## Advances in Spectrum Analysis and Array Processing, Volume III, 1/e

Published May, 1995 by Prentice Hall PTR (ECS Professional)

Cloth
ISBN 0-13-061540-4

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@chapter = Contributors. @chapter = Preface. @chapter = 1. Model-based Processing in Sensor Arrays. Mati Wax. @aheads = Introduction. The Mathematical Model. The Statistical Models. Problem Formulation. Mathematically Equivalent Problems. Preliminaries. The Signal Subspace. The MDL Model Selection Criterion. Conditions For Uniqueness. Suboptimal Non-Model-Based Solutions. Delay-and-Sum. Minimum Variance. Adapted Angular Response. Suboptimal Model-Based Solutions. Estimator of the Eigensystem. Detection of the Number of Sources. Estimation of the Locations. Optimal Solution For The DSWN Model. The Maximum Likelihood Estimator. Simultaneous Detection and Localization. Beamforming. Optimal Solution For The SSWN Model. The Maximum Likelihood Estimator. Simultaneous Detection and Localization. Beamforming. Suboptimal Solution to the SSCN Model. Simultaneous Detection and Localization. References. @chapter = 2. Fundamental Limitations on Direction Finding Performance for Closely Spaced Sources. Jack Jachner and Harry B. Lee. @aheads = Introduction. Summary of Results. Assumptions and Notation. Cramerrao Bounds. Relationship to the MUSIC Null Spectrum. Analysis Approach. Asymptotic CR Bound for 1-D. Taylor Series for Matrices A and D. Behavior of [I-A(AhA)-1AH] for Small 8w CR Bound Bc for Small 8w. CR Bound for Small 8w. Notes On 1-D Expression for Bc. CR Bound on Var (w^). Alternate Form of CR Bound. Numerical Example For 1-D. Resolution Thresholds In 1-D. Asymptotic CR Bound For Multi-D. Taylor Series for Matrices A and W (w). Behavior of [I-A(AhA)-1AH] for Small 8w CR Bound Bc for Small 8w. Distinct Cases. Behavior of [I-A(AhA)-1AH] for Small 8w CR Bound Bc for Small 8w. CR Bound BC for Small 8w. Notes on Multi-D Expression For Bc. CR Bound on Var (w)CR Bound in Preferred Directions. Numerical Examples For 2-D. Resolution Thresholds in Multi-D. Degenerate Scenarios. Conclusions. Appendix 2A. Assumptions For 1-D Direction-Finding Scenarios. Appendix. Assumptions For 2-D. Direction-Finding Scenarios. Appendix 2C. Proof Of (2.163) and (2.164). References. @chapter = 3. Robustness and Sensitivity Analysis for Eigenspace Localization Methods. W. Radich, R. Hamza, and K. Buckley. @aheads = Introduction. Notation. Matrix and Vector Notation. Principal Symbols. Eigenspace Spatial-Spectrum Estimation. The Narrowband Observation. Spatial-Spectrum Estimation. Relative Performance Characteristics. Modeling Narrowband Source Observation Errors. Additive Modeling of Source Model Errors. xamples of Modeling Source Modeling Errors as Additive. Discussion. Robust High-Resolution Spatial Spectrum Estimation. Robust Beamforming Methods. An Expanded Source Model. Subspace Approaches for Robustness and Enhanced Resolution. Sensitivity Analysis and Robustness. Background and Assumptions. Variance Analysis. Robustness. Numerical Studies. Simulated Low-Rank Perturbations. Model Perturbations of the Array Response. Simulated Parabolic Distortion of a Line Array. EEG Electrode Array with Dipole Orientation Uncertainty. Analytical Result Verification. Analytic Performance Comparison. Concluding Remarks. References. @chapter = 4. The Scorefunction Approach to Bearing Estimation: Phase- lock Loops and Eigenstructure. R. Lynn Kirlin, Emily Su, and Brad Hedstrom. @aheads = Introduction. The Maximum Likelihood Method. An Estimate of As(i). The Scorefunction. Multiple Sources. Discussion and Performance. The Iterative, Non-Subspace, PLL Approach. Digital PLL System Description. CDPLL Performance Analysis. Coupled Loop Stability, Noise-Free. Gain and Equivalent Bandwidth for an Independent Bearing PLL. Computer Simulations. Coupled Digital PLLs For Separating Co-Channel Signals. Signal Characterization. State Observability. State Observation and Estimation. Inclusion of Amplitude Estimation. Summary. Appendix 4A. Estimation of The Source Sequence. Appendix 4B. Appendix 4C. Appendix 4D. Optimality of Noise. Eigenvector Weights. References. @chapter = 5. Closed-Form 2D Angle Estimation with Circular Arrays/Apertures via Phase Mode Excitation and Esprit. Cherian P. Mathews and Michael D. Zoltowski. @aheads = Introduction. Phase Mode Excitation For Uniform Circular Arrays. Phase Mode Excitation Based UCA Beamformers. Development of UCA-RB-Music and UCA-Esprit. The UCA-RB-Music Algorithm. The UCA Esprit Algorithm. Accounting for Mutual Coupling Effects. The UCA of Directional Elements. Performance Analysis. Performance of MUSIC for 2D Angle Estimation. Performance Analysis of UCA-RB-Music 194 Performance Analysis of UCA-Esprit. The Cramer-Rao Bound. Study of Theoretical Performance for the One-and Two-Source Cases. Results of Computer Simulations. Summary. Appendix 5A. Properties of UCA-Esprit. Appendix 5B. Study of Theoretical Estimator Performance. References. @chapter = 6. Generalized Correlation Decomposition Applied to Array Processing in Unknown Noise Environments. K.M. Wong, Q. Wu, and P. Stoica. @aheads = Introduction. Notation and Glossary. DOA Estimation in Spatially White Noise. Signal Model. The MUSIC Algorithm. The Maximum Likelihood Estimation (MLE). Array Processing in Unknown Noise. Generalized Correlation Analysis. Canonical Correlation Decomposition (CCD). Generic Properties of GCD. Asymptotic Properties of the Eigensubspaces. DOA Estimation in Unknown Correlated Noise. The un-Music Algorithm. The UN-CLE Algorithm. Asymptotic Properties of the UN-Music and UN-CLE Criteria. Relations of UN-MUSIC and UN-CLE to Algorithms in Spatially White Noise. Performance Analysis of UN-Music and UN-CLE. Bias and Variance of the UN-Music Estimates. Bias and Variance of the UN-CLE Estimates. Optimum UN-Music and Optimum UN- CLE. Optimum Weighting Matrices. Optimality of Canonical Correlation Decomposition. Numerical Experiments. Determination of The Number of Signals in Unknown Noise Environments. Properties of the UN-CLE Criterion. The Likelihood Function. Information-Theoretic Criteria. Methods Based on Constant False Alarm Rate. The CCT Likelihood Ratio Test. Parade A New Criterion for Determining the Number of Signals. Numerical Experiments. Summary and Conclusions. Appendix 6A. Some Results From Matrix Operations. Appendix 6B. The First and Second Moments of vec$\Delta\Sigma$. Appendix 6C. Computation of The UN-CLE Criterion. References. @chapter = 7. Detection and Localization of Multiple Signals Using Subarrays Data. Jacob Sheinvald and Mati Wax. @aheads = Introduction. Problem Formulation. THE Maximum Likelihood Estimator. The Generalized Least-Squares (GLS) Estimator. Estimation of the Directions-of-Arrival. Detection of the Number of Signals. Simulation Results. Concluding Remarks. Appendix 7A. The MLE For a Single Source. Appendix 7B. Derivation of the Whitening Matrix. Appendix 7C. Cconsitency of the Parameter Estimates. Appendix 7D. Consistency of the Detection Criterion. Appendix 7E. The Efficiency Of the Estimator and the CRB for Subarray Sampling. Appendix 7F. Estimation of Hermitian $\hat{P}$ and Real $\hat{\sigma}^{2}$. References. @chapter = 8. Task-specific Criteria for Adaptive Beamforming with Slow Fading Signals. Alfred O. Hero III and Ronald A. DeLap. @aheads = Introduction. Notation. Array Signal and Noise Models. Wide- Sense-Stationarity and Spherical Symmetry. Signal Propagation. Multi- Element Spatial Arrays. Array Model for Slow Fading Signals. Task- Specific Adaptive Beamforming Methods. Narrowband Beamsummer. Signal Detection Criteria for Weight Selection. Adaptive Beamsumming via Empirical Signal Quality Indices. OPTIMAL DESIGN USING CR BOUND. Optimal Design for Constant Modulus Parameters. Adaptive Beamsummer Algorithms for Constant Modulus Parameter Estimation. Optimal Design for DOA Estimation. An Adaptive Implementation of the Optimal Beamsummer for DOA. Estimation and Detection Performance Comparisons. Simulation Results. Conclusion. Appendix 8A. Deflection Index for Optimal Detection. Appendix 8B. CR Bound for Constant Modulus Parameters. Appendix 8C. CR Bound for DOA Estimation. Rererences. @chapter = 9. Cumulants and Array Processing: A Unified Approach. Mithat C. Dogan and Jerry M. Mendel. @aheads = Introduction. An Interpretation of Cumulants for Array Processing. Cumulants--Definitions and Properties. An Interpretation for Array Processing. Examples of Aperture Extension. Third-Order Cumulants. Overview. Array Calibration Issues: Virtual-Esprit Algorith,. The Array Calibration Problem. Joint Calibration and Parameter Estimation. Simulations. Overview. Extensions. Minimum Redundancy Array Design for Cumulant-Bases Direction Finding. Bounds on Aperture Extension. Lower Bound. Minimum Redundancy Arrays (MRA). Cumulant-Based MRA Design. Two-Dimensional Arrays. Linear Arrays. Overview. Non-Gaussian Noise Suppression. Non-Gaussian Noise Suppression (Uncorrelated Noises). Non-Gaussian Noise Suppression (Correlated Noises). Virtual-Esprit and Non-Gaussian Noise. Combining Second-and Fourth-Order Statistics. Simulations. Overview. Appendix. Single-Sensor Detection and Classification of Multiple Sources. Formulation of the Problem. Analogy with Array Processing. Simulations. Overview and Extensions. Conclusions. References. @chapter = 10. Array Processing Using Radial-Basis Function Neural Network. Henry Leung and Titus Lo. @aheads = Introduction. DOA Estimation Using Associative Memory. Associative Memory Using the Radial-Basis Function Neural Network. DOA Estimation Using the RBF Associative Memory. Computer Simulations and Analysis. Application to an Experimental Direction-Finding System. Conclusion. References. @contentsend = This is the third and the final volume in a series of books which I have had the honor of editing on Advances in Spectrum Analysis and Array Processing. The first two volumes were published in 1991. The present volume is organized in 10 chapters. Chapter 1 by Mati Wax presents optimal and suboptimal model-based processing techniques for the detection, localization, and beamforming of multiple narrowband sources by means of passive arrays. Chapter 2 by Jack Jachner and Harry Lee utilizes the Cram\'{e}r Rao lower bound on parameter estimation variance to identify fundamental limitations of unbiased direction-finding algorithms for closely spaced source scenarios. Chapter 3 by W. Radich, R. Hamza, and Kevin Buckley addresses another fundamental issue, namely, the robustness of subspace-based direction-finding algorithms. Chapter 4 by Lynn Kirlin, Emily Su, and Brad Hedstrom uses analogy with phase-back loop solutions to shed further light on the array processing problem. Chapter 5 by Cherian Mathews and Michael Zoltowski focuses on the special case of uniform circular arrays, describing subspace-based methods for two-dimensional angle estimation. Chapter 6 by Max Wong, Qiang Wu, and Peter Stoica describes the development of a new technique called generalized correlation decomposition and its application to the array processing problem in an unknown noise background. Chapter 7 by Jacob Sheinvald and Mati Wax presents a new technique for solving the array processing problem, which permits sampling arbitrary subarrays sequentially in a computationally efficient manner. Chapter 8 by Alfred Hero III and Ronald DeLap develops task-specific criteria for adaptive beamforming, with the aim of optimizing the best achievable signal detection or parameter estimation at the output of the beamformer. Chapter 9 by Mithat Dogan and Jerry Mendel exploits cumulants as a tool for extracting more phase information than is possible by using only second-order statistics as is ordinarily the case. By so doing, significant improvements in the performance of array processing systems are realized. Finally, Chapter 10 by Henry Leung and Titus Lo describes the use of another new tool, neural networks, as the basis for using array data to solve the inverse problem of source location. Much of the material presented in this book has not appeared in book form before. It has been my distinct pleasure to have worked with these fine researchers in editing the book. Simon Haykinkin @copyright =  …• 1995,  = 560 pp.,  @binding = cloth  @isbn =  (0-13-061540-4)  @tcode =  (06154-9)  = EE10100

Contributors.
Preface.
1. Model-based Processing in Sensor Arrays. Mati Wax.

Introduction. The Mathematical Model. The Statistical Models. Problem Formulation. Mathematically Equivalent Problems. Preliminaries. The Signal Subspace. The MDL Model Selection Criterion. Conditions For Uniqueness. Suboptimal Non-Model-Based Solutions. Delay-and-Sum. Minimum Variance. Adapted Angular Response. Suboptimal Model-Based Solutions. Estimator of the Eigensystem. Detection of the Number of Sources. Estimation of the Locations. Optimal Solution For The DSWN Model. The Maximum Likelihood Estimator. Simultaneous Detection and Localization. Beamforming. Optimal Solution For The SSWN Model. The Maximum Likelihood Estimator. Simultaneous Detection and Localization. Beamforming. Suboptimal Solution to the SSCN Model. Simultaneous Detection and Localization. References.

2. Fundamental Limitations on Direction Finding Performance for Closely Spaced Sources. Jack Jachner and Harry B. Lee.

Introduction. Summary of Results. Assumptions and Notation. Cramerrao Bounds. Relationship to the MUSIC Null Spectrum. Analysis Approach. Asymptotic CR Bound for 1-D. Taylor Series for Matrices A and D. Behavior of [I-A(AhA)-1AH] for Small 8w CR Bound Bc for Small 8w. CR Bound for Small 8w. Notes On 1-D Expression for Bc. CR Bound on Var (w^). Alternate Form of CR Bound. Numerical Example For 1-D. Resolution Thresholds In 1-D. Asymptotic CR Bound For Multi-D. Taylor Series for Matrices A and W (w). Behavior of [I-A(AhA)-1AH] for Small 8w CR Bound Bc for Small 8w. Distinct Cases. Behavior of [I-A(AhA)-1AH] for Small 8w CR Bound Bc for Small 8w. CR Bound BC for Small 8w. Notes on Multi-D Expression For Bc. CR Bound on Var (w)CR Bound in Preferred Directions. Numerical Examples For 2-D. Resolution Thresholds in Multi-D. Degenerate Scenarios. Conclusions. Appendix 2A. Assumptions For 1-D Direction-Finding Scenarios. Appendix. Assumptions For 2-D. Direction-Finding Scenarios. Appendix 2C. Proof Of (2.163) and (2.164). References.

3. Robustness and Sensitivity Analysis for Eigenspace Localization Methods. W. Radich, R. Hamza, and K. Buckley.

Introduction. Notation. Matrix and Vector Notation. Principal Symbols. Eigenspace Spatial-Spectrum Estimation. The Narrowband Observation. Spatial-Spectrum Estimation. Relative Performance Characteristics. Modeling Narrowband Source Observation Errors. Additive Modeling of Source Model Errors. xamples of Modeling Source Modeling Errors as Additive. Discussion. Robust High-Resolution Spatial Spectrum Estimation. Robust Beamforming Methods. An Expanded Source Model. Subspace Approaches for Robustness and Enhanced Resolution. Sensitivity Analysis and Robustness. Background and Assumptions. Variance Analysis. Robustness. Numerical Studies. Simulated Low-Rank Perturbations. Model Perturbations of the Array Response. Simulated Parabolic Distortion of a Line Array. EEG Electrode Array with Dipole Orientation Uncertainty. Analytical Result Verification. Analytic Performance Comparison. Concluding Remarks. References.

4. The Scorefunction Approach to Bearing Estimation: Phase- lock Loops and Eigenstructure. R. Lynn Kirlin, Emily Su, and Brad Hedstrom.

Introduction. The Maximum Likelihood Method. An Estimate of As(i). The Scorefunction. Multiple Sources. Discussion and Performance. The Iterative, Non-Subspace, PLL Approach. Digital PLL System Description. CDPLL Performance Analysis. Coupled Loop Stability, Noise-Free. Gain and Equivalent Bandwidth for an Independent Bearing PLL. Computer Simulations. Coupled Digital PLLs For Separating Co-Channel Signals. Signal Characterization. State Observability. State Observation and Estimation. Inclusion of Amplitude Estimation. Summary. Appendix 4A. Estimation of The Source Sequence. Appendix 4B. Appendix 4C. Appendix 4D. Optimality of Noise. Eigenvector Weights. References.

5. Closed-Form 2D Angle Estimation with Circular Arrays/Apertures via Phase Mode Excitation and Esprit. Cherian P. Mathews and Michael D. Zoltowski.

Introduction. Phase Mode Excitation For Uniform Circular Arrays. Phase Mode Excitation Based UCA Beamformers. Development of UCA-RB-Music and UCA-Esprit. The UCA-RB-Music Algorithm. The UCA Esprit Algorithm. Accounting for Mutual Coupling Effects. The UCA of Directional Elements. Performance Analysis. Performance of MUSIC for 2D Angle Estimation. Performance Analysis of UCA-RB-Music 194 Performance Analysis of UCA-Esprit. The Cramer-Rao Bound. Study of Theoretical Performance for the One-and Two-Source Cases. Results of Computer Simulations. Summary. Appendix 5A. Properties of UCA-Esprit. Appendix 5B. Study of Theoretical Estimator Performance. References.

6. Generalized Correlation Decomposition Applied to Array Processing in Unknown Noise Environments. K.M. Wong, Q. Wu, and P. Stoica.

Introduction. Notation and Glossary. DOA Estimation in Spatially White Noise. Signal Model. The MUSIC Algorithm. The Maximum Likelihood Estimation (MLE). Array Processing in Unknown Noise. Generalized Correlation Analysis. Canonical Correlation Decomposition (CCD). Generic Properties of GCD. Asymptotic Properties of the Eigensubspaces. DOA Estimation in Unknown Correlated Noise. The un-Music Algorithm. The UN-CLE Algorithm. Asymptotic Properties of the UN-Music and UN-CLE Criteria. Relations of UN-MUSIC and UN-CLE to Algorithms in Spatially White Noise. Performance Analysis of UN-Music and UN-CLE. Bias and Variance of the UN-Music Estimates. Bias and Variance of the UN-CLE Estimates. Optimum UN-Music and Optimum UN- CLE. Optimum Weighting Matrices. Optimality of Canonical Correlation Decomposition. Numerical Experiments. Determination of The Number of Signals in Unknown Noise Environments. Properties of the UN-CLE Criterion. The Likelihood Function. Information-Theoretic Criteria. Methods Based on Constant False Alarm Rate. The CCT Likelihood Ratio Test. Parade A New Criterion for Determining the Number of Signals. Numerical Experiments. Summary and Conclusions. Appendix 6A. Some Results From Matrix Operations. Appendix 6B. The First and Second Moments of vec$\Delta\Sigma$. Appendix 6C. Computation of The UN-CLE Criterion. References.

7. Detection and Localization of Multiple Signals Using Subarrays Data. Jacob Sheinvald and Mati Wax.

Introduction. Problem Formulation. THE Maximum Likelihood Estimator. The Generalized Least-Squares (GLS) Estimator. Estimation of the Directions-of-Arrival. Detection of the Number of Signals. Simulation Results. Concluding Remarks. Appendix 7A. The MLE For a Single Source. Appendix 7B. Derivation of the Whitening Matrix. Appendix 7C. Cconsitency of the Parameter Estimates. Appendix 7D. Consistency of the Detection Criterion. Appendix 7E. The Efficiency Of the Estimator and the CRB for Subarray Sampling. Appendix 7F. Estimation of Hermitian $\hat{P}$ and Real $\hat{\sigma}^{2}$. References.

8. Task-specific Criteria for Adaptive Beamforming with Slow Fading Signals. Alfred O. Hero III and Ronald A. DeLap.

Introduction. Notation. Array Signal and Noise Models. Wide- Sense-Stationarity and Spherical Symmetry. Signal Propagation. Multi- Element Spatial Arrays. Array Model for Slow Fading Signals. Task- Specific Adaptive Beamforming Methods. Narrowband Beamsummer. Signal Detection Criteria for Weight Selection. Adaptive Beamsumming via Empirical Signal Quality Indices. OPTIMAL DESIGN USING CR BOUND. Optimal Design for Constant Modulus Parameters. Adaptive Beamsummer Algorithms for Constant Modulus Parameter Estimation. Optimal Design for DOA Estimation. An Adaptive Implementation of the Optimal Beamsummer for DOA. Estimation and Detection Performance Comparisons. Simulation Results. Conclusion. Appendix 8A. Deflection Index for Optimal Detection. Appendix 8B. CR Bound for Constant Modulus Parameters. Appendix 8C. CR Bound for DOA Estimation. Rererences.

9. Cumulants and Array Processing: A Unified Approach. Mithat C. Dogan and Jerry M. Mendel.

Introduction. An Interpretation of Cumulants for Array Processing. Cumulants--Definitions and Properties. An Interpretation for Array Processing. Examples of Aperture Extension. Third-Order Cumulants. Overview. Array Calibration Issues: Virtual-Esprit Algorith,. The Array Calibration Problem. Joint Calibration and Parameter Estimation. Simulations. Overview. Extensions. Minimum Redundancy Array Design for Cumulant-Bases Direction Finding. Bounds on Aperture Extension. Lower Bound. Minimum Redundancy Arrays (MRA). Cumulant-Based MRA Design. Two-Dimensional Arrays. Linear Arrays. Overview. Non-Gaussian Noise Suppression. Non-Gaussian Noise Suppression (Uncorrelated Noises). Non-Gaussian Noise Suppression (Correlated Noises). Virtual-Esprit and Non-Gaussian Noise. Combining Second-and Fourth-Order Statistics. Simulations. Overview. Appendix. Single-Sensor Detection and Classification of Multiple Sources. Formulation of the Problem. Analogy with Array Processing. Simulations. Overview and Extensions. Conclusions. References.

10. Array Processing Using Radial-Basis Function Neural Network. Henry Leung and Titus Lo.

Introduction. DOA Estimation Using Associative Memory. Associative Memory Using the Radial-Basis Function Neural Network. DOA Estimation Using the RBF Associative Memory. Computer Simulations and Analysis. Application to an Experimental Direction-Finding System. Conclusion. References.