T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 1 out of 55 University of Siegen Extra Illustrations By Y. L. Neo Supervisor : Prof. Ian Cumming Industrial Collaborator : Dr. Frank Wong

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 2 out of 55 University of Siegen Azimuth Invariance

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 3 out of 55 University of Siegen Bistatic SAR signal range azimuth

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 4 out of 55 University of Siegen A point target signal Two-dimensional signal in time and azimuth Simplest way to focus is using two- dimensional matched filtering

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 5 out of 55 University of Siegen 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

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 6 out of 55 University of Siegen Simple Illustration of Frequency based algorithms Rg time Az timeAz freqAz Time

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 7 out of 55 University of Siegen POSP

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 8 out of 55 University of Siegen 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

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 9 out of 55 University of Siegen 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

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 10 out of 55 University of Siegen SRC

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 11 out of 55 University of Siegen Cross Coupling

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 12 out of 55 University of Siegen

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 13 out of 55 University of Siegen LBF

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 14 out of 55 University of Siegen LBF Expand around individual stationary phase

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 15 out of 55 University of Siegen 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

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 16 out of 55 University of Siegen LINK between MSR, LBF and DMO

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 17 out of 55 University of Siegen Typical example X band example Squint angles θ sqT = -θ sqR Large baseline to range Ratio of 2h/R = 0.83

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 18 out of 55 University of Siegen 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

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 19 out of 55 University of Siegen DMO

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 20 out of 55 University of Siegen 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

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 21 out of 55 University of Siegen DMO (seismic processing) Tx Rx θdθd Mono survey tbtb tmtm

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 22 out of 55 University of Siegen θdθd Tx Rx θdθd Mono SAR θsqθsq tbtb tmtm DMO applied to SAR

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 23 out of 55 University of Siegen DMO Operator for bistatic SAR to Monostatic SAR transformation Phase modulator Migration operator DMO operator transform Bistatic Trajectory to Monostatic trajectory

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 24 out of 55 University of Siegen

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 25 out of 55 University of Siegen Bistatic RDA/ Approximate bistatic RDA

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 26 out of 55 University of Siegen 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

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 27 out of 55 University of Siegen 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). Range FT Azimuth FT Azimuth Compression With Azimuth IFT Baseband Signal Focused Image Range Compression And SRC Range IFT RCMC

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 28 out of 55 University of Siegen NLCS (parallel)

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 29 out of 55 University of Siegen 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 –Assumes negligible QRCM (for SAR with short wavelength) –shown to work on Monostatic case and the Bistatic case where receiver is stationary

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 30 out of 55 University of Siegen 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

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 31 out of 55 University of Siegen Applying QRCMC and SRC Range compression LRCMC / Linear phase removal Azimuth compression Baseband Signal Focused Image Non-Linear Chirp Scaling Residual QRCMC The scaling function is a polynomial function of azimuth time NLCS applied in the time domain SRC and QRCMC --- range Doppler/2D freq domain Azimuth matched filtering --- range Doppler domain Residual QRCMC and SRC Non-Linear Chirp Scaling

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 32 out of 55 University of Siegen Monostatic Case Az time Range time A B C 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. –After range compression and LRCMC, Point B and Point C now lie in the same range gate. Although they have different FM rates

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 33 out of 55 University of Siegen 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. FM Rate Equalization (monostatic)

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 34 out of 55 University of Siegen FM Rate Equalization (monostatic or nonparallel case) – cubic perturbation function Azimuth Phase

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 35 out of 55 University of Siegen Longer wavelength experiment Without residual QRCMC (20 % range and azimuth broadening) With residual QRCMC, resolution and PSLR improves 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

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 36 out of 55 University of Siegen 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. Second order Third order

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 37 out of 55 University of Siegen Requirement for SRC L-band 1 m resolution

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 38 out of 55 University of Siegen 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

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 39 out of 55 University of Siegen Simulation results with NLCS processing Accurate compression Registration to ground plane

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 40 out of 55 University of Siegen NLCS (Stationary Receiver)

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 41 out of 55 University of Siegen NLCS (Stationary Receiver) D F’ E’ –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

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 42 out of 55 University of Siegen FM Rate Equalization (stationary receiver case) – quartic perturbation function Azimuth Phase F’ D E’ D F’ Stationary Receiver Azimuth Range DE’ F’

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 43 out of 55 University of Siegen 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

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 44 out of 55 University of Siegen Simulation results with NLCS processing Focused Image Registration to Ground plane