Fast Factorized Backprojection Algorithm for UWB Bistatic.pdf

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

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

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.

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.

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.

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

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

BiFBP Development on BiGBP
• BiFBP
– Two processing stages:
• Beam forming.
• Local backprojection
– Low computational cost.

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

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

From BiFBP to BiFFBP
• BiFFBP
– More than two processing stages:
• Firtst beam forming.
• ...
• Final beam forming
• Local backprojection
– Lower computational cost than BiFBP.

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

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

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

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

• 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.

• Quasi-monostatic:
– Work.
– Similar monostatic

• Azimuth-invariant:
– Work.
– Beter resolution.

• General bistatic:
– Work.
– Familiar features

• Compared to BiGBP

• Comparison between BiGBP and

– Phase error due to approximations in BiFFBP is
observed.

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.

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.

Fast Factorized Backprojection Algorithm for UWB Bistatic.pdf

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Fast Factorized Backprojection Algorithm for UWB Bistatic.pdf