Table of Contents
Preface xv
Acknowledgments xix
Selected Symbols xxi
Selected Acronyms xxix
1 Introduction to Radar Systems and Signal Processing 1
1.1 History and Applications of Radar 1
1.2 Basic Radar Functions 2
1.3 Elements of a Radar 5
1.3.1 Radar Frequencies 7
1.3.2 Radar Waveforms and Transmitters 8
1.3.3 Antennas 10
1.3.4 Virtual Elements and Virtual Arrays 16
1.3.5 Receivers 17
1.4 Common Threads in Radar Signal Processing 22
1.4.1 Signal-to-Interference Ratio 22
1.4.2 Resolution and Region of Support 23
1.4.3 Integration and Phase History Modeling 28
1.5 A Preview of Basic Radar Signal Processing 30
1.5.1 Radar Time Scales 30
1.5.2 Phenomenology 32
1.5.3 Signal Conditioning and Interference Suppression 32
1.5.4 Detection 35
1.5.5 Measurements and Track Filtering 37
1.5.6 Imaging 38
1.6 Radar Literature 40
1.6.1 Introductions to Radar Systems and Applications 40
1.6.2 Basic Radar Signal Processing 40
1.6.3 Advanced Radar Signal Processing 41
1.6.4 Radar Applications 41
1.6.5 Current Radar Research 42
References 42
Problems 43
2 Signal Models 47
2.1 Components of a Radar Signal 47
2.2 Modeling Amplitude 48
2.2.1 Simple Point Target Radar Range Equation 48
2.2.2 Distributed Target Forms of the Range Equation 51
2.2.3 Radar Cross Section 57
2.2.4 Radar Cross Section for Meteorological Targets 58
2.2.5 Statistical Description of Radar Cross Section 60
2.2.6 Target Fluctuation Models 76
2.2.7 Swerling Models 79
2.2.8 Effect of Target Fluctuations on Doppler Spectrum 80
2.3 Modeling Clutter 81
2.3.1 Behavior of σ0 82
2.3.2 Signal-to-Clutter Ratio 84
2.3.3 Temporal and Spatial Correlation of Clutter 85
2.3.4 Compound Models of Radar Cross Section 87
2.4 Noise Model and Signal-to-Noise Ratio 89
2.5 Jamming 92
2.6 Electromagnetic Interference 92
2.7 Frequency Models: The Doppler Shift 93
2.7.1 Doppler Shift 93
2.7.2 The Stop-and-Hop Approximation and Phase History 95
2.7.3 Measuring Doppler Shift: Spatial Doppler 97
2.8 Spatial Models 99
2.8.1 Coherent Scattering 99
2.8.2 Variation with Angle 101
2.8.3 Variation with Range 104
2.8.4 Noncoherent Scattering 105
2.8.5 Projections 106
2.8.6 Multipath 106
2.9 Spectral Model 108
2.10 Summary 109
References 110
Problems 112
3 Radar Data Acquisition and Organization 117
3.1 A Signal Processor's Radar Architecture Model 118
3.2 Measuring a Range Profile 119
3.2.1 Pulsed Radar Range Profile: One Pulse in Fast Time 119
3.2.2 FMCW Radar Range Profile: One Sweep in Fast Time 125
3.3 Multiple Range Profiles: Slow Time and the CPI 131
3.4 Multiple Channels: The Datacube 138
3.5 Dwells 140
3.6 Sampling the Doppler Spectrum 141
3.6.1 The Nyquist Rate in Doppler 141
3.6.2 Straddle Loss 143
3.7 Sampling in the Spatial and Angle Dimensions 148
3.7.1 Spatial Array Sampling 148
3.7.2 Sampling in Angle 149
3.8 I/Q Imbalance and Digital I/Q 151
3.8.1 I/Q Imbalance and Offset 152
3.8.2 Correcting I/Q Errors 154
3.8.3 Digital I/Q 157
3.9 Summary 161
References 162
Problems 163
4 Radar Waveforms 167
4.1 Introduction 167
4.2 The Waveform Matched Filter 169
4.2.1 The Matched Filter 169
4.2.2 Matched Filter for the Simple Pulse 171
4.2.3 All-Range Coherent Matched Filtering 173
4.2.4 Straddle Loss 174
4.2.5 Range Resolution of the Matched Filter 174
4.3 Matched Filtering of Moving Targets 175
4.4 The Ambiguity Function 177
4.4.1 Definition and Properties of the Ambiguity Function 177
4.4.2 Ambiguity Function of the Simple Pulse 181
4.5 The Pulse Burst Waveform 184
4.5.1 Matched Filter for the Pulse Burst Waveform 184
4.5.2 Pulse-by-Pulse Processing 186
4.5.3 Range Ambiguity 187
4.5.4 Doppler Response of the Pulse Burst Waveform 190
4.5.5 Ambiguity Function for the Pulse Burst Waveform 191
4.5.6 The Slow-Time Spectrum and the Periodic Ambiguity Function 195
4.6 Frequency-Modulated Pulse Compression Waveforms 196
4.6.1 Linear Frequency Modulation 197
4.6.2 The Principle of Stationary Phase 200
4.6.3 Ambiguity Function of the LFM Waveform 202
4.6.4 Range-Doppler Coupling 204
4.6.5 Stretch Processing 205
4.7 Range Sidelobe Control for FM Waveforms 210
4.7.1 Matched Filter Frequency Response Shaping 210
4.7.2 Matched Filter Impulse Response Shaping 213
4.7.3 Waveform Spectrum Shaping 213
4.8 Frequency-Coded Waveforms 216
4.8.1 The Stepped Frequency Waveform 216
4.8.2 The Stepped Chirp Waveform 220
4.8.3 Costas Frequency Codes 221
4.9 Phase-Modulated Pulse Compression Waveforms 223
4.9.1 Biphase Codes 225
4.9.2 Polyphase Codes 230
4.9.3 Mismatched Phase Code Filters 234
4.10 Continuous Wave Radar 235
4.10.1 Single-Frequency CW 236
4.10.2 Periodically Modulated CW 237
4.10.3 Linear Frequency-Modulated CW 238
4.10.4 "Fast Chirp" Linear Frequency-Modulated CW 240
4.10.5 Sidelobe Control in Linear FMCW 242
4.10.6 Other CW Waveforms 242
4.11 Frequency-Modulated versus Phase-Modulated Waveforms 242
4.12 Summary 243
References 244
Problems 245
5 Doppler Processing 251
5.1 Introduction 251
5.2 Moving Platform Effects on the Doppler Spectrum 253
5.3 Moving Target Indication 256
5.3.1 Pulse Cancellers 259
5.3.2 Vector Formulation of the Matched Filter 262
5.3.3 Matched Filters for Clutter Suppression 263
5.3.4 Blind Speeds and Staggered PRFs 266
5.3.5 MTI Figures of Merit 273
5.3.6 Limitations to MTI Performance 278
5.4 Pulse Doppler Processing 280
5.4.1 The Discrete-Time Fourier Transform of a Moving Target 281
5.4.2 Sampling the DTFT: The Discrete Fourier Transform 283
5.4.3 The DFT of Noise 285
5.4.4 Pulse Doppler Processing Gain 286
5.4.5 Matched Filter and Filterbank Interpretations of Pulse Doppler Processing with the DFT 286
5.4.6 Fine Doppler Estimation 288
5.4.7 Modern Spectral Estimation in Pulse Doppler Processing 294
5.4.8 CPI-to-CPI Stagger and Blind Zone Maps 295
5.5 Pulse Pair Processing 300
5.6 Additional Doppler Processing Issues 305
5.6.1 Range Migration and the Keystone Transform 305
5.6.2 Combined MTI and Pulse Doppler Processing 309
5.6.3 Transient Effects 310
5.6.4 PRF Regimes 311
5.6.5 PRF Selection 314
5.6.6 Ambiguity Resolution 317
5.7 Clutter Mapping 321
5.8 The Moving Target Detector 322
5.9 MTI for Moving Platforms: Ground Moving Target Indication 323
5.9.1 Simplified GMTI Clutter and Target Models 324
5.9.2 DPCA and ATI 326
5.9.3 Clutter Suppression Interferometry 330
5.9.4 Analysis of Adaptive DPCA 331
5.10 Summary 334
References 335
Problems 337
6 Detection Fundamentals 343
6.1 Introduction 343
6.2 Radar Detection as Hypothesis Testing 344
6.2.1 The Neyman-Pearson Detection Rule 345
6.2.2 The Likelihood Ratio Test 345
6.3 Threshold Detection in Coherent Systems 354
6.3.1 The Gaussian Case for Coherent Receivers 355
6.3.2 Unknown Parameters and Threshold Detection 358
6.3.3 Linear and Square Law Detectors 364
6.3.4 Other Unknown Parameters 365
6.4 Threshold Detection of Radar Signals 366
6.4.1 Coherent, Noncoherent, and Binary Integration 366
6.4.2 Nonfluctuating Targets 368
6.4.3 Albersheim's Equation 373
6.4.4 Fluctuating Targets 375
6.4.5 Simplified Equations for PD for Some Swerling Cases 378
6.4.6 Shnidman's Equation 381
6.4.7 Detection in Clutter 383
6.4.8 Binary Integration 385
6.4.9 Integration Summary 389
6.5 Constant False Alarm Rate Detection 390
6.5.1 The Effect of Unknown Interference Power on False Alarm Probability 390
6.5.2 Cell-Averaging CFAR 392
6.5.3 Analysis of Cell-Averaging CFAR 394
6.5.4 CA CFAR Limitations 398
6.5.5 Extensions to Cell-Averaging CFAR 404
6.5.6 Order Statistic CFAR 408
6.5.7 Adaptive CFAR 412
6.5.8 CFAR for Two-Parameter PDFs 413
6.5.9 Temporal CFAR 414
6.5.10 Distribution-Free CFAR 417
6.6 System-Level Control of False Alarms 418
6.7 Summary 419
References 420
Problems 422
7 Measurements and Introduction to Tracking 425
7.1 Estimators 426
7.1.1 Estimator Properties 426
7.1.2 The Cramèr-Rao Lower Bound 429
7.1.3 The CRLB and Signal-to-Noise Ratio 431
7.1.4 Maximum Likelihood Estimators 432
7.2 Range, Doppler, and Angle Estimators 434
7.2.1 Range Estimators 434
7.2.2 Doppler Signal Estimators 446
7.2.3 Angle Estimators 455
7.3 Introduction to Tracking 469
7.3.1 Optimal Combination of Two Noisy Measurements 470
7.3.2 Sequential Least Squares Estimation 471
7.3.3 The α-β Filter 475
7.3.4 The Kalman Filter 480
7.3.5 The Tracking Cycle 487
7.4 Summary 492
References 493
Problems 495
8 Introduction to Synthetic Aperture Imaging 499
8.1 Fundamental SAR Concepts and Relations 503
8.1.1 Cross-Range Resolution in Radar 503
8.1.2 The Synthetic Aperture Viewpoint 505
8.1.3 Doppler Viewpoint 512
8.1.4 SAR Coverage and Sampling 514
8.2 Stripmap SAR Data Characteristics 518
8.2.1 Stripmap SAR Geometry 518
8.2.2 Stripmap SAR Data Set 521
8.3 Stripmap SAR Image Formation Algorithms 524
8.3.1 Doppler Beam Sharpening 525
8.3.2 Quadratic Phase Error Effects 528
8.3.3 Range-Doppler Algorithms 533
8.3.4 Depth of Focus 539
8.3.5 Range Migration Algorithm 540
8.4 Spotlight SAR Data Characteristics 544
8.5 The Polar Format Image Formation Algorithm for Spotlight SAR 550
8.6 Backprojection 552
8.7 Interferometric SAR 556
8.7.1 The Effect of Height on a SAR Image 556
8.7.2 IFSAR Processing Steps 559
8.8 Other Considerations 564
8.8.1 Motion Compensation 564
8.8.2 Autofocus 567
8.8.3 Speckle Reduction 574
8.8.4 Moving Targets 575
8.9 Summary 580
References 581
Problems 583
9 Introduction to Array Processing 587
9.1 Virtual Arrays 587
9.2 Beamforming and Beam Steering 591
9.2.1 Time Delay Steering 592
9.2.2 Phase Steering 593
9.2.3 Narrowband Phase Beamforming 595
9.2.4 Adaptive Beamforming 598
9.2.5 Adaptive Beamforming with Preprocessing 603
9.3 Space-Time Signal Environment 606
9.4 Space-Time Signal Modeling 609
9.5 Processing the Space-Time Signal 613
9.5.1 Optimum Matched Filtering 613
9.5.2 STAP Metrics 613
9.5.3 Relation to Displaced Phase Center Antenna Processing 617
9.5.4 Adaptive Matched Filtering 619
9.6 Reduced-Dimension STAP 622
9.7 Advanced STAP Algorithms and Analysis 623
9.8 Limitations to STAP 625
9.9 Summary 626
References 626
Problems 628
A Selected Topics in Probability and Random Processes 631
A.1 Probability Density Functions and Likelihood Functions 631
A.2 Common Probability Distributions in Radar 632
A.2.1 Power Distributions 633
A.2.2 Amplitude Distributions 641
A.2.3 The Unfortunate Tendency in Radar to Call Power Distributions by the Name of the Amplitude Distribution 644
A.2.4 Phase Distributions 644
A.3 Estimators and the Cramèr-Rao Lower Bound 645
A.3.1 The Cramèr-Rao Lower Bound on Estimator Variance 646
A.3.2 The CRLB for Transformed Parameters 648
A.3.3 Signals in Additive White Gaussian Noise 648
A.3.4 Signals with Multiple Parameters in AWGN 649
A.3.5 Complex Signals and Parameters in AWGN 650
A.3.6 Finding Minimum Variance Estimators 651
A.4 Random Signals in Linear Systems 652
A.4.1 Correlation Functions 652
A.4.2 Correlation and Linear Estimation 653
A.4.3 Power Spectrum 654
A.4.4 White Noise 655
A.4.5 The Effect of LSI Systems on Random Signals 655
References 658
B Selected Topics in Digital Signal Processing 659
B.1 Fourier Transforms 659
B.2 Windowing 664
B.3 Sampling, Quantization, and A/D Converters 668
B.3.1 Sampling 668
B.3.2 Quantization 672
B.3.3 A/D Conversion Technology 675
B.4 Spatial Frequency 676
B.5 Correlation 678
B.6 Vector-Matrix Representations and Eigenanalysis 680
B.6.1 Basic Definitions and Operations 680
B.6.2 Basic Eigenanalysis 682
B.6.3 Eigenstructure of Sinusoids in White Noise 683
B.7 Instantaneous Frequency 685
B.8 Decibels 685
References 687
Problems 687
Index 689
