Basic radar analysis

Dedication......Page 4
Title page......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 16
Acknowledgements......Page 18
 1.2 Radar Types......Page 19
 1.3 Range Measurement......Page 21
 1.4 Ambiguous Range......Page 22
 1.5 Usable Range and Instrumented Range......Page 24
 1.6 Range-Rate Measurement (Doppler)......Page 25
 1.8 dB Arithmetic......Page 29
 1.9 Complex Signal Notation......Page 30
 1.10 Radar Block Diagram......Page 32
 1.11 Exercises......Page 33
 References......Page 35
 2.2 Basic Radar Range Equation......Page 36
  2.2.1 Derivation of ES......Page 38
  2.2.2 Derivation of EN......Page 45
 2.3 A Power Approach to SNR......Page 48
 2.4 Example 1......Page 49
 2.6 Search Radar Range Equation......Page 51
 2.7 Example 2......Page 54
 2.8 Radar Range Equation Summary......Page 57
 2.9 Exercises......Page 58
 References......Page 60
 Appendix 2A: Derivation of Search Solid Angle Equation......Page 61
 3.2 RCS of Simple Shapes......Page 63
 3.3 Swerling RCS Models......Page 69
  3.3.1 Swerling Statistics......Page 70
  3.3.2 Swerling Fluctuation Models......Page 71
  3.3.3 Math Behind the Fluctuation Model......Page 73
 3.4 Relation of Swerling Models to Actual Targets......Page 76
  3.4.1 Simulating Swerling Targets......Page 77
 3.5 Frequency Agility and SW2 or SW4 Targets......Page 82
  3.5.1 Special Cases......Page 85
 3.6 Exercises......Page 86
 References......Page 87
 4.1 Introduction......Page 89
  4.2.1 Thevenin Equivalent Circuit of a Noisy Resistor......Page 90
  4.2.2 Multiple Noisy Resistors......Page 91
 4.3 Equivalent/Effective Noise Temperature for Active Devices......Page 92
  4.4.1 Derivation of Noise Figure......Page 93
  4.4.2 Attenuators......Page 94
 4.5 Noise Figure of Cascaded Devices......Page 96
 4.6 An Interesting Example......Page 99
 4.9 Exercises......Page 100
 References......Page 102
 5.2 Transmit Losses......Page 103
 5.3 Antenna Losses......Page 107
 5.4 Propagation Losses......Page 113
 5.5 Receive Antenna and RF Losses......Page 116
 5.6 Processor and Detection Losses......Page 118
 5.7 Exercises......Page 124
 References......Page 126
 Appendix 5A: Waveguide Attenuation......Page 128
 Appendix 5B: Atmospheric and Rain Attenuation......Page 134
   5B.1.1 Compute International Civil Aviation Organization (ICAO) Standard Atmosphere 1964......Page 135
   5B.1.2 Absorption Coefficient for Oxygen......Page 137
   5B.1.3 Absorption Coefficient for Water Vapor......Page 139
  5B.2 Function troprefract.m......Page 140
  5B.3 Function troploss.m......Page 141
  5B.4 Function rainAttn2way.m......Page 142
 6.1 Introduction......Page 144
 6.2 Noise in Receivers......Page 146
  6.2.1 IF Configuration......Page 147
  6.2.2 Baseband Configuration......Page 149
  6.3.1 Introduction and Background......Page 150
  6.3.2 Signal Model for SW0/SW5 Targets......Page 152
  6.3.3 Signal Model for SW1/SW2 Targets......Page 154
  6.3.4 Signal Model for SW3/SW4 Targets......Page 155
  6.4.1 General Formulation......Page 156
  6.4.2 Signal-Plus-Noise Model for SW1/SW2 Targets......Page 157
  6.4.3 Signal-Plus-Noise Model for SW0/SW5 Targets......Page 158
  6.4.4 Signal-Plus-Noise Model for SW3/SW4 Targets......Page 160
  6.5.1 Introduction......Page 163
  6.5.3 Detection Logic......Page 164
  6.5.4 Calculation of Pd and Pfa......Page 165
  6.5.5 Behavior Versus Target Type......Page 171
 6.6 Determination of False Alarm Probability......Page 173
  6.6.1 Example 1—Computing Pfa......Page 175
  6.6.2 Example 2—Detection Contour......Page 176
 6.8 Exercises......Page 180
 References......Page 181
 7.2 Problem Definition......Page 183
 7.3 Problem Solution......Page 184
  7.4.1 General Formulation......Page 189
  7.4.2 Response for an Unmodulated Pulse......Page 190
  7.4.3 Response for an LFM Pulse......Page 193
 7.5 Summary......Page 196
 7.6 Exercises......Page 198
 References......Page 199
 8.1 Introduction......Page 201
  8.2.1 SNR Analysis......Page 202
  8.2.2 Detection Analysis......Page 205
 8.3 Noncoherent Integration......Page 209
  8.3.1 Example 1......Page 215
  8.3.2 Example 2......Page 221
 8.4 Cumulative Detection Probability......Page 224
  8.4.1 Example 3......Page 225
 8.5 m-of-n Detection......Page 226
 8.6 Exercises......Page 235
 References......Page 237
 Appendix 8A: Noise Autocorrelation at the Output of a Matched Filter......Page 238
 Appendix 8B: Probability of Detecting SW1 and SW3 Targets on m Closely Spaced Pulses......Page 240
 Appendix 8C: Cumulative Detection Probability......Page 244
 9.2 Ambiguity Function Development......Page 249
 9.3 Example 1—Unmodulated Pulse......Page 252
 9.4 Example 2—LFM Pulse......Page 255
 9.5 Numerical Techniques......Page 259
 9.6 Ambiguity Function Generation Using the FFT......Page 260
 9.7 Exercises......Page 261
 References......Page 262
 10.1 Introduction......Page 263
 10.2 FM Waveforms......Page 264
  10.2.1 LFM with Amplitude Weighting......Page 265
  10.2.2 Nonlinear FM (NLFM)......Page 267
 10.3 Phase Coded Pulses......Page 272
  10.3.1 Frank Polyphase Coding......Page 273
  10.3.2 Barker Coded Waveforms......Page 277
  10.3.3 PRN Coded Pulses......Page 280
 10.4 Step Frequency Waveforms......Page 287
  10.4.1 Doppler Effects......Page 291
 10.6 Exercises......Page 294
 References......Page 295
 Appendix 10A: LFM and the sinc2(x) Function......Page 298
 11.1 Introduction......Page 301
 11.2 Stretch Processor Configuration......Page 304
 11.3 Stretch Processor Operation......Page 306
  11.4.1 Matched Filter......Page 308
  11.4.2 Stretch Processor......Page 309
 11.5 Stretch Processor Implementation......Page 310
  11.6.1 Expanded Transmit and Receive Signal Models......Page 312
  11.6.2 Effect of Doppler Frequency on Range Resolution......Page 314
  11.6.3 Effect of Doppler Frequency Mismatch on Range Error......Page 317
 11.7 Exercises......Page 318
 References......Page 319
 12.1 Introduction......Page 321
 12.2 Two-Element Array Antenna......Page 322
 12.3 N-Element Linear Array......Page 328
 12.4 Directive Gain Pattern (Antenna Pattern)......Page 331
 12.5 Beamwidth, Sidelobes, and Amplitude Weighting......Page 335
 12.6 Steering......Page 337
 12.7 Element Pattern......Page 340
 12.9 Computation of Antenna Patterns......Page 341
 12.10 Planar Arrays......Page 342
  12.10.1 Weights for Beam Steering......Page 345
  12.10.3 Feeds......Page 346
  12.10.4 Amplitude Weighting......Page 350
  12.10.5 Computing Antenna Patterns for Planar Arrays......Page 351
  12.10.6 Directive Gain Pattern......Page 354
  12.10.7 Grating Lobes......Page 357
 12.11 Polarization......Page 362
 12.12 Reflector Antennas......Page 364
 12.13 Other Antenna Parameters......Page 367
 12.14 Exercises......Page 368
 References......Page 370
 Appendix 12A: An Equation for Taylor Weights......Page 371
 13.1 Introduction......Page 373
  13.2.1 Ground Clutter Radar Cross Section (RCS) Model......Page 374
  13.2.2 Ground Clutter Spectrum Model......Page 379
  13.2.3 Rain Clutter RCS Model......Page 381
  13.2.4 Rain Clutter Spectral Model......Page 385
  13.3.1 Signal Model Generation......Page 386
  13.3.2 Signal Analysis......Page 389
  13.4.1 Background......Page 395
  13.4.2 Moving Target Indicator (MTI)......Page 397
  13.4.3 Pulsed Doppler Processors......Page 419
  13.4.4 Chaff Analysis......Page 459
 13.5 Exercises......Page 465
 References......Page 467
 Appendix 13A: Derivation of (13.43)......Page 470
 Appendix 13B: Proof that r(t) is Wide-Sense Cyclostationary Appendix 13C: Derivation of (13.170)......Page 477
 14.1 Introduction......Page 484
 14.2 Single-Conversion Superheterodyne Receiver......Page 485
 14.3 Dual-Conversion Superheterodyne Receiver......Page 491
 14.4 Receiver Noise......Page 493
 14.5 The 1-dB Gain Compression Point......Page 496
 14.6 Dynamic Range......Page 497
  14.6.1 Sensitivity......Page 498
  14.6.2 Minimum Detectable and Minimum Discernable Signal......Page 500
  14.6.3 Intermodulation Distortion......Page 501
  14.6.4 Required Dynamic Range......Page 503
  14.7.1 Cascade Analysis Conventions......Page 505
  14.7.2 Procedure......Page 506
  14.7.4 Noise Figure and Noise Temperature......Page 508
  14.7.5 1-dB Compression Point......Page 509
  14.7.6 Second-Order Intercept......Page 510
  14.7.7 Third-Order Intercept......Page 512
 14.8 Digital Receiver......Page 516
  14.8.1 Analog-to-Digital Converter......Page 521
 14.9 Receiver Configurations......Page 532
 14.10 Exercises......Page 540
 References......Page 542
 15.1 Introduction......Page 548
  15.2.1 Linear Array Theory......Page 549
  15.2.2 Transition to SAR Theory......Page 553
 15.3 Development of SAR-Specific Equations......Page 554
 15.4 Types of SAR......Page 556
  15.4.1 Theoretical Limits for Strip Map SAR......Page 557
  15.4.2 Effects of Imaged Area Width on Strip Map SAR Resolution......Page 558
  15.5.1 Derivation of the SAR Signal......Page 559
  15.5.2 Examination of the Phase of the SAR Signal......Page 561
  15.5.3 Extracting the Cross-Range Information......Page 562
  15.6.1 A Discrete-Time Model......Page 565
  15.6.2 Other Considerations......Page 566
 15.7 An Algorithm for Creating a Cross-Range Image......Page 568
 15.8 Example 1......Page 569
 15.9 Down-Range and Cross-Range Imaging......Page 573
  15.9.1 Signal Definition......Page 574
  15.9.2 Preliminary Processing Considerations......Page 578
  15.9.3 Quadratic Phase Removal and Image Formation......Page 582
 15.10 Algorithm for Creating a Cross- and Down-Range Image......Page 585
 15.11 Example 2......Page 586
 15.12 An Image-Sharpening Refinement......Page 588
 15.13 Closing Remarks......Page 593
 15.14 Exercises......Page 594
 References......Page 599
 16.1 Introduction......Page 601
 16.2 Spatial Processing......Page 602
  16.2.1 Signal Plus Noise......Page 603
  16.2.2 Signal Plus Noise and Interference......Page 606
  16.2.3 Example 1......Page 609
  16.3.1 Signal......Page 610
  16.3.3 Interference......Page 612
  16.3.4 Doppler Processor......Page 613
  16.3.5 Example 2......Page 615
 16.5 Space-Time Processing......Page 617
  16.5.1 Example 3......Page 620
  16.5.2 Example 4......Page 625
 16.6 Adaptivity Again......Page 628
 16.8 Exercises......Page 630
 References......Page 631
 17.1 Introduction......Page 633
 17.2 Interference Canceller......Page 634
  17.3.1 Single Interference Signal......Page 635
  17.3.2 Example 1......Page 636
  17.3.3 Multiple Interference Sources......Page 639
  17.4.1 Form of vm(t) and va(t)......Page 641
  17.4.2 Properties of vs(t), vI(t), nm(t), and nan(t)......Page 643
  17.4.4 Example 2......Page 644
  17.4.5 Practical Implementation Considerations......Page 648
  17.4.6 Example 3......Page 651
  17.5.1 Howells-Applebaum Implementation......Page 652
  17.5.2 IF Implementation......Page 654
  17.5.3 Example 4......Page 655
 17.6 Sidelobe Blanker......Page 657
 17.7 Exercises......Page 658
 Appendix 17A: Derivation of ϕ (17.40)......Page 659
 18.2 MIMO Radar......Page 663
 18.3 Cognitive Radar......Page 664
 18.4 Other Advancements in Radar Theory......Page 665
 18.5 Hardware Advancements......Page 666
 References......Page 668
A.1 Introduction......Page 671
 A.1.1 Example: Rectangular Pulse—Ideal Lowpass (Rectangular) Filter......Page 673
 A.1.2 Example: Rectangular Pulse—One-Stage Single-Tuned RLC Resonant Circuit......Page 676
 A.1.4 Example: Rectangular Pulse—Gaussian Filter or Gaussian Filter—Rectangular Pulse......Page 680
A.2 Summary......Page 681
A.3 Exercises......Page 682
References......Page 683
Appendix B Data Windowing Functions......Page 684
References......Page 686
Acronyms and Abbreviations......Page 688
About the Authors......Page 697
Index......Page 700