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E-raamat: Adaptive Antennas and Receivers

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This reference details the state of research in modeling, testing, and application of adaptive antennas and receivers, for students and professionals in diverse areas, such as surveillance, communication, navigation, artificial intelligence, computer tomography, and security. The book is divided into three parts, with each part presenting a different approach for increasing the probability of signal detection within at least some of the cells of the surveillance volume for a non-Gaussian or Gaussian 'noise' environment. Self- contained chapters contain background material on each topic. Weiner is affiliated with the Institute of Electrical and Electronics Engineers. This venerable series was formerly published by Dekker. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)

In our modern age of remote sensing, wireless communication, and the nearly endless list of other antenna-based applications, complex problems require increasingly sophisticated solutions. Conventional antenna systems are no longer suited to high-noise or low-signal applications such as intrusion detection. Detailing highly effective approaches to non-Gaussian weak signal detection, Adaptive Antennas and Receivers provides an authoritative introduction to state-of-the-art research on the modeling, testing, and application of these technologies.

Edited by innovative researcher and eminent expert Melvin M. Weiner, this book is the first to integrate three advanced approaches to non-Gaussian weak signal detection into a single reference: homogeneous partitioning of the surveillance volume, adaptive antennas, and adaptive receivers. Comprising self-contained chapters contributed by renowned experts such as Donald D. Weiner and Ronald Fante, each chapter explores the techniques, theoretical basis, and applications of the approach under discussion. The book considers signal detection in the presence of external noise such as clutter residue, interference, atmospheric noise, jammers, external thermal noise, in vivo surrounding tissue, and camouflaging material, making it ideal for use across a broad spectrum of applications.

This authoritative reference supplies more than 750 figures and tables, 1460 equations, and 640 references. Adaptive Antennas and Receivers is an ideal resource for improving performance in surveillance, communication, navigation, artificial intelligence, computer tomography, neuroscience, and intrusion detection systems, to name only a few.
Part I Homogeneous Partitioning of the Surveillance Volume
Chapter 1 Introduction
3(2)
M.M. Weiner
Chapter 2 A New Approach to Radar Detection Based on the Partitioning and Statistical Characterization of the Surveillance Volume
5(170)
M.A. Slamani
2.0. Introduction
7(1)
2.1. Radar Detection with a Priori Statistical Knowledge of the Environment
8(5)
2.1.1. Introduction
8(2)
2.1.2. SIRV
10(1)
2.1.2.1. Definitions
10(1)
2.1.2.2. Properties of SIRVs
11(1)
2.1.3. Locally Optimum Detector
12(1)
2.2. Understanding of Signal and Detection Using a Feedforward Expert System
13(7)
2.2.1. Introduction
13(1)
2.2.2. Classification of the Test Cells
14(1)
2.2.2.1. Mapping of the Space
14(1)
2.2.2.2. Indexing of the Cells
15(1)
2.2.3. Target Detection
16(4)
2.3 Signal Understanding and Detection Using a Feedback Expert System
20(9)
2.3.1. Introduction
20(1)
2.3.2. IPUS Architecture
20(1)
2.3.2.1. Introduction
20(1)
2.3.2.2. Discrepancy Detection
24(1)
2.3.2.3. Diagnosis and Reprocessing
25(1)
2.3.2.4. Interpretation Process
26(1)
2.3.2.5. SOU and Resolving Control Structure
26(3)
2.3.3. Application of IPUS to Radar Signal Understanding
29(1)
2.4. Proposed Radar Signal Processing System Using a Feedback Expert System
29(7)
2.4.1. Data Collection and Preprocessing
29(3)
2.4.2. Mapping
32(4)
2.5. Mapping Procedure
36(46)
2.5.1. Introduction
36(1)
2.5.2. Observations on BN and CL Cells
37(1)
2.5.2.1. Observations on BN Cells
37(1)
2.5.2.2. Observations on CL Cells
38(1)
2.5.3. Mapping Procedure
39(1)
2.5.3.1. Separation of CL Patches from Background Noise
39(1)
2.5.3.2. Detection of CL Patch Edges and Edge Enhancement
44(1)
2.5.3.3. Conclusion
46(1)
2.5.4. Examples of the Mapping Procedure
47(1)
2.5.4.1. Introduction
47(1)
2.5.4.2. Examples
49(21)
2.5.5. Convergence of the Mapping Procedure
70(1)
2.5.5.1. Introduction
70(1)
2.5.5.2. Separation between BN and CL Patches
73(6)
2.5.6. Extension of the Mapping Procedure to Range – Azimuth – Doppler Cells
79(2)
2.5.7. Conclusion
81(1)
2.6. Indexing Procedure
82(32)
2.6.1. Introduction
82(1)
2.6.2. Assessment Stage
83(1)
2.6.2.1. Identification of the BN and CL Patches
83(1)
2.6.2.2. Computation of CL-to-Noise Ratios
85(1)
2.6.2.3. Classification of CL Patches
85(1)
2.6.3. CL Subpatch Investigation Stage
86(1)
2.6.4. PDF Approximation of WSC CL Patches
87(1)
2.6.4.1. Test Cell Selection
88(1)
2.6.4.2. PDF Approximation
89(1)
2.6.4.3. PDF Approximation Metric
91(1)
2.6.4.4. Outliers
93(1)
2.6.4.5. PDF Approximation Strategy
96(1)
2.6.5. Examples
97(1)
2.6.5.1. Example 1
97(1)
2.6.5.2. Example 2
104(1)
2.6.5.3. Example 3
106(5)
2.6.6. Extension of the Indexing Procedure to Range—Azimuth—Doppler Cells
111(2)
2.6.7. Conclusion
113(1)
2.7. Application of IPUS to the Radar Detection Problem
114(58)
2.7.1. Summary of IPUS Concepts
114(1)
2.7.2. Role of IPUS in the Mapping Procedure
115(1)
2.7.2.1. IPUS Stages Included in the Mapping Procedure
115(1)
2.7.2.2. Observations on the Setting of NCC
117(8)
2.7.3. Examples of Mapping
125(1)
2.7.3.1. Example 1
125(1)
2.7.3.2. Example 2
125(1)
2.7.3.3. Example 3
125(1)
2.7.4. Role of IPUS in the Indexing Procedure
126(1)
2.7.4.1. IPUS Stages Included in the Assessment Stage
127(1)
2.7.4.2. IPUS Stages Included in the CL Subpatch Investigation Stage
127(1)
2.7.4.3. Examples
131(1)
2.7.4.4. IPUS Stages Included in the PDF Approximation Stage
133(14)
2.7.5. Examples of Indexing
147(1)
2.7.5.1. Example 1
148(1)
2.7.5.2. Example 2
152(1)
2.7.5.3. Example 3
163(7)
2.7.6. Conclusion
170(2)
2.8. Conclusion and Future Research
172(4)
2.8.1. Conclusion
172(1)
2.8.2. Future Research
173(2)
Chapter 3 Statistical Analysis of the Nonhomogeneity Detector (for Excluding Nonhomogeneous Samples from a Subdivision)
175(30)
M. Rangaswamy, J.H. Michels, and B. Himed
3.1. Gaussian Interference Backgrounds
176(11)
M. Rangaswamy, J. H. Michels, and B. Himed
3.1.1. Introduction
176(1)
3.1.2. Generalized Inner Product Statistics: Known Covariance Matrix
177(1)
3.1.3. Generalized Inner Product Statistics: Unknown Covariance Matrix
178(1)
3.1.4. Nonhomogeneity Detector
181(1)
3.1.5. Performance Analysis of the Adaptive Matched Filter Test
183(1)
3.1.6. Conclusions
187(1)
3.2. NonGaussian Interference Backgrounds
187(19)
M. Rangaswamy
3.2.1. Introduction
187(1)
3.2.2. Preliminaries
189(1)
3.2.3. Nonhomogeneity Detector for NonGaussian Interference Scenarios
190(1)
3.2.3.1. Covariance Matrix Estimation
190(1)
3.2.3.2. Maximally Invariant NHD Test Statistic
191(1)
3.2.3.3. PDF and Moments of the NonGaussian NHD Test Statistic
192(1)
3.2.3.4. Goodness-of-Fit Test
193(1)
3.2.4. Performance Analysis
194(1)
3.2.5. Conclusion
204(1)
Chapter 4 A New Technique for Univariate Distribution Approximation of Random Data
205(54)
R.R. Shah
4.1. Literature Review
206(15)
4.1.1. Introduction
206(1)
4.1.2. The Kolmogorov–Smirnov Test
206(1)
4.1.2.1. Example 1
207(1)
4.1.2.2. Example 2
209(1)
4.1.3. The Chi-Square Test
210(1)
4.1.3.1. Example 3
214(1)
4.1.4. Quantile–Quantile Plot
215(1)
4.1.4.1. Example 4
216(2)
4.1.5. Probability –Probability Plot
218(1)
4.1.5.1. Example 5
219(2)
4.2. The Ozturk Algorithm
221(27)
4.2.1. Introduction
221(1)
4.2.2. Definitions
222(1)
4.2.3. The Ozturk Algorithm
223(1)
4.2.3.1. Goodness of Fit Test
223(1)
4.2.3.2. Distribution Approximation
239(1)
4.2.3.3. Parameter Estimation
245(3)
4.3. Simulation Results of the Ozturk Algorithm
248(7)
4.3.1. Goodness of Fit Test Results
249(1)
4.3.1.1. The Univariate Gaussian Case
249(1)
4.3.1.2. The Weibull Case
249(1)
4.3.1.3. The Gamma Case
250(1)
4.3.1.4. The Lognormal Case
250(2)
4.3.2. Distribution Approximation Test Results
252(3)
4.4. Conclusions and Suggestions for Future Work
255(5)
4.4.1. Conclusions
255(1)
4.4.2. Suggestions for Future Work
256(3)
Chapter 5 Probability Density Distribution Approximation and Goodness-of-Fit Tests of Random Data
259(36)
Ozturk
5.1. A New Method for Distribution Approximation
260(16)
5.1.1. Introduction
260(1)
5.1.2. Approximation Procedure
261(2)
5.1.3. Performance of the Approximation Procedure
263(1)
5.1.4. Approximation of Multivariate Distributions
264(4)
5.1.5. Parameter Estimation
268(1)
5.1.5.1. Estimating the Location and Scale Parameters
268(1)
5.1.5.2. Estimating the Shape Parameters
270(2)
5.1.6. Distribution Approximation for Mixtures of Distributions
272(1)
5.1.7. Examples
273(2)
5.1.8. Conclusions
275(1)
5.2. A General Algorithm for Univariate and Multivariate Goodness-of-Fit Tests Based on Graphical Representation
276(21)
5.2.1. Introduction
276(1)
5.2.2. The Test Procedure
277(2)
5.2.3. Properties of the Test Statistics
279(3)
5.2.4. Extensions of the Test
282(1)
5.2.5. Examples
283(3)
5.2.6. Empirical Power
286(4)
5.2.7. The Test Algorithm
290(2)
5.2.8. Discussion
292(3)
Chapter 6 Applications
295(124)
W.J. Baldygo, C.T. Capraro, G.T. Capraro, D. Ferris, I.D. Keckler, M.A. Slamani, D.L. Stadelman, V. Vannicola, D.D. Weiner, W.W. Weiner, and M.C. Wicks
6.1. The Ozturk Algorithm: A New Technique for Analyzing Random Data with Applications to the Field of Neuroscience
297(52)
W.W. Weiner
6.1.1. Introduction to the Ozturk Algorithm
297(1)
6.1.1.1. Overview
298(1)
6.1.1.2. Sample Simulation
299(7)
6.1.2. Detailed Description of the Ozturk Algorithm
306(1)
6.1.2.1. The Standardized Order Statistic
306(1)
6.1.2.2. The Goodness-of-Fit Test
307(1)
6.1.2.3. Calculation of Linked Vectors in the U-V Plane
308(1)
6.1.2.4. Calculation of Confidence Ellipses
311(1)
6.1.2.5. The Best-Fit Test
312(1)
6.1.2.6. Estimation of Location and Scale Parameters
314(2)
6.1.3. Analysis of Spontaneous Auditory Nerve Activity of Chinchillas
316(1)
6.1.3.1. Analysis of Two Fibers with Different Spontaneous Rates
325(1)
6.1.3.2. Analysis of Pulse-Number Distributions
327(6)
6.1.4. Analysis of Efferent Optic-Nerve Activity in the Horseshoe Crab
333(1)
6.1.4.1. Characterization of Interburst Intervals
335(1)
6.1.4.2. Trends in the Shape Parameter
339(2)
6.1.5. Analysis of the Visual Field of the Horseshoe Crab
341(1)
6.1.5.1. Total Interommatidial Angles
344(1)
6.1.5.2. Horizontal and Vertical Interommatidial Angles
346(2)
6.1.6. Applications of the Ozturk Algorithm in Neuroscience
348(1)
6.2. Use of Image Processing to Partition a Radar Surveillance Volume into Background Noise and Clutter Patches
349(10)
M.A. Slamani and D.D. Weiner
6.2.1. Introduction
349(1)
6.2.2. Observations about BN and CL
350(1)
6.2.2.1. Observations about BN
351(1)
6.2.2.2. Observations about CL
351(1)
6.2.3. Mapping Procedure
351(1)
6.2.3.1. Separation of CL Patches from BN
351(1)
6.2.3.2. Detection of Clutter Patch Edges
354(1)
6.2.3.3. Enhancement of Clutter Patch Edges
355(1)
6.2.4. Example
355(4)
6.3. Probabilistic Insight into the Application of Image Processing to the Mapping of Clutter and Noise Regions in a Radar Surveillance Volume
359(9)
M.A. Slamani and D.D. Weiner
6.3.1. Introduction
359(1)
6.3.2. Separation between BN and CL Patches
360(1)
6.3.3. Summary
368(1)
6.4. A New Approach to the Analysis of IR Images
368(14)
M.A. Slamani, D. Ferris, and V. Vannicola
6.4.1. Introduction
368(1)
6.4.2. ASCAPE
369(1)
6.4.3. Mapping Procedure
371(1)
6.4.3.1. Identification of Lowest Average Power Level (LP)
371(1)
6.4.3.2. Detection of Patch Edges
371(1)
6.4.4. Statistical Procedure
372(1)
6.4.4.1. Introduction to Ozturk Algorithm
372(1)
6.4.4.2. Outliers
374(1)
6.4.4.3. Strategy to SubPatch Investigation Using the Statistical Procedure
374(1)
6.4.5. Expert System Shell IPUS
375(1)
6.4.6. Example: Application of ASCAPE to Real IR Data
376(1)
6.4.7. Conclusion
381(1)
6.5. Automatic Statistical Characterization and Partitioning of Environments (ASCAPE)
382(4)
M.A. Slamani, D.D. Weiner, and V. Vannicola
6.5.1. Problem Statement
382(1)
6.5.2. ASCAPE Process
385(1)
6.5.3. Application of ASCAPE to Real IR Data
385(1)
6.5.4. Conclusion
386(1)
6.6. Statistical Characterization of Nonhomogeneous and Nonstationary Backgrounds
386(14)
A.D. Keckler, D.L. Stadelman, D.D. Weiner, and M.A. Slamani
6.6.1. Introduction
386(1)
6.6.2. Application of ASCAPE to Concealed Weapon Detection
387(1)
6.6.3. The SIRV Radar Clutter Model
390(1)
6.6.4. Distribution Approximation Using the Ozturk Algorithm
392(1)
6.6.5. Approximation of SIRVs
395(1)
6.6.6. NonGaussian Receiver Performance
398(1)
6.6.7. Concluding Remarks
400(1)
6.7. Knowledge-Based Map Space Time Adaptive Processing (KBMapSTAP)
400(8)
C.T. Capraro, G.T. Capraro, D.D. Weiner, and M.C. Wicks
6.7.1. Introduction
400(1)
6.7.2. Clutter Model
401(1)
6.7.3. Representative Secondary Clutter
402(1)
6.7.4. Airborne Radar Data
402(1)
6.7.5. A Priori Data
403(1)
6.7.6. Research Problem, Hypothesis, and Preliminary Findings
403(1)
6.7.7. Conclusions and Future Work
407(1)
6.8. Improved STAP Performance Using Knowledge-Aided Secondary Data Selection
408(13)
C.T. Capraro, G.T. Capraro, D.D. Weiner, M.C. Wicks, and W.J. Baldygo
6.8.1. Introduction
408(1)
6.8.2. Radar and Terrain Data
409(1)
6.8.3. Approach
410(1)
6.8.3.1. STAP Algorithm
410(1)
6.8.3.2. Registration of the Radar with the Earth
411(1)
6.8.3.3. Data Selection
412(1)
6.8.3.4. Corrections for Visibility
412(1)
6.8.3.5. Secondary Data Guard Cells
413(1)
6.8.4. Results
413(1)
6.8.5. Conclusion
415(4)
Part II Adaptive Antennas
Chapter 7 Introduction
419(2)
M.M. Weiner
Chapter 8 Adaptive Implementation of Optimum Space—Time Processing
421(18)
L. Cai and H. Wang
8.1. Introduction
421(2)
8.2. Data Modelling
423(2)
8.3. Difference Among the Performance Potentials of the Cascade and Joint-Domain Processors
425(5)
8.4. The JDL–GLR Algorithm
430(6)
8.4.1. The JDL–GLR Principle
431(2)
8.4.2. The JDL–GLR Detection Performance
433(1)
8.4.3. Detection Performance Comparison
433(3)
8.4.4. Other Features of JDL–GLR
436(1)
8.5. Conclusions and Discussion
436(3)
Chapter 9 A Printed-Circuit Smart Antenna with Hemispherical Coverage for High Data-Rate Wireless Systems
439(4)
G. Ploussios
Chapter 10 Applications
443(160)
E.C. Barite, R.M. Davis, R.L. Fante, T.P. Guella, J.A. Torres, and J. Vaccaro
10.1. Cancellation of Specular and Diffuse Jammer Multipath Using a Hybrid Adaptive Array
446(15)
R.L. Fante
10.1.1. Introduction
446(1)
10.1.2. Why Multipath Requires Additional Degrees of Freedom
446(1)
10.1.3. Generalization
451(1)
10.1.4. Numerical Calculations
456(1)
10.1.5. Summary and Discussion
460(1)
10.2. Some Limitations on the Effectiveness of Airborne Adaptive Radar
461(29)
E.C. Barile, R.L. Fante, and J.A. Torres
10.2.1. Background
461(1)
10.2.2. Theoretical Introduction
465(1)
10.2.3. Two-Element Displaced Phase Center Antenna
472(1)
10.2.4. Simulation Results
478(1)
10.2.4.1. Internal Clutter Motion
478(1)
10.2.4.2. Aircraft Crabbing
482(1)
10.2.4.3. Near-Field Obstacles
484(1)
10.2.4.4. Antenna Errors (Channel Mismatch)
487(3)
10.2.5. Summary
490(1)
10.3. Clutter Covariance Smoothing by Subaperture Averaging
490(7)
R.L. Fante, E.C. Barile, and T.P. Guella
10.3.1. Introduction
490(1)
10.3.2. Analysis for an Airborne Radar
492(1)
10.3.3. Summary
496(1)
10.4. Cancellation of Diffuse Jammer Multipath by an Airborne Adaptive Radar
497(21)
R.L. Fante and J.A. Torres
10.4.1. Introduction
497(1)
10.4.2. Filtered Received Signals
502(1)
10.4.2.1. Received Jammer and Noise Signals
502(1)
10.4.2.2. Interference Covariance Matrix
505(1)
10.4.2.3. Steering-Vector and Received Target Signal
508(1)
10.4.3. Numerical Results
509(1)
10.4.3.1. Introduction
509(1)
10.4.3.2. Tap Spacing
512(1)
10.4.3.3. Total Extent
513(1)
10.4.3.4. Ground Clutter
513(1)
10.4.3.5. Temporal Averaging
514(1)
10.4.3.6. Beam Space
514(3)
10.4.4. Summary and Discussion
517(1)
10.5. Wideband Cancellation of Multiple Mainbeam Jammers
518(13)
R.L. Fante, R.M. Davis, and T.P. Guella)
10.5.1. Introduction
518(1)
10.5.2. Calculation of the Array Performance
520(1)
10.5.3. Simulation Results
523(1)
10.5.3.1. Spatial Span and Location of the Auxiliaries
523(1)
10.5.3.2. Required Number of Auxiliaries and Gain per Auxiliaries
524(1)
10.5.3.3. Signal-to-Interference Ratio after Cancellation
527(1)
10.5.3.4. Simultaneous Nulling of Mainlobe and Sidelobe Jammers
529(1)
10.5.4. Summary and Discussion
530(1)
10.6. Adaptive Space–Time Radar
531(9)
R.L. Fante
10.6.1. Introduction
531(1)
10.6.2. Understanding the Results in Equation 10.169 and Equation 10.170
533(1)
10.6.3. Sequential Cancellation of Jammers and Clutter
536(1)
10.6.4. Typical Results
538(1)
10.6.5. Additional Considerations
539(1)
10.6.6. Summary
540(1)
10.7. Synthesis of Adaptive Monopulse Patterns
540(3)
R.L. Fante
10.7.1. Analysis
540(1)
10.7.2. Summary
542(1)
10.8. Ground and Airborne Target Detection with Bistatic Adaptive Space-Based Radar
543(10)
R.L. Fante
10.8.1. Introduction
543(1)
10.8.2. Analysis
544(1)
10.8.2.1. Sum Beam
544(1)
10.8.2.2. Difference Beam
545(1)
10.8.3. Numerical Studies of Effectiveness
546(1)
10.8.3.1. Sum Beam
548(1)
10.8.3.2. Difference beam
551(2)
10.8.4. Summary
553(1)
10.9. Adaptive Nulling of Synthetic Aperture Radar (SAR) Sidelobe Discretes
553(10)
R.L. Fante
10.9.1. Introduction
553(1)
10.9.2. Fully Adaptive SAR
554(1)
10.9.3. Overlapped-Subarray SAR
557(1)
10.9.4. Numerical Results
559(1)
10.9.5. Summary
563(1)
10.10. Wideband Cancellation of Interference in a Global Positioning System (GPS) Receive Array
563(22)
R.L. Fante and J.J. Vaccaro
10.10.1. Introduction
563(1)
10.10.2. Adaptive Filter Weights
564(1)
10.10.2.1. Maximum Signal-to-Interference Ratio
565(1)
10.10.2.2. Minimum Mean Square Error
566(1)
10.10.2.3. Minimum Output Power
567(1)
10.10.3. Signal Distortion Introduced by the Processor
567(1)
10.10.4. Suboptimum Space—Frequency Processing
570(1)
10.10.5. Numerical Simulations
571(1)
10.10.5.1. Introduction
571(1)
10.10.5.2. Effect of Channel Mismatch
574(1)
10.10.5.3. Effect of Steering-Vector Mismatch
576(1)
10.10.5.4. Distortion Introduced by the Adaptive Filter
577(3)
10.10.6. Space—Time vs. Suboptimum Space—Frequency Processing
580(1)
10.10.7. Summary
585(1)
10.11. A Maximum-Likelihood Beamspace Processor for Improved Search and Track
585(21)
R.M. Davis and R.L. Fante
10.11.1. Introduction
585(1)
10.11.2. Maximum-Likelihood Beamspace Processor (MLBP)
586(1)
10.11.3. Analysis
589(1)
10.11.3.1. The First Stage
589(1)
10.11.3.2. The Second Stage
590(1)
10.11.3.3. Target Detection
592(1)
10.11.4. Numerical Examples
593(1)
10.11.4.1. Improved Clear Environment Search Performance
594(1)
10.11.4.2. Improved Clear Environment Angle Estimation
595(1)
10.11.4.3. Performance against a Single Mainlobe Interferer
596(4)
10.11.5. Summary
600(3)
Part III Adaptive Receivers
Chapter 11 Introduction
603(2)
M.M. Weiner
Chapter 12 Spherically Invariant Random Processes for Radar Clutter Modeling, Simulation, and Distribution Identification
605(102)
M. Rangaswamy
12.1. Introduction
606(2)
12.2. Background
608(18)
12.2.1. Introduction
608(1)
12.2.2. Definitions
609(1)
12.2.3. Characterization of SIRVs
610(5)
12.2.4. Determining the PDF of a SIRV
615(3)
12.2.5. Properties of SIRVs
618(1)
12.2.5.1. PDF Characterization
618(1)
12.2.5.2. Closure Under Linear Transformation
618(1)
12.2.5.3. Minimum Mean Square Error Estimation
618(1)
12.2.5.4. Distributions of Sums of SIRVs
621(1)
12.2.5.5. Markov Property for SIRPs
622(1)
12.2.5.6. Kalman Filter for SIRPs
624(1)
12.2.5.7. Statistical Independence
625(1)
12.2.5.8. Ergodicity of SIRPs
625(1)
12.2.6. Conclusion
626(1)
12.3. Radar Clutter Modelling Using Spherically Invariant Random Processes
626(39)
12.3.1. Introduction
626(2)
12.3.2. Problem Statement
628(2)
12.3.3. Techniques for Determining the SIRV PDF
630(1)
12.3.3.1. SIRVs with Known Characteristic PDF
630(1)
12.3.3.2. SIRVs with Unknown Characteristic PDFs
631(1)
12.3.3.3. Hankel Transform Approach
632(2)
12.3.4. Examples of Complex SIRVs
634(1)
12.3.4.1. Examples Based on the Characteristic PDF
634(1)
12.3.4.2. Examples Based on Marginal Envelope PDF
641(1)
12.3.4.3. Examples Using the Marginal Characteristic Function
651(5)
12.3.5. Significance of the Quadratic Form of the SIRV PDF
656(8)
12.3.6. Conclusion
664(1)
12.4. Computer Generation of Simulated Radar Clutter Characterized as SIRPs
665(15)
12.4.1. Introduction
665(1)
12.4.2. Preliminaries
666(4)
12.4.3. Two Canonical Simulation Procedures for Generating SIRVs
670(5)
12.4.4. Performance Assessment of the Simulation Schemes
675(2)
12.4.5. Conclusions
677(3)
12.5. Distribution Approximation to Radar Clutter Characterized by SIRPs
680(25)
12.5.1. Introduction
680(2)
12.5.2. Definitions
682(1)
12.5.3. Goodness of Fit Test
682(7)
12.5.4. Distribution Approximation
689(5)
12.5.5. Parameter Estimation
694(1)
12.5.5.1. Estimation of Location and Scale Parameters
695(1)
12.5.5.2. Shape Parameter Estimation
696(1)
12.5.6. Assessing the Distributional Properties of SIRVs
697(3)
12.5.7. Distribution Identification of SIRVs
700(4)
12.5.8. Alternative Method for Parameter Estimation
704(1)
12.5.9. Conclusions
705(1)
12.6. Conclusions
705(3)
12.6.1. General Remarks
705(1)
12.6.2. Suggestions for Future Research
706(1)
Chapter 13 Weak Signal Detection
707(92)
P. Chakravarthi
13.1. Introduction
708(4)
13.1.1. Weak Signal Problem
708(2)
13.1.2. NonGaussian Correlated Data
710(1)
13.1.3. Thesis Organization
711(1)
13.2. The Locally Optimum Detector (LOD)
712(22)
13.2.1. Literature Review
712(3)
13.2.2. Spherically Invariant Random Processes (SIRP)
715(1)
13.2.3. The Derivation of the Locally Optimum Detector
716(1)
13.2.4. The Series Approach
717(1)
13.2.4.1. The Known Signal Case
717(1)
13.2.4.2. The Random Signal Case
720(1)
13.2.5. The Lagrangian Approach
721(1)
13.2.5.1. The Known Signal Case
721(1)
13.2.5.2. The Random Signal Case
723(3)
13.2.6. Special Cases
726(1)
13.2.6.1. The Known Signal Problem
726(1)
13.2.6.2. The Random Signal Problem
729(5)
13.3. Determining Thresholds for the LOD
734(30)
13.3.1. Literature Review
734(1)
13.3.1.1. Classical Methods for Evaluating Thresholds
734(1)
13.3.2. Extreme Value Theory
735(1)
13.3.3. The Radar Problem
736(1)
13.3.4. Methods for Estimating Thresholds
737(1)
13.3.4.1. Estimates Based on Raw Data
737(1)
13.3.4.2. Estimates Motivated by the Extreme Value Theory
738(1)
13.3.5. The Generalized Pareto Distribution
739(1)
13.3.5.1. Methods for Estimating the Parameters of the GPD
742(1)
13.3.5.2. Estimation of Thresholds
748(1)
13.3.6. Numerical Results
749(1)
13.3.6.1. Characterization of Tail Shape for Known Distributions
749(1)
13.3.6.2. Empirical Properties of the Estimators for Known Distributions
749(1)
13.3.6.3. Effect of the Choice of A on the Threshold Estimates
756(2)
13.3.7. Examples
758(1)
13.3.7.1. Known Distribution Case
758(1)
13.3.7.2. An Unknown Distribution Case
759(5)
13.4. Performance of the LOD for Multivariate Student-T and K-Distributed Disturbances
764(24)
13.4.1. The Multivariate Student-T Distribution
764(1)
13.4.1.1. The Locally Optimum Detector
766(1)
13.4.1.2. Computer Simulation of Performance
768(1)
13.4.1.3. Results of the Computer Simulation
771(5)
13.4.2. The Multivariate K-Distribution
776(1)
13.4.2.1. The Locally Optimum Detector
778(1)
13.4.2.2. Computer Simulation of Performance
780(1)
13.4.2.3. Conclusions
783(2)
13.4.3. Determining LOD Threshold with Real Data
785(3)
13.5. Performance of the Amplitude Dependent LOD
788(9)
13.5.1. The Amplitude Dependent LOD for the Multivariate K-Distributed Disturbance
789(1)
13.5.1.1. Results of Computer Simulation
790(4)
13.5.2. The Amplitude Dependent LOD for the Student-T Distributed Disturbance
794(1)
13.5.2.1. Conclusions
796(1)
13.6. Conclusions
797(3)
13.6.1. Summary
797(1)
13.6.2. Suggestion for Future Research
798(1)
Chapter 14 A Generalization of Spherically Invariant Random Vectors (SIRVs) with an Application to Reverberation Reduction in a Correlation Sonar
799(114)
T.J. Barnard
14.1. Introduction
800(3)
14.2. The SIRV Representation Theorem
803(7)
14.2.1. The Traditional SIRV Model
803(2)
14.2.2. The Generalized SIRV Model
805(2)
14.2.3. A Comparison of the Traditional and Generalized Models
807(3)
14.3. Generalized SIRV Properties
810(16)
14.3.1. Linear Transformation
810(1)
14.3.2. The Generalized SIRV "Bootstrap" Theorem
811(1)
14.3.3. The Monotonicity of hNM(αx1,...,αxM)
812(1)
14.3.4. Spherical Coordinates
812(5)
14.3.5. The Generalized SIRV Bessel Function Representation
817(5)
14.3.6. Minimum Mean Square Error Estimation
822(2)
14.3.7. The Generalized SIRV Laplace Transform Representation
824(2)
14.4. The Generalized SIRV Density Function
826(30)
14.4.1. Direct Evaluation of hNM(αx)
827(1)
14.4.1.1. Case 1
828(1)
14.4.1.2. Case 2
841(3)
14.4.2. Evaluation of hNM Using the Laplace Transform
844(1)
14.4.2.1. Case 3
846(1)
14.4.2.2. Case 4
854(2)
14.5. Generalized SIRV Generation
856(7)
14.5.1. Multivariate Rejection Theorem
857(3)
14.5.2. Application of the Rejection Theorem
860(1)
14.5.3. Examples of Random Variable Generation
861(1)
14.5.3.1. Example 1
861(1)
14.5.3.2. Example 2
863(1)
14.6. Generalized SIRV Density Approximation
863(13)
14.6.1. Univariate Density Approximation
865(2)
14.6.2. 2-D Density Approximation
867(1)
14.6.3. Multivariate Density Approximation
868(1)
14.6.4. Real Data Analysis
869(7)
14.7. Correlation Sonar Fundamentals
876(20)
14.7.1. Correlation Sonar Basic Operation
876(4)
14.7.2. Correlation Sonar Reverberation Model
880(1)
14.7.2.1. Monostatic and Bistatic Reverberation
881(1)
14.7.2.2. Reverberation as Heard on a Moving Correlation Sonar Platform
883(7)
14.7.3. A Sub-Optimal Correlation Sonar Receiver
890(5)
14.7.4. Performance in Previous Pulse Interference
895(1)
14.8. M-ary Detection
896(13)
14.8.1. Optimum M-ary Detection
897(4)
14.8.2. Sub-Optimum M-ary Detection
901(3)
14.8.3. Generalized SIRV M-ary Detection
904(5)
14.9. Conclusion
909(6)
14.9.1. Suggestions for Future Research
910(3)
Chapter 15 Applications
913(126)
T.J. Barnard, A.D. Keckler, F. Khan, J.H. Michels, M. Rangaswamy, D.L. Stadelman, and D.D. Weiner
15.1. Statistical Normalization of Spherically Invariant NonGaussian Clutter
915(13)
T. Barnard and F. Khan
15.1.1. Introduction
915(1)
15.1.2. Background
916(1)
15.1.3. SIRV Examples
919(1)
15.1.4. Pareto SIRV GLRT
920(1)
15.1.5. Statistical Normalization
925(1)
15.1.6. Conclusion
927(1)
15.2. NonGaussian Clutter Modeling and Application to Radar Target Detection
928(10)
A.D. Keckler, D.L. Stadelman, and D.D. Weiner
15.2.1. Introduction
928(1)
15.2.2. Summary of the SIRV Model
929(1)
15.2.3. Distribution Approximation Using the Ozturk Algorithm
930(1)
15.2.4. Approximation of SIRVs
933(1)
15.2.5. NonGaussian Receiver Performance
936(1)
15.2.6. Concluding Remarks
938(1)
15.3. Adaptive Ozturk-Based Receivers for Small Signal Detection in Impulsive NonGaussian Clutter
938(17)
D.L. Stadelman, A.D. Keckler, and D.D. Weiner
15.3.1. Introduction
938(1)
15.3.2. Summary of the SIRV Model
940(1)
15.3.3. The Ozturk Algorithm and SIRV PDF Approximation
941(1)
15.3.4. NonGaussian SIRV Receivers
944(1)
15.3.5. Graphical Representation of SIRV Receiver Behavior
945(1)
15.3.6. Adaptive Ozturk-Based Receiver
951(1)
15.3.7. Conclusions
953(2)
15.4. Efficient Determination of Thresholds via Importance Sampling for Monte Carlo Evaluation of Radar Performance in NonGaussian Clutter
955(13)
D.L. Stadelman, D.D. Weiner, and A.D. Keckler
15.4.1. Introduction
955(1)
15.4.2. The Complex SIRV Clutter Model
956(1)
15.4.3. NonGaussian SIRV Receivers
957(1)
15.4.3.1. Known Covariance Matrix Case
959(1)
15.4.3.2. Unknown Covariance Matrix Case
959(1)
15.4.4. Importance Sampling
960(1)
15.4.5. Estimation of SIRV Detector Thresholds with Importance Sampling
962(1)
15.4.6. Extreme Value Theory Approximation
967(1)
15.5. Rejection-Method Bounds for Monte Carlo Simulation of SIRVs
968(12)
A.D. Keckler and D.D. Weiner
15.5.1. Introduction
968(1)
15.5.2. Summary of the SIRV Model
969(1)
15.5.3. Generation of SIRV Distributed Samples
970(1)
15.5.4. Generation of PDF Bounds
975(1)
15.5.5. Concluding Remarks
979(1)
15.6. Optimal NonGaussian Processing in Spherically Invariant Interference
980(44)
D. Stadelman and D.D. Weiner
15.6.1. Introduction
980(1)
15.6.2. A Review of the SIRV Model
982(1)
15.6.2.1. Definition of the SIRV Model
982(1)
15.6.2.2. SIRV Properties
984(1)
15.6.2.3. The Complex SIRV Model
987(1)
15.6.2.4. Examples
988(1)
15.6.3. Optimal Detection in NonGaussian SIRV Clutter
988(1)
15.6.3.1. Introduction
988(1)
15.6.3.2. Completely Known Signals
989(1)
15.6.3.3. Signals with Random Parameters
990(1)
15.6.3.4. Generalized Likelihood Ratio Test
1005(1)
15.6.3.5. Maximum Likelihood Matched Filter
1008(3)
15.6.4. Nonlinear Receiver Performance
1011(1)
15.6.4.1. Introduction
1011(1)
15.6.4.2. Indirect Simulation of SIRV Receiver Statistics
1012(1)
15.6.4.3. Student t SIRV Results
1014(1)
15.6.4.4. DGM Results
1018(1)
15.6.4.5. NP vs. GLRT Receiver Comparison
1020(1)
15.6.4.6. Additional Implementation Issues
1022(1)
15.6.4.7. Summary
1023(1)
15.7. Multichannel Detection for Correlated NonGaussian Random Processes Based on Innovations
1024(78)
M. Rangaswamy, J.H. Michels, and D.D. Weiner
15.7.1. Introduction
1024(1)
15.7.2. Preliminaries
1025(1)
15.7.3. Minimum Mean-Square Estimation Involving SIRPs
1026(1)
15.7.4. Innovations-Based Detection Algorithm for SIRPs Using Multichannel Data
1028(1)
15.7.4.1. Block Form of the Multichannel Likelihood Ratio
1028(1)
15.7.4.2. Sequential Form of the Multichannel Likelihood Ratio
1029(3)
15.7.5. Detection Results Using Monte-Carlo Simulation
1032(1)
15.7.6. Estimator Performance for SIRPs
1036(1)
15.7.7. Conclusion
1037(2)
Appendices 1039(78)
Appendix A. Stochastic Representation for the Normalized Generalized Inner Product (Section 3.1)
1040(1)
Appendix B. Expectation-Maximization Algorithm for Covariance Matrix Estimation (Section 3.2)
1041(3)
Appendix C. Algebraic Derivations for Johnson Distributions (Section 4.2)
1044(14)
C.1. Johnson Su Distribution
1044(5)
C.2. Johnson SB Distribution
1049(7)
C.3. Johnson SL Distribution
1056(2)
Appendix D. Connections Between ga, ka, Pa (Section 4.2)
1058(1)
Appendix E. Cancellation for an Analog Hybrid Canceler (Section 10.1)
1059(1)
Appendix F. Cancellation for a Digital Hybrid Canceler (Section 10.1)
1060(2)
Appendix G. Matrix Elements in Equation 10.10 (Section 10.1)
1062(1)
Appendix H. Asymptotic Cancellation Curves (Section 10.1)
1063(2)
Appendix I. Optimum Values of N and M (Section 10.1)
1065(2)
Appendix J. Effect of Near-Field Nulling Constraint (Section 10.2)
1067(2)
Appendix K. Equivalence of Element Space and Beam Space Results (Section 10.4)
1069(1)
Appendix L. Evaluation of the Integrals in Equation 10.128 and Equation 10.129 (Section 10.4)
1070(2)
Appendix M. Calculation of the Adaptive Weights (Section 10.5)
1072(3)
Appendix N. Elimination of False Targets (Section 10.5)
1075(1)
Appendix O. Approximate Derivation of Equation 10.165 (Section 10.5)
1076(3)
Appendix P. Interference Covariance Matrix (Section 10.10)
1079(3)
Appendix Q. Number of Time Taps Required (Section 10.10)
1082(2)
Appendix R Inclusion of Polarization (Section 10.10)
1084(1)
Appendix S. Signal Cancellation in First Stage Beamformer (Section 10.11)
1085(3)
Appendix T. Interferer-Free Limit of Equation 10.298 (Section 10.11)
1088(1)
Appendix U. Properties of SIRVs (Section 12.2)
1089(3)
U.1. Statistical Independence
1089(1)
U.2. Spherically Symmetric Characteristic Function
1090(1)
U.3. Relationship between Higher Order and Lower Order SIRV PDFs
1091(1)
Appendix V. Computer Generation of SIRVs Using Rejection Method (Section 12.4)
1092(3)
V.1. Rejection Method
1092(1)
V.2. Rejection Theorem
1093(2)
Appendix W. Maximum Likelihood Estimation Involving SIRVs (Section 12.5)
1095(7)
Appendix X. Issues Related to Extreme Value Theory (Section 13.3)
1102(7)
X.1. Limiting Forms for the Largest Order Statistic
1102(4)
X.1.1. Case 1
1103(2)
X.1.2. Cases 2 and 3
1105(1)
X.2. Tails of Probability Density Functions
1106(2)
X.2.1. Case 1
1107(1)
X.2.2. Case 2
1107(1)
X.2.3. Case 3
1107(1)
X.3. PDF of the rth Order Statistic
1108(1)
Appendix Y. Canonical Form Derivation (Section 15.6)
1109(2)
Appendix Z. Alternative Spherical Coordinate SIRV Representations (Section 15.6)
1111(6)
Acronyms 1117(16)
References 1133(36)
Computer Programs available at CRC Press Website 1169(14)
A.. GENREJ – Generalized Acceptance-Rejection Method Random Number Generator
1169(2)
A.D. Keckler
B. OZTURK – Univariate Probability Distribution approximation Algorithm
1171(3)
A.D. Keckler
C. OZSIRC – Multivariate Probability Distribution Algorithm for Spherically Invariant Random Vectors (SIRVs)
1174
A.D. Keckler
D. GMIXEM – Approximation of SIRVs With Gaussian Mixtures Using the Expectation-Maximization (EM) Algorithm
1171(8)
A.D. Keckler
E. SIRVOC – Maximum Liklihood Estimation of the Covariance Matrix for an SIRV
1179(2)
A.D. Keckler
F. THRESHOLD – Generation of Receive Thresholds for Various False Alarm Probabilities and Sampled Unknown Noise Distributions
1181(2)
P. Chakravarthi
These programs may be downloaded free of charge at the following Universal Resource Locator (URL) address: http://www.crcpress.com/e_products/downloads/download.asp?cat_no=DK6045
Index 1183


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