforms for Discrete-Time Signals 79
5 Models and Applications 83
5.1 Linear Regression Model 84
5.2 Linear Filtering Model 86
5.2.1 Block-Wise Circular Convolution 88
5.2.2 Discrete Fourier Transform and Circular Convolution Matrixes 89
5.2.3 Identification and Deconvolution 90
5.3 MIMO systems and Interference Models 91
5.3.1 DSL System 92
5.3.2 MIMO in Wireless Communication 92
5.4 Sinusoidal Signal 97
5.5 Irregular Sampling and Interpolation 97
5.5.1 Sampling With Jitter 100
5.6 Wavefield Sensing System 101
6 Estimation Theory 105
6.1 Historical Notes 105
6.2 Non-Bayesian vs. Bayesian 106
6.3 Performance Metrics and Bounds 107
6.3.1 Bias 107
6.3.2 Mean Square Error (MSE) 108
6.3.3 Performance Bounds 109
6.4 Statistics and Sufficient Statistics 110
6.5 MVU and BLU Estimators 111
6.6 BLUE for Linear Models 112
6.7 Example: BLUE of the Mean Value of Gaussian rvs 114
7 Parameter Estimation 117
7.1 Maximum Likelihood Estimation (MLE) 117
7.2 MLE for Gaussian Model 119
7.2.1 Additive Noise Model with 119
7.2.2 Additive Noise Model with 120
7.2.3 Additive Noise Model with Multiple Observations with Known 121
7.2.3.1 Linear Model 121
7.2.3.2 Model 122
7.2.3.3 Model 123
7.2.4 Model 123
7.2.5 Additive Noise Model with Multiple Observations with Unknown 124
7.3 Other Noise Models 125
7.4 MLE and Nuisance Parameters 126
7.5 MLE for Continuous-Time Signals 128
7.5.1 Example: Amplitude Estimation 129
7.5.2 MLE for Correlated Noise 130
7.6 MLE for Circular Complex Gaussian 131
7.7 Estimation in Phase/Frequency Modulations 131
7.7.1 MLE Phase Estimation 132
7.7.2 Phase Locked Loops 133
7.8 Least Square (LS) Estimation 135
7.8.1 Weighted LS with 136
7.8.2 LS Estimation and Linear Models 137
7.8.3 Under or Over-Parameterizing? 138
7.8.4 Constrained LS Estimation 139
7.9 Robust Estimation 140
8 Cramér-Rao Bound 143
8.1 Cramér-Rao Bound and Fisher Information Matrix 143
8.1.1 CRB for Scalar Problem (P=1) 143
8.1.2 CRB and Local Curvature of Log-Likelihood 144
8.1.3 CRB for Multiple Parameters (p 1) 144
8.2 Interpretation of CRB and Remarks 146
8.2.1 Variance of Each Parameter 146
8.2.2 Compactness of the Estimates 146
8.2.3 FIM for Known Parameters 147
8.2.4 Approximation of the Inverse of FIM 148
8.2.5 Estimation Decoupled From FIM 148
8.2.6 CRB and Nuisance Parameters 149
8.2.7 CRB for Non-Gaussian rv and Gaussian Bound 149
8.3 CRB and Variable Transformations 150
8.4 FIM for Gaussian Parametric Model 151
8.4.1 FIM for with 151
8.4.2 FIM for Continuous-Time Signals in Additive White Gaussian Noise 152
8.4.3 FIM for Circular Complex Model 152
Appendix A: Proof of CRB 154
Appendix B: FIM for Gaussian Model 156
Appendix C: Some Derivatives for MLE and CRB Computations 157
9 MLE and CRB for Some Selected Cases 159
9.1 Linear Regressions 159
9.2 Frequency Estimation 162
9.3 Estimation of Complex Sinusoid 164
9.3.1 Proper, Improper, and Non-Circular Signals 165
9.4 Time of Delay Estimation 166
9.5 Estimation of Max for Uniform pdf 170
9.6 Estimation of Occurrence Probability for Binary pdf 172
9.7 How to Optimize Histograms? 173
9.8 Logistic Regression 176
10 Numerical Analysis and Montecarlo Simulations 179
10.1 System Identification and Channel Estimation 181
10.1.1 Matlab Code and Results 184
10.2 Frequency Estimation 184
10.2.1 Variable (Coarse/Fine) Sampling 187
10.2.2 Local Parabolic Regression 189
10.2.3 Matlab Code and Results 190
10.3 Time of Delay Estimation 192
10.3.1 Granularity of Sampling in ToD Estimation 193
10.3.2 Matlab Code and Results 194
10.4 Doppler-Radar System by Frequency Estimation 196
10.4.1 EM Method 197
10.4.2 Matlab Code and Results 199
11 Bayesian Estimation 201
11.1 Additive Linear Model with Gaussian Noise 203
11.1.1 Gaussian A-priori: 204
11.1.2 Non-Gaussian A-Priori 206
11.1.3 Binary Signals: MMSE vs. MAP Estimators 207
11.1.4 Example: Impulse Noise Mitigation 210
11.2 Bayesian Estimation in Gaussian Settings 212
11.2.1 MMSE Estimator 213
11.2.2 MMSE Estimator for Linear Models 213
11.3 LMMSE Estimation and Orthogonality 215
11.4 Bayesian CRB 218
11.5 Mixing Bayesian and Non-Bayesian 220
11.5.1 Linear Model with Mixed Random/Deterministic Parameters 220
11.5.2 Hybrid CRB 222
11.6 Expectation-Maximization (EM) 223
11.6.1 EM of the Sum of Signals in Gaussian Noise 224
11.6.2 EM Method for the Time of Delay Estimation of Multiple Waveforms 227
11.6.3 Remarks 228
Appendix A: Gaussian Mixture pdf 229
12 Optimal Filtering 231
12.1 Wiener Filter 231
12.2 MMSE Deconvolution (or Equalization) 233
12.3 Linear Prediction 234
12.3.1 Yule-Walker Equations 235
12.4 LS Linear Prediction 237
12.5 Linear Prediction and AR Processes 239
12.6 Levinson Recursion and Lattice Predictors 241
13 Bayesian Tracking and Kalman Filter 245
13.1 Bayesian Tracking of State in Dynamic Systems 246
13.1.1 Evolution of the A-posteriori pdf 247
13.2 Kalman Filter (KF) 249
13.2.1 KF Equations 251
13.2.2 Remarks 253
13.3 Identification of Time-Varying Filters in Wireless Communication 255
13.4 Extended Kalman Filter (EKF) for Non-Linear Dynamic Systems 257
13.5 Position Tracking by Multi-Lateration 258
13.5.1 Positioning and Noise 260
13.5.2 Example of Position Tracking 263
13.6 Non-Gaussian Pdf and Particle Filters264
14 Spectral Analysis 267
14.1 Periodogram 268
14.1.1 Bias of the Periodogram 268
14.1.2 Variance of the Periodogram 271
14.1.3 Filterbank Interpretation 273
14.1.4 Pdf of the Periodogram (White Gaussian Process) 274
14.1.5 Bias and Resolution 275
14.1.6 Variance Reduction and WOSA 278
14.1.7 Numerical Example: Bandlimited Process and (Small) Sinusoid 280
14.2 Parametric Spectral Analysis 282
14.2.1 MLE and CRB 284
14.2.2 General Model for AR, MA, ARMA Spectral Analysis 285
14.3 AR Spectral Analysis 286
14.3.1 MLE and CRB 286
14.3.2 A Good Reason to Avoid Over-Parametrization in AR 289
14.3.3 Cramér-Rao Bound of Poles in AR Spectral Analysis 291
14.3.4 Example: Frequency Estimation by AR Spectral Analysis 293
14.4 MA Spectral Analysis 296
14.5 ARMA Spectral Analysis 298
14.5.1 Cramér-Rao Bound for ARMA Spectral Analysis 300
Appendix A: Which Sample Estimate of the Autocorrelation to Use? 302
Appendix B: Eigenvectors and Eigenvalues of Correlation Matrix 303
Appendix C: Property of Monic Polynomial 306
Appendix D: Variance of Pole in AR(1) 307
15 Adaptive Filtering 309
15.1 Adaptive Interference Cancellation 311
15.2 Adaptive Equalization in Communication Systems 313
15.2.1 Wireless Communication Systems in Brief 313
15.2.2 Adaptive Equalization 315
15.3 Steepest Descent MSE Minimization 317
15.3.1 Convergence Analysis and Step-Size 318
15.3.2 An Intuitive View of Convergence Conditions 320
15.4 From Iterative to Adaptive Filters 323
15.5 LMS Algorithm and Stochastic Gradient 324
15.6 Convergence Analysis of LMS Algorithm 325
15.6.1 Convergence in the Mean 326
15.6.2 Convergence in the Mean Square 326
15.6.3 Excess MSE 329
15.7 Learning Curve of LMS 331
15.7.1 Optimization of the Step-Size 332
15.8 NLMS Updating and Non-Stationarity 333
15.9 Numerical Example: Adaptive Identification 334
15.10 RLS Algorithm 338
15.10.1 Convergence Analysis 339
15.10.2 Learning Curve of RLS 341
15.11 Exponentially-Weighted RLS...
Details
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Nachrichtentechnik |
| Genre: | Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 608 |
| Inhalt: | 608 S. |
| ISBN-13: | 9781119293972 |
| ISBN-10: | 1119293979 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Spagnolini, Umberto |
| Hersteller: |
Wiley
John Wiley & Sons |
| Maße: | 250 x 175 x 37 mm |
| Von/Mit: | Umberto Spagnolini |
| Erscheinungsdatum: | 05.02.2018 |
| Gewicht: | 1,209 kg |
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