Principles of Modern Radar: Advanced Techniques

Principles of Modern Radar, Vol. II: Advanced Techniques......Page 4
Brief Contents......Page 8
Contents......Page 10
Why this Book was Written......Page 16
Acknowledgements......Page 17
To our Readers......Page 18
Publisher Acknowledgments......Page 19
Editors and Contributors......Page 21
1.1 Introduction......Page 26
1.2 Radar Modes......Page 27
1.3 Radar and System Topologies......Page 30
1.4.1 Waveforms and Spectrum......Page 31
1.4.2 Synthetic Aperture Radar......Page 33
1.4.3 Array Processing and Interference Mitigation Techniques......Page 35
1.4.4 Post-Processing Considerations......Page 37
1.4.5 Emerging Techniques......Page 38
1.5 Comments......Page 39
1.6 References......Page 40
PART I: Waveforms and Spectrum......Page 42
2.1 Introduction......Page 44
2.1.2 Key Points......Page 45
2.1.3.1 Common Variables......Page 46
2.1.3.2 Stretch Processing......Page 47
2.1.3.4 Nonlinear Frequency Modulated Waveforms......Page 48
2.1.3.6 Quadriphase Codes......Page 49
2.1.4 Acronyms......Page 50
2.2.2 Processing Bandwidth......Page 51
2.2.4.1 Transmit Waveform......Page 52
2.2.4.2 Receiver......Page 53
2.2.4.3 Processor Architecture......Page 55
2.2.4.4 Spectrum of the Baseband Signal......Page 56
2.2.4.5 Range Resolution......Page 57
2.2.4.7 Oscillator Over Sweep......Page 58
2.2.4.9 Compressed Range Response......Page 59
2.2.5 Example System Parameters......Page 61
2.2.6 Processing Gain......Page 62
2.2.7 Range-Sidelobe Suppression......Page 63
2.2.9 Summary......Page 64
2.3.2 Transmit Waveform......Page 65
2.3.3 Received Waveform......Page 66
2.3.4.1 Time Domain......Page 67
2.3.4.2 Frequency Domain......Page 68
2.3.4.3 Summary of Frequency-Domain Processing Steps......Page 70
2.3.4.4 Frequency-Domain Example......Page 71
2.3.5 Summary......Page 72
2.4 Nonlinear Frequency Modulated Waveforms......Page 73
2.4.1.1 Principle of Stationary Phase......Page 74
2.4.1.3 Parametric Equations......Page 75
2.4.2 Design Approaches......Page 76
2.4.3 Design Example......Page 77
2.4.5 Summary......Page 82
2.5 Stepped Frequency Waveforms......Page 83
2.5.2 Phase Rotation Used to Measure Range......Page 84
2.5.4 Creating a Range Profile......Page 85
2.5.5.1 Straddle Loss......Page 88
2.5.5.2 Range Ambiguities Associated with Frequency Stepping......Page 90
2.5.5.4 Choosing a Pulse Width in a Target- or Clutter-Rich Environment......Page 91
2.5.6 Impacts of Doppler......Page 93
2.6.2 BTQ Transformation......Page 95
2.6.4.1 Spectrum......Page 97
2.6.4.3 Ambiguity Surface......Page 99
2.7.3.1 Minimum ISR Filter......Page 100
2.7.3.2 Minimum ISR Example......Page 101
2.7.3.4 Tailoring the Sidelobe Response......Page 103
2.7.3.5 Reduced Peak Sidelobe Filters......Page 104
2.9 References......Page 106
2.10 Problems......Page 109
3.1 Introduction......Page 112
3.1.3 Acronyms......Page 113
3.2 Optimum MIMO Waveform Design for the Additive Colored Noise Case......Page 114
3.3 Optimum MIMO Design for Maximizing Signal-to-Clutter Ratio......Page 120
3.4 Optimum MIMO Design for Target Identification......Page 124
3.5 Constrained Optimum MIMO Radar......Page 129
3.6 Adaptive MIMO Radar......Page 134
3.6.1 Transmit-Independent Channel Estimation......Page 135
3.6.2 Dynamic MIMO Calibration......Page 136
3.7 Summary......Page 138
3.9 References......Page 139
3.10 Problems......Page 140
4.1.1 Organization......Page 144
4.1.2 Notation......Page 145
4.2 An Overview of MIMO Radar......Page 146
4.3 The MIMO Virtual Array......Page 147
4.4.1 Signal Model......Page 149
4.4.2 MIMO Signal Correlation Matrix......Page 152
4.4.3 MIMO Spatial Beamforming......Page 155
4.4.5 Phased Array versus Orthogonal Waveforms......Page 156
4.5.1 Classes of Waveforms for MIMO Radar......Page 160
4.5.3 Example: Up- and Down-Chirp......Page 161
4.6.1 MIMO SAR......Page 163
4.6.2 MIMO GMTI......Page 165
4.6.3 Distributed Apertures......Page 166
4.7 Summary......Page 167
4.9 References......Page 168
4.10 Problems......Page 170
5.1.1 Organization......Page 172
5.1.3 Notation......Page 173
5.1.4 Acronyms......Page 174
5.2.1 The Linear Model......Page 175
5.2.2 The Linear Model in Radar......Page 176
5.2.2.1 Radio Frequency Tomography Example......Page 177
5.2.2.2 The Ambiguity Function......Page 178
5.2.2.3 Multichannel Example......Page 180
5.2.2.4 Comments......Page 182
5.2.3 Regularization of the Linear Model through Sparsity......Page 183
5.2.4 l1 Regularization......Page 184
5.2.5 Performance Guarantees......Page 186
5.2.5.1 Kruskal Rank......Page 187
5.2.5.2 The Restricted Isometry Property......Page 188
5.2.5.3 Matrices that Satisfy RIP......Page 189
5.2.5.4 Mutual Coherence......Page 190
5.3 SR Algorithms......Page 191
5.3.1.1 Equivalent Optimization Problems and the Pareto Frontier......Page 193
5.3.1.2 Solvers......Page 195
5.3.2 Thresholding Algorithms......Page 197
5.3.2.1 Soft Thresholding......Page 198
5.3.3 Iterative Reweighting Schemes......Page 200
5.3.4 Greedy Methods......Page 201
5.3.5.1 Averaging Solutions......Page 203
5.3.5.2 Graphical Models......Page 204
5.3.6 Structured Sparsity......Page 205
5.3.7 Matrix Uncertainty and Calibration......Page 207
5.4 Sample Radar Applications......Page 208
5.4.1 Moving Target Imaging......Page 210
5.4.2 Multipass 3-D Circular SAR......Page 212
5.4.3 Multistatic Underground Imaging......Page 213
5.4.4 A Herglotz Kernel Method......Page 216
5.4.5 Single-Pulse Target Detection......Page 218
5.6 Further Reading......Page 221
5.8 References......Page 222
5.9 Problems......Page 232
PART II: Synthetic Aperture Radar......Page 234
6.1 Introduction......Page 236
6.1.2 Key Points......Page 237
6.1.4 Acronyms......Page 238
6.2.1 The Fourier Transform......Page 239
6.2.2 The Sinc Function......Page 240
6.2.3 Spatial Frequency and Plane Waves......Page 243
6.3 Spotlight SAR Nomenclature......Page 245
6.4 Sampling Requirements and Resolution......Page 250
6.4.1.1 Deramp on Receive......Page 251
6.4.2 Along-Track Sampling Requirements......Page 254
6.4.3 PRF Constraints......Page 256
6.5.1 The Tomographic Paradigm......Page 259
6.5.2 The Polar Formatting Algorithm......Page 260
6.5.3 Other Reconstruction Algorithms......Page 264
6.6 Image Metrics......Page 265
6.6.1.1 Ambiguity-to-Signal Ratio......Page 267
6.6.1.2 Integrated Sidelobe Ratio......Page 268
6.7 Phase Error Effects......Page 269
6.7.2 Quadratic Phase Errors......Page 271
6.7.3 Sinusoidal Phase Errors......Page 272
6.7.4 Wideband Phase Errors......Page 273
6.8 Autofocus......Page 275
6.8.1 Phase Difference Autofocus......Page 277
6.9 Summary and Further Reading......Page 278
6.10 References......Page 280
6.11 Problems......Page 282
7.1 Introduction......Page 284
7.1.2 Key Points......Page 286
7.1.3 Notation......Page 287
7.2 Review of Radar Imaging Concepts......Page 289
7.2.1 Resolution and Sampling......Page 290
7.2.2 Point Spread Response......Page 291
7.2.4 Doppler Beam Sharpening......Page 294
7.3.1 Azimuth Dechirp......Page 296
7.3.2 Range Migration Compensation......Page 301
7.3.3 Notes on Doppler Beam Sharpening......Page 310
7.4.1 Matched Filtering......Page 311
7.4.2 Range Stacking Algorithm......Page 313
7.4.3.1 Full Range-Doppler Algorithm......Page 317
7.4.3.2 Depth of Focus......Page 321
7.4.3.3 Frequency-Domain PSR for RDA......Page 323
7.4.3.4 RDA Approximations......Page 324
7.4.3.5 The Modified Range-Doppler Algorithm......Page 327
7.4.3.6 Notes on the Range-Doppler Algorithm......Page 329
7.5 Range Migration Algorithm......Page 330
7.5.2 Coordinate Systems and Frequencies......Page 331
7.5.3 Stolt Interpolation and RMA......Page 332
7.5.4 Simulated RMA Examples......Page 333
7.5.5 Stolt Approximation......Page 338
7.5.6 Chirp Scaling Algorithm......Page 340
7.6.1 PRF Lower Limits......Page 343
7.6.2 PRF Upper Limits......Page 346
7.6.3 Antenna Area and System Utility......Page 347
7.6.4 Slant Plane and Ground Plane......Page 348
7.6.5 Other Imaging Approahces......Page 349
7.6.6 Squinted Operation......Page 350
7.7.1 Remote Sensing Applications......Page 352
7.7.2 Penetration Applications......Page 354
7.8 Summary......Page 355
7.9 Further Reading......Page 356
7.10 References......Page 357
7.11 Problems......Page 358
8.1 Introduction......Page 362
8.1.3 Notation......Page 364
8.1.4 Acronyms......Page 366
8.2 Digital Terrain Models......Page 367
8.3.1 The Effect of Scatterer Elevation on 2-D SAR Images......Page 369
8.3.2 Measuring Depression Angle with Pairs of Range Measurements......Page 370
8.3.3 Estimating Elevation Variations from Phase Measurements......Page 372
8.3.4 Wrapped Phase......Page 376
8.3.6 Estimating Elevation Relative to a Reference Profile......Page 379
8.3.7 Range Foreshortening and Layover......Page 380
8.3.8 Other Three-Dimensional Coherent SAR Techniques......Page 383
8.4.1 One-Pass versus Repeat-Pass Operation......Page 384
8.4.2 Spaceborne versus Airborne InSAR......Page 385
8.4.3 Relation to Other Technologies for Estimating Elevation Profiles......Page 386
8.5 InSAR Processing Steps......Page 387
8.5.1 Image Pair Generation and Registration......Page 388
8.5.2 Estimation of the Wrapped Interferometric Phase Difference......Page 390
8.5.3.1 Path-Following Method......Page 391
8.5.3.2 Least Squares Method......Page 394
8.5.3.3 Network Flow Method......Page 396
8.5.4 Differences and Commonality of 2-D Phase Unwrapping Methods......Page 397
8.5.5 Multibaseline InSAR......Page 398
8.5.7 Absolute Elevation Estimation......Page 399
8.6 Error Sources......Page 400
8.6.1.1 Thermal and Quantization Noise......Page 401
8.6.1.2 Baseline Decorrelation......Page 402
8.6.1.4 Atmospheric and Weather Effects......Page 403
8.6.1.5 Interferogram Phase Statistics and Multilook Averaging......Page 404
8.6.1.6 Coherence and Interferometric System Design......Page 405
8.6.2.2 Other Systematic Error Sources......Page 406
8.7 Some Notable InSAR Systems......Page 407
8.7.1 Spaceborne Systems......Page 409
8.7.2 Airborne Systems......Page 410
8.8.1 Terrain Motion Mapping......Page 411
8.8.2 Coherent Change Detection......Page 413
8.8.3 Along-Track Interferometry......Page 414
8.10 Further Reading......Page 417
8.11 References......Page 418
8.12 Problems......Page 422
PART III: Array Processing and Interference Mitigation Techniques......Page 424
9.1 Introduction......Page 426
9.1.3 Notation......Page 427
9.1.4 Acronyms......Page 428
9.2 Digital Beamforming Fundamentals......Page 429
9.2.1 DBF Implementation Challenges......Page 431
9.2.2 Subarrays......Page 436
9.2.4 Multiple Simultaneous Beams on Receive......Page 439
9.3 Adaptive Jammer Cancellation......Page 444
9.3.1 Wiener Filter......Page 447
9.3.2 Maximum SINR......Page 448
9.3.3 Constrained Optimization......Page 450
9.3.3.1 Linearly Constrained Minimum Variance......Page 451
9.3.3.2 Generalized Sidelobe Canceller......Page 452
9.3.3.3 Beamformer Constraint Design......Page 453
9.3.4 Adaptive Weight Estimation......Page 454
9.3.4.1 Sample Matrix Inversion......Page 455
9.3.4.2 Weight Jitter Stabilization......Page 456
9.3.5 Performance Metrics......Page 457
9.3.5.3 SINR......Page 458
9.3.5.5 Cumulative Distribution Functions......Page 459
9.4.1 Sidelobe Blanker......Page 460
9.4.2 Sidelobe Canceller......Page 462
9.4.3 Beamspace Adaptive Cancellation......Page 465
9.5 Wideband Cancellation......Page 466
9.5.1 Jammer Dispersion over Bandwidth......Page 468
9.5.2 Joint Spatial-Frequency Domain Wideband Beamformer......Page 469
9.5.4 LFM/Strectch......Page 471
9.8 References......Page 474
9.9 Problems......Page 476
10.1 Introduction......Page 478
10.1.1 STAP Overview......Page 479
10.1.2 Organization......Page 480
10.1.4 Notation and Operations......Page 481
10.1.5 Variable Names......Page 482
10.1.6 Acronyms......Page 483
10.2.1 Spatial Sampling and Beamforming......Page 484
10.2.2 Temporal Sampling and Doppler Processing......Page 489
10.2.3 Space-Time Signals......Page 491
10.3 Space-Time Properties of Ground Clutter......Page 497
10.4 Space-Time Processing......Page 499
10.4.1.1 Detection......Page 501
10.4.1.2 SINR Loss......Page 502
10.5.1 Maximum SINR Filter......Page 503
10.5.2 Minimum Variance Beamformer......Page 506
10.5.3 Generalized Sidelobe Canceller......Page 507
10.6 STAP Processing Architectures and Methods......Page 508
10.6.1 Reduced-Dimension STAP......Page 509
10.6.1.1 Element Space Post-Doppler......Page 510
10.6.1.2 Post-Doppler Beamspace......Page 511
10.6.1.3 Post-Doppler STAP Performance......Page 512
10.6.2 Pre-Doppler STAP......Page 513
10.6.3 Reduced-Rank STAP......Page 514
10.6.5 Processing Block Diagram......Page 515
10.7 Other Considerations......Page 516
10.7.2 Nonstationary Angle-Doppler Region of Support......Page 517
10.9 Summary......Page 518
10.10 References......Page 519
10.11 Problems......Page 521
11.1 Introduction......Page 524
11.2.1.1 Principle and objectives......Page 525
11.2.1.2 Limitations of Digital Beam Forming......Page 526
11.2.2.1 Principles......Page 527
11.2.2.2 Circulating pulse......Page 529
11.2.2.3 Fast Scanning (intra-pulse scanning) [6]......Page 530
11.2.2.4 Circulating code [7],[5]......Page 531
11.2.2.5 Bidimensional frequency coding [15]......Page 532
11.2.3.1 Target coherence......Page 534
11.2.3.2 Diversity gain......Page 537
11.2.4 Colored transmission trade-offs and applications......Page 538
11.3 Interleaved Scanning (Slow-Time Space-Time Coding)......Page 540
11.4.1 Time domain: periodic vs high time-bandwidth waveforms......Page 542
11.4.2 Space domain: sub-arrays and grating lobes......Page 543
11.5 Wideband MTI [12], [4]......Page 545
11.6 Conclusion......Page 549
11.8 References......Page 550
11.9 Problems......Page 551
12.1 Introduction......Page 554
12.1.3 Notation......Page 555
12.1.4 Abbreviations......Page 556
12.2.1 Electronic Attack Overview......Page 558
12.2.2 Jammer Types......Page 560
12.2.2.1 Noncoherent Jammers......Page 561
12.2.2.2 Coherent Jammers......Page 562
12.2.3.1 Noncoherent Masking Techniques......Page 565
12.2.4.1 False Targets......Page 567
12.2.4.2 Range and Velocity Track Deception......Page 568
12.2.4.3 Angle Track Deception......Page 569
12.3.1 Signal and Thermal Noise Formulas......Page 570
12.3.2 Keeping Track of Losses......Page 571
12.3.3 Noise Jammer Formulas......Page 572
12.3.4 Noise Jammer Computation Example......Page 573
12.3.5 Coherent Jammer Formulas......Page 574
12.3.6 Coherent Jammer Computation Example......Page 576
12.3.7 Jammer Received Power Computation......Page 577
12.4 EP Overview......Page 578
12.5 Antenna-Based EP......Page 579
12.5.3 Sidelobe Blanking......Page 580
12.5.4 Sidelobe Cancellation......Page 581
12.5.5 Main Lobe Cancellation......Page 582
12.5.8 Passive Conical Scanning......Page 583
12.5.9 Monopulse Angle Measurement......Page 584
12.5.10 Low Cross Polarization Antenna......Page 585
12.6.2 Transmit Power Reduction......Page 586
12.7.1 Wide-Pulse Waveform......Page 587
12.7.3 Burnthrough Waveforms......Page 588
12.7.5 Pulse Compression Range Resolution......Page 589
12.7.6 Doppler Resolution Waveform......Page 590
12.7.8 Multiple Simultaneous Frequency Radiation......Page 591
12.8.1 RF Preselection......Page 592
12.8.2 Image Rejection......Page 593
12.8.4 Notch Filtering......Page 594
12.8.5 Wideband Limiting......Page 595
12.8.8 Least Jammed Frequency Selection......Page 596
12.9.2 Alternate Constant False Alarm Rate Detection......Page 597
12.9.4 Data Editing......Page 599
12.9.5 Guard Gates......Page 600
12.10 Data Processor-Based EP......Page 601
12.10.2 Radar Cross Section Statistics......Page 602
12.10.4 Range-Doppler Track Comparison......Page 603
12.10.5 Track Filter Acceleration Limit......Page 604
12.10.7 Angle Gating......Page 605
12.11 Summary......Page 606
12.13 References......Page 609
12.14 Problems......Page 610
PART IV: Post-Processing Considerations......Page 612
13.1 Introduction......Page 614
13.1.2 Key Points......Page 616
13.1.3 List of Symbols......Page 617
13.1.4 Acronyms......Page 618
13.2.1 Fundamentals of Wave Polarization......Page 619
13.2.1.2 Circular Polarization......Page 620
13.2.1.3 Eliptical Polarization......Page 621
13.2.2 Stokes Parameters and Poincaré Sphere......Page 623
13.3 Scattering Matrix......Page 626
13.3.1 Sinclair Formulation......Page 627
13.3.2 Optimal Polarizations......Page 629
13.3.3 Partial Polarization and Mueller Matrix......Page 632
13.4.1 Targets......Page 636
13.4.1.1 Target Feature Extraction......Page 637
13.4.2 Rain Clutter......Page 641
13.4.4 Sea Clutter......Page 642
13.5 Measurement of the Scattering Matrix......Page 643
13.7 Further Reading......Page 647
13.8 References......Page 648
13.9 Problems......Page 651
14.1 Introduction......Page 656
14.2 Unified Framework for ATR......Page 658
14.3.1 Common Metrics......Page 659
14.3.2.1 Performance Prediction in the Neyman-Pearson Framework......Page 660
14.3.2.2 Performance Prediction in the Bayesian Framework......Page 661
14.3.3 Using Performance Prediction Tools in the Design Process......Page 662
14.4.1 Step 1: Identify the Target Set......Page 663
14.4.2 Step 2: Select the Feature Set......Page 664
14.4.2.2 Candidate Features......Page 665
14.4.3.2 Image Formation and Pre-processing Techniques......Page 668
14.4.3.3 Pre-screening and Discrimination Algorithms......Page 669
14.4.4 Test the Feature Set......Page 671
14.5.1 Image Formation......Page 677
14.5.2 Scattering Models......Page 678
14.5.3 Candidate Features......Page 679
14.6 Passive Radar ATR......Page 681
14.7 High-Resolution Range Profiles......Page 683
14.9 Further Reading......Page 686
14.10 References......Page 687
14.11 Problems......Page 693
15.1 Review of Tracking Concepts......Page 694
15.1.1 Covariances......Page 696
15.1.2 Measurement-to-track Data Association......Page 697
15.1.2.1 Gating......Page 698
15.1.2.3 Assignment Algorithms......Page 699
15.1.3 Track Filtering......Page 700
15.2.1 Measurement-to-track Data Association......Page 702
15.2.1.1 Feature-assisted Tracking......Page 703
15.2.1.2 Multiple Hypothesis Tracking......Page 707
15.2.2 Modeling Target Dynamics......Page 711
15.2.2.1 Interacting Multiple Model (IMM) Estimators......Page 713
15.2.3 VS-IMM Estimators......Page 715
15.3.1 Sensor Fusion Architectures......Page 716
15.3.3 Track-level Fusion and Associated Challenges......Page 717
15.3.4 Sensor Fusion Challenges Common to Both Paradigms......Page 719
15.5 Further Reading......Page 720
15.6 References......Page 721
15.7 Problems......Page 723
PART V: Emerging Techniques......Page 728
16.1 Introduction......Page 730
16.1.2 Notation......Page 733
16.2 Characterizing the Human Radar Return......Page 735
16.2.1 Expected Radar Return from a Human Target......Page 736
16.2.2 Human Kinematic Models......Page 737
16.2.3 Computing Time-Varying Ranges with the Boulic-Thalmann Model......Page 741
16.2.4 Modeling Human Radar Cross Section......Page 743
16.3 Spectrogram Analysis of Human Returns......Page 744
16.4.2 Mitigating the Effects of Clutter with STAP......Page 747
16.4.3 Inherent Output SNR Losses for Human Targets in Typical Detectors......Page 750
16.5 Exploiting Knowledge for Detection and Classification......Page 752
16.7 Further Reading......Page 754
16.8 References......Page 755
16.9 Problems......Page 761
17.1 Introduction......Page 764
17.1.1 Organization......Page 768
17.1.3 Notation......Page 769
17.1.4 Acronyms......Page 771
17.2 Evaluation of the 2D-CCF for the Passive Radar Coherent Integration......Page 772
17.2.1 Efficient Implementations of the 2D-CCF Based on the Fast Fourier Transform......Page 774
17.2.2 Suboptimum Implementations of the 2D-CCF......Page 776
17.3 Direct Signal and Multipath/Clutter Cancellation Techniques......Page 780
17.3.1 Extensive Cancellation Algorithm......Page 783
17.3.2 ECA Batches......Page 785
17.3.3 ECA Batches and Stages (ECA-B&S)......Page 786
17.4 Signal Processing Techniques for Reference Signal Cleaning and Reconstruction......Page 791
17.4.1 Constant Modulus Algorithm for Reference Signal Cleaning Using Analog Modulation......Page 792
17.4.2 Reference Signal Reconstruction for Digital Transmissions......Page 796
17.5 2D-CCF Sidelobe Control......Page 800
17.5.1 Range Sidelobes Control for 2D-CCF in WiFi-Based PBR......Page 801
17.5.2 Range Sidelobes Control for 2D-CCF in WiMAX-Based PBR......Page 805
17.5.3 2D-CCF Shape Control for DVB-T Signals......Page 811
17.6.1 Linear–Nonlinear Integration of Multiple Frequency Passive Radar Channels......Page 816
17.6.2 Exploitation of Multiple Polarimetric Passive Radar Channels......Page 828
17.6.3 Adaptive Antenna Array for
Passive Radar......Page 833
17.7 Summary......Page 839
17.10 References......Page 840
17.11 Problems......Page 844
Appendix A: Answers to Selected Problems......Page 848
Supplements......Page 854
Index......Page 858