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Adaptive Detection of Multichannel Signals Exploiting Persymmetry

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This book offers a systematic presentation of persymmetric adaptive detection, including detector derivations and the definition of key concepts, followed by detailed discussion relating to theoretical underpinnings, design methodology, design considerations, and techniques enabling its practical implementation.

The received data for modern radar systems are usually multichannel, namely, vector-valued, or even matrix-valued. Multichannel signal detection in Gaussian backgrounds is a fundamental problem for radar applications. With an overarching focus on persymmetric adaptive detectors, this book presents the mathematical models and design principles necessary for analyzing the behavior of each kind of persymmetric adaptive detector. Building upon that, it also introduces new design approaches and techniques that will guide engineering students as well as radar engineers toward efficient detector solutions, especially in challenging sample-starved environments where training data are limited.

This book will be of interest to students, scholars, and engineers in the field of signal processing. It will be especially useful for those who have a solid background in statistical signal processing, multivariate statistical analysis, matrix theory, and mathematical analysis.

Author(s): Jun Liu, Danilo Orlando, Chengpeng Hao, Weijian Liu
Publisher: CRC Press
Year: 2022

Language: English
Pages: 313
City: Boca Raton

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
List of Abbreviations
List of Symbols
1. Basic Concept
1.1. Multichannel Radar
1.2. Adaptive Detection of Multichannel Signal
1.3. Persymmetric Structure of Covariance Matrix
1.4. Organization and Outline of the Book
1.A. Detector Design Criteria
1.A.1. Nuisance Parameter
1.A.1.1. Rao Test
1.A.1.2. Wald Test
1.A.1.3. GLRT
1.A.2. No Nuisance Parameter
1.A.2.1. Rao Test
1.A.2.2. Wald Test
1.A.2.3. GLRT
Bibliography
2. Output SINR Analysis
2.1. Problem Formulation
2.1.1. Unstructured SMI Beamformer
2.1.1.1. Matched Case
2.1.1.2. Mismatched Case
2.1.2. Persymmetric SMI Beamformer
2.2. Average SINR in Matched Case
2.3. Average SINR in Mismatched Cases
2.3.1. Homogeneous Case
2.3.2. Non-Homogeneous Case
2.4. Simulation Results
2.A. Derivation of E(p match per)
2.B. Proof of Theorem 2.3.1
2.C. Derivations of (2.B.22)
2.D. Derivations of (2.B.28)
2.E. Derivations of (2.B.36)
2.F. Derivation of E(ww) in the Mismatched Case
Bibliography
3. Invariance Issues under Persymmetry
3.1. Preliminary Theory
3.2. Homogeneous Environment
3.2.1. Stochastic Representation
3.2.2. Invariant Detectors
3.2.3. Statistical Characterization
3.2.3.1. LRT-Based Decision Schemes
3.3. Partially Homogeneous Environment
3.3.1. Invariant Detectors for Partially Homogeneous Scenarios
3.A. Proof of Theorem 3.2.1
3.B. Derivation of (3.38)
3.C. Proof of Theorem 3.2.2
3.D. Proof of Theorem 3.2.3
3.E. Proof of Theorem 3.2.5
3.F. Proof of Theorem 3.3.1
Bibliography
4. Persymmetric Adaptive Subspace Detector
4.1. Problem Formulation
4.2. Persymmetric One-Step GLRT
4.3. Threshold Setting
4.3.1. Transformation from Complex Domain to Real Domain
4.3.2. Statistical Characterizations
4.3.2.1. Equivalent Form of XTPX
4.3.2.2. Equivalent Form of XTM-1X
4.3.2.3. Statistical Distribution of Λ
4.3.3. Probability of False Alarm
4.4. Numerical Examples
4.A. Derivations of (4.13)
4.B. Derivations of (4.38)
4.C. Derivations of (4.62)
Bibliography
5. Persymmetric Detectors with Enhanced Rejection Capabilities
5.1. Problem Formulation
5.2. Detector Design
5.2.1. Persymmetric Rao Test
5.2.2. Persymmetric GLRT
5.3. Numerical Examples
5.A. Derivations of (5.32)
Bibliography
6. Distributed Target Detection in Homogeneous Environments
6.1. Persymmetric One-Step GLRT
6.1.1. Detector Design
6.1.2. Analytical Performance
6.1.2.1. Transformation from Complex Domain to Real Domain
6.1.2.2. Statistical Properties
6.1.2.3. Detection Probability
6.1.2.4. Probability of False Alarm
6.2. Persymmetric Two-Step GLRT
6.2.1. Detector Design
6.2.2. Analytical Performance
6.2.2.1. Statistical Properties
6.2.2.2. Probability of False Alarm
6.2.2.3. Detection Probability
6.3. Numerical Examples
6.A. Derivations of (6.31)
6.B. Derivations of (6.39)
6.C. Derivations of (6.69)
6.D. Proof of Theorem 6.2.1
Bibliography
7. Robust Detection in Homogeneous Environments
7.1. Problem Formulation
7.2. Detection Design
7.2.1. GLRT Criterion
7.2.1.1. One-Step GLRT
7.2.1.2. Two-Step GLRT
7.2.2. Wald Criterion
7.2.2.1. One-Step Wald Test
7.2.2.2. Two-Step Wald Test
7.2.3. Rao Criterion
7.3. Numerical Examples
7.A. Derivations of (7.36)
Bibliography
8. Adaptive Detection with Unknown Steering Vector
8.1. Problem Formulation
8.2. Per-SNT Detector
8.2.1. Detector Design
8.2.2. Threshold Setting for Per-SNT
8.2.2.1. Transformation from Complex Domain to Real Domain
8.2.2.2. Probability of False Alarm for Per-SNT
8.3. Per-GLRT Detector
8.3.1. Detector Design
8.3.2. Threshold Setting for Per-GLRT
8.4. Numerical Examples
8.4.1. Probability of False Alarm
8.4.2. Detection Performance
8.4.3. Measured Data
8.A. Derivations of (8.13)
8.B. Proof of Theorem 8.2.1
8.C. Derivations of (8.41) and (8.42)
8.D. Derivation of (8.64)
8.E. CFARness of the Per-GLRT
Bibliography
9. Adaptive Detection in Interference
9.1. Problem Formulation
9.2. GLRT Detection
9.2.1. One-Step GLRT
9.2.2. Two-Step GLRT
9.3. Probability of False Alarm for 1S-PGLRT-I
9.3.1. p is 1
9.3.2. p is 2
9.3.3. p is 3
9.3.4. p is 4
9.3.5. H = 1
9.3.6. H = 2
9.3.7. Arbitrary H and p
9.4. Numerical Examples
9.A. Derivations of (9.47)
Bibliography
10. Adaptive Detection in Partially Homogeneous Environments
10.1. Detector Design
10.1.1. One-Step GLRT
10.1.2. Two-Step GLRT
10.1.3. Rao and Wald Tests
10.2. Numerical Examples
Bibliography
11. Robust Detection in Partially Homogeneous Environments
11.1. Problem Formulation
11.2. Robust Detection
11.2.1. GLRT
11.2.2. Wald Test
11.2.3. Rao Test
11.3. CFARness Analysis
11.4. Numerical Examples
11.A. Derivations of (11.47)
Bibliography
12. Joint Exploitation of Persymmetry and Symmetric Spectrum
12.1. Problem Formulation
12.2. Rao Test
12.3. Two-Step GLRT and Wald Test
12.3.1. Homogeneous Environment
12.3.2. Partially Homogeneous Environment
12.4. Numerical Examples
12.4.1. Homogeneous Environment
12.4.2. Partially Homogeneous Environment
Bibliography
13. Adaptive Detection after Covariance Matrix Classification
13.1. Problem Formulation
13.2. Architecture Design
13.2.1. Classification Stage
13.2.2. Detection Stage
13.2.2.1. Detector under H1
13.2.2.2. Detector under H2
13.2.2.3. Detector under H3
13.2.2.4. Detector under H4
13.2.2.5. Detector under H5
13.2.2.6. Detector under H6
13.2.3. Threshold Setting
13.3. Numerical Results
Bibliography
14. MIMO Radar Target Detection
14.1. Persymmetric Detection in Colocated MIMO Radar
14.1.1. Problem Formulation
14.1.2. Adaptive Detector
14.1.3. Analytical Performance
14.1.3.1. Transformation from Complex Domain to Real Domain
14.1.3.2. Statistical Properties
14.1.3.3. Detection Probability
14.1.3.4. Probability of False Alarm
14.1.4. Numerical Examples
14.2. Persymmetric Detection in Distributed MIMO Radar
14.2.1. Signal Model
14.2.2. Persymmetric GLRT Detector
14.2.2.1. Detector Design
14.2.2.2. Performance Analysis
14.2.3. Persymmetric SMI Detector
14.2.4. Simulations Results
14.A. Derivation of (14.94)
14.B. Equivalent Transformation of Λ
Bibliography