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2. 2 SAR Signal Processing

3. 3 Table of Contents 1.Introduction 2.SAR Signal Processing 3.SAR Image Formation Algorithms 4.Summary

4. 4 1.Introduction

5. 5 SAR Imaging Process A two-step imaging process: Data Acquisition + Image Formation

6. 6 Data Acquisition Illumination of the scattering target + Collection of the received echo returns Raw data

7. 7 Image formation or focusing of the radar signals in 2D Image of the scattered target or target scene Image Formation Process

8. 8 2. SAR Signal Processing

9. 9  Nominal altitude, h Azimuth direction, y Ground range direction, x Altitude direction, z Ideal trajectory, (0, y, h) Target-i at arbitrary coordinates (r i, y i ) RiRi riri Geometry of Generic SAR

10. 10 Chirp signal: Transmit Chirp Signal Amplitude, a() Duration,  p Pulse repetition interval, PRI Bandwidth, B Transmitted signal: Chirp rate

11. 11 After demodulation, the backscattered signal received from a point scatterer located at (r i, y i ) is given by, Transmitted signal:  g(  ) is the system impulse response Transmitted and Received Signals

12. 12 The raw signal s(r, y): The SAR imaging problem is to design an appropriate filter such that we can recover the best estimate of f(r, y) based on the received signal s(r, y). SAR Processor s(r,y) Raw data f(r,y) Image SAR Image Formation Target signature

13. 13 In the 2D Fourier Domain, G(  ) is the transfer function of g(  ), where 2D FT Analysis

14. 14 Asymptotic Closed-Form Solution for G(.) Neglect non-essential amplitude term, and Apply the method of stationary phase where Spatial bandwidth

15. 15 Taylor Series Expansion Responsible for azimuth focusing (azimuth compression) Range migration correction (RMC) factor Secondary range compression (SRC) factor

16. 16 Chirp signal: First remove the carrier frequency, fc, then demodulate the signal by applying a matched filter: In the time domain, this is a convolution: In the frequency domain, this is a multiplication: The Matched Filter Transmitted signal:

17. 17 From Echo Return to Image Two-dimensional chirp  Range chirp is the delayed replica of the transmitted chirp + The azimuth chirp is formed by relative motion between the platform and the illuminated target + Range migration  Two-dimensional pulse compression with matched filtering + Range migration correction  2D resolving capability

18. 18 The return echo received from a point target of RCS  at the i-th element is, where the amplitude of transmit pulse is assumed to be 1. Return Echo from a Point Target Amplitude associated with target RCS k = 2  / Round-trip delay of 2R i Initial phase of transmit pulse

19. 19 The previous expression can be converted to a complex form as, Hence, the phase correction necessary for the i-th element of the aperture I, which is achieved by multiplying the recorded echo s i by a factor of, Return Echo in Complex Form

20. 20 After phase correction, the resulting signals from n elements are coherently added and then squared to give an output power of, The output power is proportional to the target RCS and is maximized for that particular target. This SAR focusing operation must be repeated for all possible range positions over the imaged swath, and also at all subsequent azimuth positions to produce a SAR image. Square-Law Detection

21. 21 3. SAR Image Formation Algorithms

22. 22 General Understanding of SAR Image Formation – Point Target Return RC RCMC AC

23. 23 Space-Variant Properties for Multi-Point Targets Azimuth Range Near Range Reference Range Far Range

24. 24 SAR Image Formation Algorithms Consist of the Range-Doppler (RDA), Chirp Scaling (CSA), and Omega-K (  KA) algorithms. They are the three most common precision SAR processing algorithms used for SAR remote sensing data.

25. 25 #1: Range Doppler Algorithm (RDA)

26. 26 Raw Data Processing Azimuth compression Range compression Range migration

27. 27 Simulated Point Target

28. 28 Range Compression

29. 29 Azimuth Compression

30. 30 RD Algorithm (Bennett & Cuming, ‘79) Developed in 1976 – 1978 for SEASAT SAR data. RDA is the basic of most precision SAR processor. RDA is efficient, solves the problems of azimuth focusing and RMC. Operates in (r, k y ) domain. Cannot easily incorporate SRC factor Requires interpolation

31. 31 Features of RDA Block processing Frequency domain operation in both range and azimuth direction. One dimensional operation Range cell migration correction (RCMC) between two one-dimensional operation.

32. 32 Raw Signal s(r,y) Range FT P*(kr)P*(kr) SAR Image f(r,y) exp[j  (k y )r] Range FT -1 Azimuth FT Azimuth FT -1 RM Correction Range Compression Range Migration Correction (Interpolation) Azimuth Compression Azimuth Inverse Fourier Transform Azimuth Fourier Transform Block Diagram of RDA

33. 33 Advantages of RDA Easiest to understand and implement Basic algorithm that can be adapted to most SAR processing tasks as long as the aperture and squint are not too large Efficient processing in both RMC and azimuth matched filter 1D operation - can implement in an efficient pipeline architecture No spatial invariance assumptions are required, except SRC

34. 34 Disadvantages of RDA An interpolator is used for RMC – time-consuming operation Accuracy is not the highest (due to SRC, approximations made in interpolation) Restrictive beamwidth and squint limitations

35. 35 #2: Wavenumber Domain Algorithm (  kA)

36. 36  k Algorithm (Cafforio et. al. 1991) Based on the wave equation formulations Dealing directly with the natural polar coordinate system arising from wave propagation Operate in (k r, k y ) domain (2D frequency domain) with a relatively simple phase multiplier

37. 37 where New reflectivity function 2D Fourier Domain

38. 38  kA Processing Steps The raw signal is first transformed into (k r, k y ) domain (2D FT) Range compression in (k r, k y ) domain (x P * (k r )) The spectrum of the reflectivity function F(  ) is computed over the new grid [k r ’ (k r, k y ), k y ], instead of the conventional [k r, k y ] The final processing step involves a 2D IFT to restore the target reflectivity function in (r, y) domain.

39. 39 [k r ’ (k r, k y ), k y ]  [k r, k y ] This requires a complex interpolation to retrieve the nonlinear nature of the two-dimensional mapping. This nonlinear mapping is referred to as: –Stolt mapping (Stolt, 1978; Cafforio et. al., 1991) –Gird deformation (Franceschetti & Lanari, 1999)

40. 40 Raw Signal s(r,y) 2D FT P*(kr)P*(kr) SAR Image f(r,y) Nonlinear Mapping 2D FT -1 Range Compression Stolt Mapping (Interpolation) 2D Inverse Fourier Transform 2D Fourier Transform Block Diagram of  kA Processing

41. 41 Advantages of  kA Exact SAR processing for all squint angles and aperture widths SRC is applied accurately (including its slant range and azimuth frequency dependencies) When SRC is negligible, the approximation form of the  kA is very efficient

42. 42 Disadvantages of  kA Interpolation is not as easy or accurate to apply as phase multipliers Processing is done in 2D frequency domain: large array sizes are needed to accommodate the range matched filter

43. 43 #3: Chirp Scaling Algorithm (CSA)

44. 44 CS Algorithm (Raney, et. at. 1994) Based on curvature equalization, such that by the time the signal is transformed into the 2D frequency domain, all of the range migration trajectories have been adjusted to have congruent loci.

45. 45 Features of CSA Processing Operates in both (r, k y ) and (k r, k y ) domains Valid only for the case of linear FM with large time- bandwidth phase modulation No interpolations for RMC Operating domain: Azimuth FT  Range FT  Range IFT  Azimuth IFT

46. 46 Linear FM chirp signal: Linear FM Chirp Signal Range FT (by using principle of stationary phase): (transmitted pulse spectrum) is the FM chirp rate change to r domain where

47. 47 Azimuth FT = Range IFT of S(k r, k y ): Azimuth FT of s(r, y) where

48. 48 Scaled Transmitted Pulse Function where The range delay term r fi causes range migration due to the chirp scaling factor,  (  ). The effective FM chirp rate  ’ leads to range defocus as the result of secondary range compression (SRC) factor,  (  ).

49. 49 Chirp Scaling Multiplier in (r, k y )

50. 50 Range FT: Range Compression Range Migration Correction X RC & RMC in (k r, k y )

51. 51 Azimuth Compression in (r, k y ) Range IFT: X Azimuth IFT:

52. 52 Block Diagram of CSA Processing Raw Signal s(r,y) Azimuth FT exp{  1 (r,k y )} SAR Image f(r,y) Range FT -1 Chirp Scaling Range Compression Range Inverse Fourier Transform Azimuth Fourier Transform Range FT exp{  2 (k r,k y )} Range Fourier Transform Azimuth FT -1 exp{  3 (r,k y )} Azimuth Compression Azimuth Inverse Fourier Transform

53. 53 Advantages of CSA No interpolation is required for RMC and SRC All the range dependencies of the azimuth matched filter can be accommodated

54. 54 Disadvantages of CSA If the range compression has already been performed (e.g. onboard platform) or a chirp was not used, the data have to be expanded with a chirp before the CSA is applied Data corresponding to range matched filter must be retained in memory until the range IFT Data enter the 2D frequency domain in an uncompressed state: large array sizes are needed SRC is assumed to be range invariant

55. 55 RDA  kA CSA Operation Domain(r, k y )(k r, k y )(r, k y ), (k r, k y ) Approximations in Transfer Function Phase YesNoYes Interpolation for RMCYes No CommentsSRC factor can not be easily incorporated Frequency interpolation is required Require linear FM chirp Comparison of SAR Algorithms

56. 56 Summary of SAR Image Formation Algorithm The RDA is the most widely used algorithm. It is conceptually the simplest, and can accommodate range varying parameters in the processing. The CSA is a useful alternative to the RDA. It requires no interpolation for the RMC, which slightly improves the image quality. For SARs with a wide beamwidth or moderate to high squint, the  kA is an excellent choice. Its approximation can be used for smaller beamwidths or squints.

57. 57 Summary SAR signal properties SAR signal processing SAR image formation algorithm: –Range-Doppler (RDA) –Chirp Scaling (CSA) –Omega-K (  KA) algorithms

58. 58 References “Introduction to radar systems”, Merrill l. Skolnik, Boston : McGraw Hill, 2001. “Radar Signal Analysis and Processing Using MATLAB”, Mahafza, Bassem R., Chapman and Hall/CRC, 2008. “Microwave Remote Sensing: Active and Passive, Volume II: Radar Remote Sensing and Surface Scattering and Emission Theory”, F.T. Ulaby, R.K. Moore, A.K. Fung, Artech House, 1986. “Radar Handbook”, Merrill Skolnik, McGraw Hill Professional, 2008. “Synthetic Aperture Radar – Systems and Signal Processing”, Curlander, J.C. and McDonough, R.N. New York: John Wiley & Sons, 1991. Cook, C.E., and Bernfeld, M. (1993). Radar Signals: An Introduction to Theory and Application. Boston: Artech House Cumming, I.G., and Wong, F.H. (2005). Digital Processing of Synthetic Aperture Radar Data, Norwood, Artech House Franceschetti, G., and Lanari, R. (1999). Synthetic Aperture Radar Processing, CRC Press LLC