1. Fast Factorized Backprojection
Algorithm for UWB Bistatic
SAR Image Reconstruction
Viet Vu, Thomas Sjögren and Mats Pettersson
Blekinge Institute of Technology, Karlskrona, Sweden.

2. Outline
• Motivation
• Contribution
• Development from GBP to BiFFBP
– From monostatic GBP to bistatic GBP
– Bistatic FBP development on bistatic GBP
– From bistatic FBP to bistatic FFBP
• Simulation Results and Evaluation
• Conclusion

3. Motivation
• Algorithms for NB bistatic SAR
– Frequency-domain: Range Doppler (RD), Range
Migration (RM), Chirp Scaling (CS).
– Time-domain: Global Backprojection applied to
bistatic cases (BiGBP).
• Algorithms for UWB monostatic SAR
– Frequency-domain: not recommended [1].
– Time-domain: GBP, Fast Backprojection (FBP), Fast
Factorized Backprojection (FFBP).
[1] V. T. Vu et. al., “A comparison between fast factorized backprojection and
frequency-domain algorithms in UWB low frequency SAR,” in Proc. IEEE
IGARSS’2008, Boston, MA, Jul. 2008, pp. 1293–1296.

4. Motivation (cont.)
• Algorithms for UWB bistatic SAR
– BiGBP:
• Avaibilable in principal.
• Require huge computational burden.
– BiFBP:
• Shown to work with UWB bistatic SAR data [2].
• Require low computational cost.
– BiFFBP:
• Need to be investigated.
• Supposed to require even lower computational cost.
[2] V. T. Vu et. al., “Fast backprojection algorithm for UWB bistatic SAR,” in Proc.
IEEE RadarCon’2011, Kansas City, MO, May 2011, pp. 431-434.

5. Contribution
• BiFFBP, a fast time-domain algorithm
– Aim at UWB bistatic SAR systems but available for
NB bistatic SAR systems.
– Inherit time-domain characteristics such as unlimited
scene size, local processing, motion compensation
and so on.
– Tested with different bistatic configurations and
shown to be not limited by any bistatic configuration.
– Low computational cost.

6. From GBP to BiGBP
• GBP
– Reconstructed either on a slant-range plane or ground
plane.
– Time-domain characteristics.
– Spherical mapping.
– Huge computational burden.
ti

 g v t , c  R dt
2
hxm , rn   pl
ti

2

7. From GBP to BiGBP (cont.)
• BiGBP
– Reconstructed only on a ground plane.
– Time-domain chracteristics.
– Ellipsoidal mapping.
– No limitation of bistatic configuration.
– Also huge computational burden.
ti

2
hxm , rn    g v t , v t , c  R dt
t r
ti

2

8. BiFBP Development on BiGBP
• BiFBP
– Reconstructed only on a ground plane.
– Time-domain chracteristics.
– Ellipsoidal mapping.
– No limitation of bistatic configuration.
– Two processing stages:
• Beam forming.
• Local backprojection
– Low computational cost.

9. BiFBP Development on BiGBP (cont.)
• Beam forming from radar echoes
– Linear superpositions of radar echoes.
– References for superposition are centers of
• Transmitter subaperture
• Receiver subaperture
• Subimage.
bvt tl , vr tl , c  Rl ,k 
ts
tl 
2
  g v t , v t , c  R dt
ts
t l r l l ,k
tl 
2

10. BiFBP Development on BiGBP (cont.)
• Local backprojection from formed beam
– Over elipsoidal mapping.
– Foci determined by centers of subapertures.
– Major axis defined by line connecting foci.
 
L
hxm , yn    b vt tl , vr tl , R  Rlc,k
l 1

11. From BiFBP to BiFFBP
• BiFFBP
– Reconstructed only on a ground plane.
– Time-domain chracteristics.
– Ellipsoidal mapping.
– No limitation of bistatic configuration.
– More than two processing stages:
• Firtst beam forming.
• ...
• Final beam forming
• Local backprojection
– Lower computational cost than BiFBP.

12. From BiFBP to BiFFBP (cont.)
• Beam forming from beam previously formed
– Linear superpositions of beam formed in previous
stage. Reconstructed only on a ground plane.
– References for superposition are centers of
• New (longer) transmitter subaperture
• New (longer) receiver subaperture
• New (smaller) subimage.
 
b2 tl1 ,   Rl1 ,k1  Rlc ,k2  Rlc1,k1 
1 1
L1
l2
  
L2
 b1 tl1 ,   Rl1 ,k1  Rlc ,k2  Rlc1,k1
L1
1 1
l1 1 l2 1
L2

13. From BiFBP to BiFFBP (cont.)
• Mathematical expression for BiFFBP with two
beam forming stages
K2 L1
k1 l2
K1 K1 L2 L2
h  xm , y n      
k1 1 K 2 l2 1 L
k 2 1  k1 1 l1 1 l2 1 1
K1 L2
ts
tl 
 
2
 g vt tl , vr tl , c  Rl1 ,k1  Rlc1,k2  Rlc1,k1  R  Rlc22,k2 dt
1 1
ts
tl 
2

14. Simulations and Evaluation
• Simulation parameters
Parameter CARABAS-II LORA
(transmitter) (receiver)
The maximum frequency 82 MHz
The minimum frequency 22 MHz
Platform speed ������������������ 126 m/s 130 m/s
Aperture step 0.9375 m 0.9673 m
Aperture length 3840 m 3950 m
Flight altitude 3700 m 2900 m
Minimum range ������0 5900 m 3000 m
PRF 137 Hz
Bistatic angle 00/00/600

15. Simulations and Evaluation (cont.)
• Simulated ground scene
– Series of point-like scaterers.
– Equally spaced.
– The same radar cross sections (RCS).
– No noise added.

16. Simulations and Evaluation (cont.)
• Considered bisatic configurations
– Quasi-monostatic: transmitter and receiver are
mounted on a single platform.
– Azimuth-invariant: transmitter and receiver are
mounted on two different platforms whose flight
tracks are parallel.
– General bistatic: transmitter and receiver are mounted
on two different platforms whose flight tracks are
arbitrary, e.g. 600.

17. Simulations and Evaluation (cont.)
• Quasi-monostatic:
– Work.
– Similar monostatic

18. Simulations and Evaluation (cont.)
• Azimuth-invariant:
– Work.
– Beter resolution.

19. Simulations and Evaluation (cont.)
• General bistatic:
– Work.
– Familiar features

20. Simulations and Evaluation (cont.)
• Compared to BiGBP

21. Simulations and Evaluation (cont.)
• Comparison between BiGBP and
– Phase error due to approximations in BiFFBP is
observed.

22. Phase Error Calculation
• Phase error equation [3]
– Calculate the phase error generated by approximations
in BiFFBP.
– Select subimage and subaperture size.
– Minimize phase error.
[3] V. T. Vu et. al., “Phase error calculation for fast time-domain bistatic SAR
algorithms,” in Proc. IEEE Trans. Aerosp. Electron. Syst., submitted for publication.

23. Conclusion
• Propose an algorithm BiFFBP.
• Derive BiFFBP analytically.
• Test BiFFBP with simulated UWB bistatic SAR
data.
• Test BiFFBP with different bistatic configurations.
• Compare with BiGBP.

24. Thanks for your attention!