Digital Processing of Synthetic Aperture Radar Data Algorithms and Implementation Ian G. Cumming Frank H. Wong ARTECH H O U SE BOSTON|LONDON artechhouse.com Contents Foreword xix Preface xxiii Acknowledgments xxv I Fundamentals of Synthetic Aperture Radar 1 1 Introduction 3 1.1 Brief Background of SAR 3 1.2 Radar in Remote Sensing 5 1.3 SAR Fundamentals 5 1.4 Spaceborne SAR Sensors 10 1.5 Outline of the Book 14 1.5.1 Example of a Spaceborne SAR Image 16 References 19 2 Signal Processing Fundamentals 21 2.1 Introduction 21 2.2 Linear Convolution 22 2.2.1 Continuous-Time Convolution 22 2.2.2 Discrete-Time Convolution 24 2.3 Fourier Transforms 27 2.3.1 Continuous-Time Fourier Transform 27 2.3.2 Discrete Fourier Transform 28 vn viii Contents 2.3.3 Fourier Transform Properties 30 2.3.4 Examples of Fourier Transforms 34 2.4 Convolution Using DFTs 36 2.5 Sampling of Signals 38 2.5.1 Spectrum of Sampled Signals 38 2.5.2 Signal Types 40 2.5.3 Nyquist Sampling Rate and Aliasing 42 2.6 Smoothing Windows 49 2.7 Interpolation 51 2.7.1 Sine Interpolation 52 2.7.2 Spectra of Interpolation Kernels 56 2.7.3 Nonbaseband and Complex Interpolation 58 2.8 Point Target Analysis 59 2.9 Summary 64 2.9.1 Magellan Image of Venus Crater 65 References 66 3 Pulse Compression of Linear FM Signals 69 3.1 Introduction 69 3.2 Linear FM Signals 70 3.2.1 Time Domain Representation 70 3.2.2 Spectrum of the Linear FM Pulse 72 3.2.3 Sampling of FM Signals 76 3.2.4 Frequency and Time Discontinuities 78 3.3 Pulse Compression 80 3.3.1 Principles of Pulse Compression 80 3.3.2 Time Domain Compression of Linear FM Signals . . .. 82 3.3.3 Frequency Domain Matched Filter 87 3.3.4 The Effect of Windows 90 3.3.5 Oversampling Ratio Revisited 93 3.4 Matched Filter Implementation 93 3.4.1 Target Registration and Matched Filter Throwaway . . 96 3.5 FM Rate Mismatch 98 Contents ix 3.5.1 Effect of Mismatch in a Baseband Signal 98 3.5.2 Effect of Mismatch in a Nonbaseband Signal 102 3.5.3 Filter Mismatch and Time Bandwidth Product 102 3.6 Summary 103 3.6.1 A Wide Swath ENVISAT/ASAR Image 104 References 107 Appendix А:З Derivation of the Matched Filter Output 108 3A.1 Signal and Matched Filter of Equal Length 108 3A.2 Signal and Matched Filter of Unequal Length 110 Appendix 3B: Derivation of the Phase Error Due to Mismatch . .. Ill 4 Synthetic Aperture Concepts 113 4.1 Introduction 113 4.2 SAR Geometry 114 4.2.1 Definition of Terms 114 4.2.2 Satellite Ground Range Geometry 120 4.2.3 Satellite Orbit Geometry 122 4.3 The Range Equation 125 4.3.1 Hyperbolic Form of the Range Equation 125 4.3.2 Relationships Between Velocities and Angles 128 4.4 SAR Signal in the Range Direction 130 4.4.1 Transmitted Pulse 130 4.4.2 Data Acquisition 131 4.5 SAR Signal in the Azimuth Direction 133 4.5.1 What Is Doppler Frequency in the SAR Context? . .. 133 4.5.2 Coherent Pulses 134 4.5.3 Choice of PRF 136 4.5.4 Azimuth Signal Strength and Doppler History 137 4.5.5 Azimuth Parameters 140 4.6 The Two-Dimensional Signal 141 4.6.1 Data Arrangement in Signal Memory 142 4.6.2 Demodulated Baseband Signal 144 4.6.3 The SAR Impulse Response 146 x Contents 4.6.4 Typical Radar Parameter Values 147 4.7 SAR Resolution and Synthetic Aperture 147 4.7.1 Resolution Derived from Bandwidth 147 4.7.2 Synthetic Aperture 151 4.8 Summary 153 4.8.1 ScanSAR Narrow Image of Vancouver Island 155 References 156 Appendix 4A: Derivation of the Approximate Radar Velocity . . .. 157 Appendix 4B: Quadrature Demodulation 159 4B.1 Theory of Quadrature Demodulation 160 4B.2 Errors and Corrections 161 Appendix 4C: Concept of Synthetic Aperture 164 5 SAR Signal Properties 169 5.1 Introduction 169 5.2 Signal Spectrum in the Low-Squint Case 170 5.2.1 Spectrum in the Range Doppler Domain 171 5.2.2 Two-Dimensional Spectrum 172 5.3 Signal Spectrum in the General Case 172 5.3.1 Range Fourier Transform 174 5.3.2 Azimuth Fourier Transform 175 5.3.3 Range Inverse Fourier Transform 178 5.4 Azimuth Aliasing and the Doppler Centroid 182 5.4.1 Origin of Azimuth Aliasing and Ambiguities 182 5.4.2 The Doppler Centroid 185 5.4.3 The Doppler Ambiguity 188 5.4.4 Doppler Centroid Variation with Range 189 5.5 Range Cell Migration 194 5.5.1 RCM Components 195 5.5.2 Multiple Targets at the Same Range 198 5.5.3 Target Trajectory Wraparound 199 5.6 Point Target Examples 200 5.6.1 Simulation Parameters 200 Contents xi 5.7 Prelude to SAR Processing Algorithms 204 5.7.1 Time Domain Matched Filtering 205 5.7.2 Real-Time Processed Airborne Radar Image 207 5.7.3 Unfocused SAR 209 5.7.4 Moving on to Better Processing Algorithms 210 5.8 Summary 211 References 214 Appendix 5A: Range/Azimuth Coupling 215 Appendix 5B: A Note on the Azimuth FM Rate 219 5B.1 Geometric Interpretation from Slopes 220 5B.2 Approximate Signal Representation 221 II SAR Processing Algorithms 223 6 The Range Doppler Algorithm 225 6.1 Introduction 225 6.2 Algorithm Overview 226 6.3 RDA in the Low Squint Case 229 6.3.1 Raw Radar Signal Data (Raw Data) 229 6.3.2 Range Compression 231 6.3.3 Azimuth Fourier Transform 232 6.3.4 Range Cell Migration Correction 235 6.3.5 Broadening Due to Residual RCM 241 6.3.6 Azimuth Compression 243 6.3.7 Example of a Low Squint RADARSAT-1 Image . . .. 248 6.4 The High Squint Case 250 6.4.1 Modifications to Handle Squint 250 6.4.2 Implementation of SRC 253 6.4.3 SRC Options Needed for Satellite and Airborne Cases . 256 6.4.4 SRC Simulation Experiments 258 6.4.5 An L-Band Airborne Radar Image Example 264 6.5 Multilook Processing 265 6.5.1 Frequency and Time Relationship of Looks 265 xii Contents 6.5.2 Look Extraction, Detection, and Summation 267 6.5.3 Equivalent Number of Looks 270 6.5.4 An Example of Multilook Processing 271 6.5.5 FM Rate Error 276 6.5.6 Multilook Processed Image 278 6.6 Summary 280 References 281 7 The Chirp Scaling Algorithm 283 7.1 Introduction 283 7.1.1 Overview of the Chirp Scaling Algorithm 284 7.2 The Chirp Scaling Concept 287 7.3 Applying Chirp Scaling to RCMC 294 7.3.1 Bulk and Differential RCMC 295 7.3.2 A More Accurate Expression for RCM 298 7.4 Derivation of the Scaling Function 300 7.4.1 Examples of the Size of Differential RCM 302 7.5 CSA Processing Details 304 7.5.1 Range Processing 304 7.5.2 Azimuth Processing 309 7.6 Processing Examples 310 7.6.1 Simulations with Point Targets 310 7.6.2 Processing of SRTM/X-SAR Data 315 7.7 Summary 316 References 319 8 The Omega-K Algorithm 323 8.1 Introduction 323 8.1.1 Overview of the Omega-K Algorithm 324 8.2 Reference Function Multiply 328 8.3 Stolt Interpolation 330 8.3.1 The Change of Variables 330 8.4 Interpretations of the Stolt Mapping 335 8.4.1 Components of the Stolt Mapping 335 Contents xiii 8.4.2 Interpretation Via Fourier Transform Properties . . .. 336 8.4.3 Interpretation Via the Region of Support 340 8.4.4 Interpretation Via Imaging Geometry 341 8.5 Error Analysis 343 8.6 Approximate Version of the Omega-K Algorithm 345 8.6.1 Approximation Components 346 8.6.2 Relation to the RDA and the CSA 348 8.6.3 Discussion of Errors in the Approximate LJKA . . .. 348 8.7 Processing Examples 349 8.7.1 Simulation of the Full LJKA Algorithm 349 8.7.2 Approximate Version of the LJKA 356 8.7.3 An X-Band Airborne Radar Spotlight Image Example . 357 8.8 Summary 358 References 359 Appendix 8A: Stolt Mapping in the Wavenumber Domain 362 9 The SPECAN Algorithm 369 9.1 Introduction 369 9.1.1 Overview of the SPECAN Algorithm 370 9.2 Derivation of the SPECAN Algorithm 372 9.2.1 From Convolution to SPECAN 372 9.2.2 Geometric Interpretation 373 9.2.3 Aliasing and FFT Length 377 9.2.4 Output Sample Spacing 379 9.2.5 Number of Good FFT Output Points 380 9.2.6 Placement of Subsequent FFTs 382 9.2.7 Stitching the FFT Outputs Together 385 9.3 Multilook Processing 385 9.4 Processing Efficiency 389 9.5 Range Cell Migration Correction 393 9.5.1 Time Domain Linear RCMC 394 9.5.2 Skewing and Deskewing 394 9.6 Phase Compensation 396 9.7 Image Quality Issues 400 9.7.1 Frequency Discontinuities at the Stitching Points . . .. 400 9.7.2 Azimuth FM Rate Error 403 9.7.3 Radiometric Scalloping 405 9.8 Processing Examples 416 9.8.1 Simulated Point Targets 416 9.8.2 ERS Image Processed by SPECAN 418 9.9 Summary 420 References 421 10 Processing ScanSAR Data 425 10.1 Introduction 425 10.2 ScanSAR Data Acquisition 427 10.3 Compression of a Single-Burst Target 431 10.4 Full-Aperture Processing 434 10.5 The SPECAN Algorithm 437 10.6 The Modified SPECAN Algorithm 438 10.6.1 Outline of the Algorithm 438 10.6.2 SRTM Processing Example 442 10.7 The Short IFFT Algorithm 442 10.8 The Extended Chirp Scaling Algorithm 447 10.9 Stitching Processed Bursts Together 450 10.10 Summary 453 10.10.1 RADARSAT-1 ScanSAR Image 454 References 455 11 Comparison of Algorithms 461 11.1 Introduction 461 11.2 Recap of the Precision Processing Algorithms 461 11.2.1 Range Doppler Algorithm 461 11.2.2 Chirp Scaling Algorithm 462 11.2.3 Omega-K Algorithm 462 11.3 Comparison of Processing Functions 463 11.3.1 Form of Range Equation 465 Contents xv 11.3.2 Implementation of the Azimuth Matched Filter 465 11.3.3 Implementation of Range Cell Migration Correction . . 465 11.3.4 Implementation of Secondary Range Compression . . . 466 11.4 Summary of Processing Errors 466 11.4.1 QPE in the Azimuth Matched Filter 467 11.4.2 QPE in Secondary Range Compression 468 11.4.3 Residual RCM 469 11.4.4 Examples of the Size of the Processing Errors 470 11.5 Computation Load 473 11.5.1 Basic Algorithm Operations 473 11.5.2 Range Doppler Algorithm 473 11.5.3 Chirp Scaling Algorithm 474 11.5.4 Omega-K Algorithm 475 11.6 Pros and Cons of Each Algorithm 476 11.6.1 Pros and Cons of the RDA 476 11.6.2 Pros and Cons of the CSA 477 11.6.3 Pros and Cons of the ШКА 478 11.7 Summary 479 11.7.1 ASAR Image of the Strait of Messina 480 III Doppler Parameter Estimation 481 12 Doppler Centroid Estimation 483 12.1 Introduction 483 12.1.1 Doppler Centroid Frequency 483 12.1.2 Satellite SAR System Geometry 484 12.1.3 Outline of This Chapter 487 12.2 Doppler Centroid Accuracy Requirements 489 12.2.1 Baseband Centroid Accuracy Requirements 489 12.2.2 Doppler Ambiguity Accuracy Requirements 497 12.3 Calculating Doppler Centroid from Geometry 497 12.3.1 Examples of Doppler Centroid Calculations 501 12.3.2 Yaw and Pitch Steering 503