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E-book: High-Resolution and Robust Signal Processing

Edited by (University of California, Riverside, USA), Edited by (McMaster University, Hamilton, Ontario, Canada), Edited by (University of Western Sydney, Kingswood, Australia)
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High-Resolution and Robust Signal Processing describes key methodological and theoretical advances achieved in this domain over the last twenty years, placing emphasis on modern developments and recent research pursuits. Applications-grounded, this sophisticated resource links theoretical background with high-resolution methods used in wireless communications, brain signal analysis, and space-time radar signal processing.

Chapter extras include theorem proofs, derivations, and computational shortcuts, as well as open problems, numerical measurement, and performance examples, and simulation results

Sixteen illustrious field leaders invest High-Resolution and Robust Signal Processing with: in-depth reviews of parametric high-resolution estimation and detection techniques; robust array processing solutions for adaptive beam forming and high-resolution direction finding; Parafac techniques for high-resolution array processing and specific areas of application; high-resolution nonparametric methods and implementation tactics for spectral analysis; multidimensional high-resolution data models and discussion of R-D unitary ESPRIT with colored noise; multidimensional high-resolution parameter estimation techniques applicable to channel sounding; estimation procedures for high-resolution space-time radar signal processing using 2-D or 1-D/1-D models; and models and methods for EEG/MEG space-time dipole source estimation and sensory array design.
SERIES INTRODUCTION iii
PREFACE v
CONTRIBUTORS xv
ABBREVIATIONS xix
SYMBOLS xxiii
1 A REVIEW OF PARAMETRIC HIGH-RESOLUTION METHODS 1 (62)
Qi Cheng and Yingbo Hua
1.1 Introduction
1(3)
1.1.1 Data Model
2(2)
1.2 Estimation Techniques Using Algebraic Principles
4(17)
1.2.1 Linear Prediction
5(6)
1.2.2 Matrix Pencil
11(5)
1.2.3 Iterative Quadratic Maximum Likelihood
16(5)
1.3 Estimation Techniques Using Large-Sample Theorems
21(20)
1.3.1 Subspace Rotation Invariance - ESPRIT
21(5)
1.3.2 Subspace Fitting - MUSIC
26(3)
1.3.3 Maximum Likelihood Methods
29(8)
1.3.4 Smoothing for Coherent Signals
37(4)
1.4 Detection Techniques Using a Single Measurement
41(5)
1.4.1 Effective Singular Values
41(1)
1.4.2 Noise Significance Level
42(1)
1.4.3 Least Squares Data Fitting
42(2)
1.4.4 Variations of Information Theoretic Criteria
44(2)
1.5 Detection Techniques Using Multiple Measurements
46(6)
1.5.1 Information Theoretic Criteria
46(3)
1.5.2 Treating Eigenvalues as the Observations
49(1)
1.5.3 Thresholding Eigenvalues
49(1)
1.5.4 Bayesian Approach
50(2)
1.6 Conclusions
52(1)
REFERENCES
53(10)
2 ROBUSTNESS ISSUES IN ADAPTIVE BEAMFORMING AND HIGH-RESOLUTION DIRECTION FINDING 63(48)
Alex B. Gershman
2.1 Introduction
63(1)
2.2 Robust Adaptive Beamforming
64(21)
2.2.1 Required Types of Robustness
64(2)
2.2.2 Conventional Solutions
66(4)
2.2.3 Robust Ad-Hoc Solutions
70(5)
2.2.4 Robust Solutions Based on Optimization of the Worst-Case Performance
75(7)
2.2.5 Numerical Examples
82(3)
2.3 Robust Direction Finding
85(15)
2.3.1 Required Types of Robustness
85(1)
2.3.2 Conventional Subspace Methods
86(3)
2.3.3 Direction Finding in Partly Calibrated Sensor Arrays
89(9)
2.3.4 Numerical Examples
98(2)
2.4 Conclusions
100(1)
REFERENCES
101(10)
3 PARAFAC TECHNIQUES FOR HIGH-RESOLUTION ARRAY PROCESSING 111(40)
Xianggian Liu and Nicholas Sidiropoulos
3.1 Introduction
111(5)
3.1.1 Bilinear Decomposition
112(1)
3.1.2 Trilinear Decomposition
113(1)
3.1.3 An Example
114(2)
3.1.4 Generalization
116(1)
3.2 Uniqueness of Low Rank Decomposition
116(4)
3.2.1 k-Rank
116(2)
3.2.2 Sufficient Conditions
118(1)
3.2.3 Necessary Conditions
119(1)
3.3 Algorithms for Low-Rank Decomposition
120(1)
3.3.1 Trilinear ALS (TALS)
120(1)
3.3.2 Quadrilinear ALS (QALS)
120(1)
3.4 Application in Multiple Invariance Sensor Array Processing (MI-SAP)
121(5)
3.4.1 MI-SAP Modeling
121(3)
3.4.2 Identifiability Results for MI-SAP
124(1)
3.4.3 Special Cases
124(2)
3.5 Application in Blind Reception of Frequency Hopped Signals
126(12)
3.5.1 Frequency Hopped Spread Spectrum Data Model
126(2)
3.5.2 Hop-free Subset Detection
128(2)
3.5.3 Direction-of-Arrival Estimation
130(1)
3.5.4 Single User Tracking
131(4)
3.5.5 Simulations
135(3)
3.6 Joint DOA and Hop Timing Estimation
138(5)
3.6.1 Another View of the Data Model
138(2)
3.6.2 The DP-2DHR Algorithm
140(2)
3.6.3 Simulations
142(1)
3.7 Conclusions and Open Problems
143(4)
REFERENCES
147(4)
4 HIGH-RESOLUTION NONPARAMETRIC SPECTRAL ANALYSIS: THEORY AND APPLICATIONS 151 (102)
Erik G. Larsson, Jian Li and Petre Stoica
4.1 Introduction
151(1)
4.2 The Spectral Estimation Problem
152(1)
4.3 Nonparametric Spectral Analysis via Weighted Least-Squares
153(7)
4.3.1 The Discrete Fourier Transform (DFT) Method
156(1)
4.3.2 The Averaged Fourier Method
156(1)
4.3.3 The Capon Method
156(1)
4.3.4 The APES Method
157(1)
4.3.5 MMSE Spectral Estimation
158(2)
4.4 Matched-Filterbank Interpretations
160(2)
4.4.1 DFT and Averaged DFT
161(1)
4.4.2 Capon
161(1)
4.4.3 APES
162(1)
4.5 Extensions to Two-Dimensional Data
162(3)
4.5.1 Representation of Two-dimensional Filterbanks
164(1)
4.5.2 Filterbank Interpretations of Two-Dimensional Estimators
164(1)
4.6 Forward-Backward Averaging
165(3)
4.6.1 FB Averaging of the Covariance Matrices
165(2)
4.6.2 Filterbank Interpretation of FB Averaged Estimators
167(1)
4.7 Performance Analysis
168(3)
4.7.1 Large-Sample Analysis
168(1)
4.7.2 Leakage Analysis
169(2)
4.7.3 Bias Analysis
171(1)
4.8 Fast Implementations of Capon and APES
171(5)
4.8.1 Some Results on Fast Computation
172(3)
4.8.2 Fast Implementation
175(1)
4.8.3 Discussion
176(1)
4.9 Performance Examples and Applications of Capon and APES
176(29)
4.9.1 1D Examples
176(17)
4.9.2 2D Examples
193(7)
4.9.3 Synthetic Aperture Radar (SAR) Imaging Examples
200(5)
4.10 Nonparametric Spectral Analysis of Gapped Data
205(24)
4.10.1 Spectral Estimation of Gapped Data via WLS
207(9)
4.10.2 APES for Gapped Data: GAPES
216(13)
4.11 Special Topics
229(6)
4.11.1 APES and Capon for Real-Valued Data
229(1)
4.11.2 Combining APES and Capon: CAPES
230(1)
4.11.3 APES and Capon for Damped Sinusoids
230(2)
4.11.4 Time-Recursive Implementations of Capon and APES
232(3)
4.12 Conclusions
235(2)
APPENDICES
237(10)
4.A Proof of Theorem 4.1
237(1)
4.B Proof of Theorem 4.2
238(3)
4.C Fast Matrix-Vector Multiplication
241(2)
4.D Fast Multiplication of Trigonometric Polynomials
243(1)
4.E Fast Cholesky Factorization of the Sample Covariance Matrix
244(3)
REFERENCES
247(6)
5 MULTIDIMENSIONAL HIGH-RESOLUTION PARAMETER ESTIMATION WITH APPLICATIONS TO CHANNEL SOUNDING 253 (86)
Martin Haardt, Reiner S. Thoma, and Andreas Richter
5.1 Introduction
253(5)
5.2 Multidimensional Data Model
258(9)
5.2.1 R-Dimensional Invariance Structure
259(2)
5.2.2 Real-Valued Subspace Estimation
261(6)
5.3 R-D Unitary ESPRIT with Colored Noise
267(29)
5.3.1 R Transformed Invariance Equations
268(1)
5.3.2 Covariance Approach
269(2)
5.3.3 Square-Root Approach
271(2)
5.3.4 Equivalence of both Subspace Estimates
273(2)
5.3.5 R-D Smoothing as a Preprocessing Step
275(1)
5.3.6 Simultaneous Schur Decomposition (SSD)
276(3)
5.3.7 Estimation of the Path Amplitudes
279(3)
5.3.8 Truncated Signal Subspace Estimation
282(3)
5.3.9 Unitary ESPRIT for CUBA Configurations
285(3)
5.3.10 Antenna Array Calibration
288 (8)
5.4 Multidimensional Propagation Measurements and Parameter Estimation
296(35)
5.4.1 Wireless Channel Characteristics
296(2)
5.4.2 Multidimensional Parametric Channel Model
298(2)
5.4.3 Multidimensional Real-Time Channel Sounding
300(3)
5.4.4 Antenna Array Architecture Design and Calibration
303(9)
5.4.5 Multidimensional Joint Channel Parameter Estimation
312(8)
5.4.6 Measurement Examples
320(11)
5.5 Conclusions
331(2)
REFERENCES
333(6)
6 HIGH-RESOLUTION SPACE-TIME SIGNAL PROCESSING FOR RADAR 339 (54)
Fredrik Athley, Mats Viberg and Jonny Eriksson
6.1 Introduction
339(2)
6.2 Pulsed Doppler Radar
341(2)
6.3 Sensor Arrays
343(6)
6.3.1 Spatial Data Model
343(4)
6.3.2 Signal and Noise Models
347(2)
6.4 Problem Formulation
349(3)
6.5 Estimation Using the 2-D Model
352(10)
6.5.1 General CRB for Parameterized Signals
352(2)
6.5.2 CRB for the 2-D Model
354(1)
6.5.3 Asymptotic CRB for the 2-D Model
355(1)
6.5.4 2-D Maximum Likelihood Estimation
356(3)
6.5.5 2-D Weighted Least Squares
359(2)
6.5.6 Performance Analysis
361(1)
6.6 Estimation Using a Decoupled 1-D/1-D Model
362(5)
6.6.1 CRB for the 1-D Models
362(1)
6.6.2 Asymptotic CRB for the 1-D Models
363(1)
6.6.3 1-D/1-D Weighted Least Squares
364(3)
6.7 Computing the Estimates
367(2)
6.7.1 Local Optimization
367(1)
6.7.2 Computing Initial Estimates
368(1)
6.8 Numerical Examples and Simulation Results
369(8)
6.8.1 Cramer-Rao Bounds
370(1)
6.8.2 Performance of the WLS Estimators
370(7)
6.9 Conclusions
377(2)
APPENDICES
379(8)
6.A Derivation of the 2-D CRB
379(3)
6.B Derivation of the Asymptotic 2-D CRBs
382(5)
REFERENCES
387(6)
7 EEG/MEG SPATIO-TEMPORAL DIPOLE SOURCE ESTIMATION AND SENSOR ARRAY DESIGN 393
Aleksandar Dogandzic and Arye Nehorai
7.1 Introduction
393(3)
7.2 Source and Measurement Models
396(3)
7.2.1 Source Model
396(2)
7.2.2 Measurement Model
398(1)
7.3 Maximum Likelihood Estimation
399 (6)
7.3.1 Simultaneous Estimation of the Dipole Parameters and Noise Covariance
399(3)
7.3.2 Ordinary and Generalized Least Squares
402(1)
7.3.3 Estimated Generalized Least Squares
402(1)
7.3.4 ML versus OLS
403(2)
7.4 Nonparametric Basis Functions
405(1)
7.5 Scanning Methods
406(2)
7.6 Fisher Information Matrix and Cramer-Rao Bound
408(3)
7.7 Goodness-of-fit Measures
411(1)
7.8 EEG/MEG Sensor Array Design
412(3)
7.8.1 Reparametrization Invariance
413 (1)
7.8.2 Relationship between Optimal Array Design and Information Theory
414(1)
7.9 Numerical Examples
415(11)
7.10 Conclusions
426(1)
APPENDICES
427(10)
7.A ML Estimation
427(1)
7.B Parameter Identifiability
428(2)
7.C Asymptotic Properties of the OLS Estimates
430(1)
7.D ML versus OLS
431(1)
7.E Nonparametric Basis Functions
432(1)
7.F Scanning
433(2)
7.G Derivation of the Fisher Information Matrix
435(2)
REFERENCES
437
Yingbo Hua, Alex Gershman, Qi Cheng
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