Basic Radar Analysis (Artech House Radar)

This authoritative new resource presents fundamentals of radar analysis including the range equation, detection theory, ambiguity functions, antennas, receivers, SP, and chaff analysis for modern radars. This book addresses details behind the detection probability equations and origins radar engineers commonly use to perform signal processor analyses. This book consolidates discussions of receiver design and analysis and treats areas of digital receivers not commonly found in other books. Packed with details on how to perform radar range equation and detection analyses, RCS modeling, ambiguity function generation and antenna pattern generation. This book also includes detailed analyses of coherent and non-coherent integration, design and analysis of analog and digital receivers, stretch processor implementation and SAR signal processor implementation. This resource also covers Basic STAP implementation and analysis as well as SLC design and implementation. This book is accompanied by a MATLAB on CD. This new resource is intended as a text for a series of courses in radar and as a theory and practice reference for practicing radar engineers. 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