Extra Illustrations

1. Extra Illustrations By Y. L. Neo Supervisor : Prof. Ian Cumming Industrial Collaborator : Dr. Frank Wong University of Siegen

2. Azimuth Invariance University of Siegen

3. Bistatic SAR signal azimuth range University of Siegen

4. A point target signal • Two-dimensional signal in time and azimuth • Simplest way to focus is using two-dimensional matched filtering University of Siegen

5. Overview of Existing Algorithms • Time domain algorithms are accurate but slow – BPA, TDC • Monostatic algorithms make use • Azimuth-Invariance • Efficiency achieved in azimuth frequency domain • Traditional monostatic frequency domain algorithms • RDA, CSA and ωKA University of Siegen

6. Az time Az freq Az Time Rg time Simple Illustration of Frequency based algorithms University of Siegen

7. POSP University of Siegen

8. Principle of Stationary Phase (POSP) • 1.) Want to find spectrum S(f) • 2.) POSP takes note of contribution to integral of rapidly changing signal is zero. • 3.) Most of the contribution is near the stationary point where phase do not change rapidly. • 4.) Therefore we are interested in the azimuth times where d/d=0, i.e. at solution to the stationary phase (f) • 5.) Expanding around this solution (f) we end up with the result given next University of Siegen

9. POSP Analytical Spectrum Difficult to derive directly Most of the contribution of integral comes from around stationary point Expanding around stationary point, the analytical spectrum can be derived University of Siegen

10. SRC University of Siegen

11. Cross Coupling University of Siegen

12. University of Siegen

13. LBF University of Siegen

14. LBF Expand around individual stationary phase University of Siegen

15. LBF • Make use of the fact that sum of 2 quadratic functions is another scaled and shifted quadratic function. • Apply POSP, we get approximate stationary phase solution University of Siegen

16. LINK between MSR, LBF and DMO University of Siegen

17. Typical example • X band example • Squint angles θsqT = -θsqR • Large baseline to range • Ratio of 2h/R = 0.83 University of Siegen

18. Summary • MSR is the most general of the three spectra – MSR, DMO and LBF • DMO is accurate when short baseline/Range ratio • LBF is accurate under conditions – higher order bistatic deformation terms are negligible and University of Siegen

19. DMO University of Siegen

20. DMO • Pre-processing technique – transform bistatic data to monostatic data • Technique from seismic processing • Transform special bistatic configuration (Tandem Configuration or Leader-Follower) to monostatic University of Siegen

21. tb tm DMO (seismic processing) Mono survey Rx Tx θd University of Siegen

22. θsq θd θd tm tb DMO applied to SAR Mono SAR Rx Tx University of Siegen

23. DMO Operator for bistatic SAR to Monostatic SAR transformation Migration operator Phase modulator DMO operator transform Bistatic Trajectory to Monostatic trajectory Monostatic trajectory University of Siegen

24. University of Siegen

25. Bistatic RDA/Approximate bistatic RDA University of Siegen

26. Phase terms of spectrum • Range Modulation– range chirp • Range Doppler Coupling– removed in the 2D frequency domain, evaluated at the reference range. For wider scene, requires range blocks. • Range Cell Migration term– linear range frequency term, removed in the range Doppler domain • Azimuth Modulation– removed by azimuth matched filter in range Doppler domain • Residual phase– range varying but can be ignored if magnitude is the final product University of Siegen

27. Approximate RDA • For coarse range resolution and lower squint, the range Doppler coupling has only a small dependency on azimuth frequency. • Thus, SRC is evaluated at Doppler centroid and can be combined with Range Compression (as in Monostatic Case). Baseband Signal Azimuth FT Range FT RCMC Range Compression And SRC Range IFT Azimuth Compression With Azimuth IFT Focused Image University of Siegen

28. NLCS (parallel) University of Siegen

29. Non-Linear Chirp Scaling • Existing Non-Linear Chirp Scaling • Based on paper by F. H. Wong, and T. S. Yeo, “New Applications of Nonlinear Chirp Scaling in SAR Data Processing," in IEEE Trans. Geosci. Remote Sensing, May 2001. • Assumes negligible QRCM (for SAR with short wavelength) • shown to work on Monostatic case and the Bistatic case where receiver is stationary University of Siegen

30. NLCS • We have extended NLCS to handle non parallel tracks cases • Able to higher resolutions, longer wavelength cases • Correct range curvature, higher order phase terms and SRC • Develop fast frequency domain matched filter using MSR • Registration to Ground Plane University of Siegen

31. Residual QRCMC and SRC Non-Linear Chirp Scaling Applying QRCMC and SRC • NLCS applied in the time domain • SRC and QRCMC --- range Doppler/2D freq domain • Azimuth matched filtering --- range Doppler domain Range compression LRCMC / Linear phase removal Baseband Signal The scaling function is a polynomial function of azimuth time Non-Linear Chirp Scaling Residual QRCMC Azimuth compression Focused Image University of Siegen

32. After range compression and LRCMC, Point B and Point C now lie in the same range gate. Although they have different FM rates FM Rate Difference • The trajectories of three point targets in a squinted monostatic case is shown • Point A and Point B have the same closest range of approach and the same FM rate. C A B Monostatic Case Range time Az time University of Siegen

33. FM Rate Equalization (monostatic) • After LRCMC, trajectories at the same range gate do not have the same chirp rates, an equalizing step is necessary • This equalization step is done using a perturbation function in azimuth time • Once the azimuth chirp rate is equalized, the image can be focused by an azimuth matched filter. University of Siegen

34. FM Rate Equalization (monostatic or nonparallel case) – cubic perturbation function Phase Azimuth University of Siegen

35. Longer wavelength experiment • Uncorrected QRCM will lead to broadening in range and azimuth • QRCMC is necessary in longer wavelength cases • Higher order terms can be ignored in most cases Without residual QRCMC (20 % range and azimuth broadening) With residual QRCMC, resolution and PSLR improves University of Siegen

36. Expansion of phase up to third order necessary- e.g. C band 55deg squint 2m resolution • Azimuth Frequency Matched Filter • Accuracy is attained by including enough terms. Third order Second order University of Siegen

37. Requirement for SRC • L-band • 1 m resolution University of Siegen

38. Simulation results • C-band • Non-parallel tracks • range resolution of 1.35m and azimuth resolution of 2.5m • Unequal velocities Vt = 200 m/s • Vr = 221 m/s • track angle difference 1.3 degree • 30° and 47.3° squint University of Siegen

39. Simulation results with NLCS processing Registration to ground plane Accurate compression University of Siegen

40. NLCS (Stationary Receiver) University of Siegen

41. NLCS (Stationary Receiver) • Data is inherently azimuth-variant • Targets D E’ F’ lie on the same range gate but have different FM rates • Point E’ and Point F’ have the same closest range of approach and the same FM rate but different from Point D F’ D E’ University of Siegen

42. FM Rate Equalization (stationary receiver case) – quartic perturbation function D F’ E’ F’ D Phase E’ Azimuth Range Stationary Receiver F’ E’ D Azimuth University of Siegen

43. Simulation Experiment • S-band • Transmitter at broadside • Range resolution of 2.1m and azimuth resolution of 1.4m • Unequal velocities Vt = 200 m/s • Vr = 0 m/s University of Siegen

44. Simulation results with NLCS processing Focused Image Registration to Ground plane University of Siegen