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Advanced Digital Signal ProcessingElectrical Engineering

@chapter = Contributors.
@chapter = Preface.
@chapter = 1. Modelbased 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 NonModelBased Solutions. DelayandSum. Minimum
Variance. Adapted Angular Response. Suboptimal ModelBased
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 1D. Taylor Series for
Matrices A and D. Behavior of [IA(AhA)1AH] for Small 8w CR
Bound Bc for Small 8w. CR Bound for Small 8w. Notes On 1D
Expression for Bc. CR Bound on Var (w^). Alternate Form of CR
Bound. Numerical Example For 1D. Resolution Thresholds In 1D.
Asymptotic CR Bound For MultiD. Taylor Series for Matrices A and W
(w). Behavior of [IA(AhA)1AH] for Small 8w CR Bound Bc for
Small 8w. Distinct Cases. Behavior of [IA(AhA)1AH] for
Small 8w CR Bound Bc for Small 8w. CR Bound BC for Small 8w.
Notes on MultiD Expression For Bc. CR Bound on Var (w)CR
Bound in Preferred Directions. Numerical Examples For 2D.
Resolution Thresholds in MultiD. Degenerate Scenarios. Conclusions.
Appendix 2A. Assumptions For 1D DirectionFinding Scenarios.
Appendix. Assumptions For 2D. DirectionFinding 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 SpatialSpectrum
Estimation. The Narrowband Observation. SpatialSpectrum
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 HighResolution 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 LowRank 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, NonSubspace, PLL
Approach. Digital PLL System Description. CDPLL Performance
Analysis. Coupled Loop Stability, NoiseFree. Gain and
Equivalent Bandwidth for an Independent Bearing PLL. Computer
Simulations. Coupled Digital PLLs For Separating CoChannel
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. ClosedForm 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 UCARBMusic and UCAEsprit. The UCARBMusic 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 UCARBMusic 194 Performance Analysis of
UCAEsprit. The CramerRao Bound. Study of Theoretical
Performance for the Oneand TwoSource Cases. Results of Computer
Simulations. Summary. Appendix 5A. Properties of UCAEsprit. 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 unMusic Algorithm. The UNCLE
Algorithm. Asymptotic Properties of the UNMusic and UNCLE
Criteria. Relations of UNMUSIC and UNCLE to Algorithms in
Spatially White Noise. Performance Analysis of UNMusic and UNCLE.
Bias and Variance of the UNMusic Estimates. Bias and
Variance of the UNCLE Estimates. Optimum UNMusic 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 UNCLE Criterion. The Likelihood
Function. InformationTheoretic 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
UNCLE 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 LeastSquares (GLS) Estimator. Estimation
of the DirectionsofArrival. 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. Taskspecific 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
SenseStationarity 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. CumulantsDefinitions and Properties. An
Interpretation for Array Processing. Examples of Aperture
Extension. ThirdOrder Cumulants. Overview. Array
Calibration Issues: VirtualEsprit Algorith,. The Array Calibration
Problem. Joint Calibration and Parameter Estimation.
Simulations. Overview. Extensions. Minimum Redundancy
Array Design for CumulantBases Direction Finding. Bounds on
Aperture Extension. Lower Bound. Minimum Redundancy Arrays
(MRA). CumulantBased MRA Design. TwoDimensional
Arrays. Linear Arrays. Overview. NonGaussian Noise
Suppression. NonGaussian Noise Suppression (Uncorrelated
Noises). NonGaussian Noise Suppression (Correlated Noises).
VirtualEsprit and NonGaussian Noise. Combining Secondand
FourthOrder Statistics. Simulations. Overview.
Appendix. SingleSensor 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 RadialBasis Function Neural
Network. Henry Leung and Titus Lo.
@aheads = Introduction. DOA Estimation Using Associative Memory.
Associative Memory Using the RadialBasis Function Neural Network.
DOA Estimation Using the RBF Associative Memory. Computer Simulations
and Analysis. Application to an Experimental DirectionFinding 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
modelbased 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 directionfinding
algorithms for closely spaced source scenarios.
Chapter 3 by W. Radich, R. Hamza, and Kevin Buckley
addresses another fundamental issue, namely, the robustness of
subspacebased directionfinding algorithms.
Chapter 4 by Lynn Kirlin, Emily Su, and Brad Hedstrom
uses analogy with phaseback 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
subspacebased methods for twodimensional 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
taskspecific 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 secondorder 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 = (0130615404)
@tcode = (061549)
= EE10100
Contributors.
Preface.
1. Modelbased 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 NonModelBased Solutions. DelayandSum. Minimum
Variance. Adapted Angular Response. Suboptimal ModelBased
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 1D. Taylor Series for
Matrices A and D. Behavior of [IA(AhA)1AH] for Small 8w CR
Bound Bc for Small 8w. CR Bound for Small 8w. Notes On 1D
Expression for Bc. CR Bound on Var (w^). Alternate Form of CR
Bound. Numerical Example For 1D. Resolution Thresholds In 1D.
Asymptotic CR Bound For MultiD. Taylor Series for Matrices A and W
(w). Behavior of [IA(AhA)1AH] for Small 8w CR Bound Bc for
Small 8w. Distinct Cases. Behavior of [IA(AhA)1AH] for
Small 8w CR Bound Bc for Small 8w. CR Bound BC for Small 8w.
Notes on MultiD Expression For Bc. CR Bound on Var (w)CR
Bound in Preferred Directions. Numerical Examples For 2D.
Resolution Thresholds in MultiD. Degenerate Scenarios. Conclusions.
Appendix 2A. Assumptions For 1D DirectionFinding Scenarios.
Appendix. Assumptions For 2D. DirectionFinding 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 SpatialSpectrum
Estimation. The Narrowband Observation. SpatialSpectrum
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 HighResolution 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 LowRank 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, NonSubspace, PLL
Approach. Digital PLL System Description. CDPLL Performance
Analysis. Coupled Loop Stability, NoiseFree. Gain and
Equivalent Bandwidth for an Independent Bearing PLL. Computer
Simulations. Coupled Digital PLLs For Separating CoChannel
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. ClosedForm 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 UCARBMusic and UCAEsprit. The UCARBMusic 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 UCARBMusic 194 Performance Analysis of
UCAEsprit. The CramerRao Bound. Study of Theoretical
Performance for the Oneand TwoSource Cases. Results of Computer
Simulations. Summary. Appendix 5A. Properties of UCAEsprit. 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 unMusic Algorithm. The UNCLE
Algorithm. Asymptotic Properties of the UNMusic and UNCLE
Criteria. Relations of UNMUSIC and UNCLE to Algorithms in
Spatially White Noise. Performance Analysis of UNMusic and UNCLE.
Bias and Variance of the UNMusic Estimates. Bias and
Variance of the UNCLE Estimates. Optimum UNMusic 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 UNCLE Criterion. The Likelihood
Function. InformationTheoretic 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
UNCLE 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 LeastSquares (GLS) Estimator. Estimation
of the DirectionsofArrival. 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. Taskspecific Criteria for Adaptive Beamforming with
Slow Fading Signals. Alfred O. Hero III and Ronald A. DeLap.
Introduction. Notation. Array Signal and Noise Models. Wide
SenseStationarity 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. CumulantsDefinitions and Properties. An
Interpretation for Array Processing. Examples of Aperture
Extension. ThirdOrder Cumulants. Overview. Array
Calibration Issues: VirtualEsprit Algorith,. The Array Calibration
Problem. Joint Calibration and Parameter Estimation.
Simulations. Overview. Extensions. Minimum Redundancy
Array Design for CumulantBases Direction Finding. Bounds on
Aperture Extension. Lower Bound. Minimum Redundancy Arrays
(MRA). CumulantBased MRA Design. TwoDimensional
Arrays. Linear Arrays. Overview. NonGaussian Noise
Suppression. NonGaussian Noise Suppression (Uncorrelated
Noises). NonGaussian Noise Suppression (Correlated Noises).
VirtualEsprit and NonGaussian Noise. Combining Secondand
FourthOrder Statistics. Simulations. Overview.
Appendix. SingleSensor Detection and Classification of Multiple
Sources. Formulation of the Problem. Analogy with Array
Processing. Simulations. Overview and Extensions.
Conclusions. References.
10. Array Processing Using RadialBasis Function Neural
Network. Henry Leung and Titus Lo.
Introduction. DOA Estimation Using Associative Memory.
Associative Memory Using the RadialBasis Function Neural Network.
DOA Estimation Using the RBF Associative Memory. Computer Simulations
and Analysis. Application to an Experimental DirectionFinding System.
Conclusion. References.
