1. Nonlinear Range Cell Migration (RCM)
Compensation Method for Spaceborne/Airborne
Forward-Looking Bistatic SAR
Zhe Liu , Jianyu Yang, Xiaoling Zhang
School of Electronic Engineering, University of Electronic Science and
Technology of China, Chengdu, 611731, China
Presentation by Zhe Liu
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2. Outline
 Introduction to the SA-FBSAR and its nonlinear RMC
 Nonlinear RCM compensation method
 Simulation results
 Conclusions and further work
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3. Introduction－What is SA-FBSAR
Spaceborne/Airborne Forward-
Looking Bistatic SAR (SA-FBSAR) transmitter
 Platforms: Transmitter and receiver of
SA-FBSAR are low earth orbit (LEO)
satellite and aircraft, respectively.
 Working Modes: Transmitter antenna
works in side-looking or squint-looking
mode; receiver antenna in forward-
looking mode. receiver
 Target imaging scene: Target scene is
along the receiver’s forward-looking Imaging scene
direction
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4. Introduction－Emergence of SA-FBSAR
Bistatic/ • Diversity of target information
Monostatic Multistatic
SAR • High immunity to attacks
SAR(B/M SAR)
• Low cost
• Wide coverage, high SNR
S-A B/M
Spaceborne Airborne
SAR • Platform flexibility
B/M SAR B/M SAR • Power saving
SA-BSAR • wide band
with radar
Commu. Broadcast satellite
Radar • repeated observation
satellite satellite satellite
• attractive potential for
SA-FBSAR aircraft landing and 4
navigation

5. Introduction－Emergence of SA-FBSAR
Fig.1 Imaging result of the first SA-FBSAR feasibility experiment in 2009
In Nov. 2009, FGAN (German Aerospace Center) launched
the first experiment to test the feasibility of SA-FBSAR.
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6. Introduction－Challenges of SA-FBSAR imaging
Satellite height：500-
· Dramatic geometric difference 800km
Aircraft height：1 - 5km
· Essential velocity difference Satellite velocity：7.4 -
7.6km/s
Aircraft velocity：100m/s
· Different working mode Satellite : side-looking
Aircraft : forward-looking
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7. Introduction－Challenges of SA-FBSAR imaging
Range cell migration
· Dramatic geometric difference
(RCM) features are :
Vary with the target’s
· Essential velocity difference range and azimuth
location
exhibits significant
nonlinearity with target’s
· Different working mode
range location
Severe distortion and nonlinear
misregistration will occur, if such
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RCM is not properly compensated

8. Introduction－effect of nonlinear RCM on imaging results
(a) original point scatterers (b) without RCM compensation
Fig2. Imaging result of point targets
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9. Introduction－effect of nonlinear RCM on imaging results
y
x
(a) original area target (b) Without RCMC
Fig3. Imaging result of area targets
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10. Introduction－Our work
 Purpose: find a nonlinear two-dimensional RCM
compensation method for SA-FBSAR in frequency
domain
 Main idea:
1. Set up SA-FBSAR response spectrum model
2. Deduce nonlinear RCM analytic formula
3. Propose SA-FBSAR nonlinear RCM compensation
method
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11. Nonlinear RCM Compensation for SA-FBSAR
－system geometric model
z
S , P : denote transmitter and receiver platforms, respectively
A0 : reference point scatterer located at  0, y0 ,0 
S A: non-reference point scatterer located at  x, y,0 
xS 0 vS
zP 0 vS , vP : velocity of platforms
S
r , T : range and azimuth time distance of A from A0
P
vP
r0 S 0 r0 S 0 ,r0 P 0 : closest range from platforms to A0
P r0S
r0 P 0 r0 S ,r0 P : closest range from platforms to A
r0 P
x
t0 S 0 ,t0 P 0 : azimuth time when A0 is closest to platforms
A0
t ,t :
Imaging scene 0 S 0 P
azimuth time when A is closest to platforms
x
 S , P : the depression angles of platforms' antenna
r x
y
vST
A
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Fig.4 SA-FBSAR system geometry

12. Origin of nonlinear RCM
1. Transmitter closeset range: r0 S   r0 S 0  r    r  ctg S 
2 2
Transmitter operates in side-looking mode, and it is asymmetrical with
targets along range direction, the conditon  r  ctgξ S  r 2  2r0 S 0 r holds.
2
the variance of the transmitter's closest approach is about linearly proportional
with target's range position, i.e. r0 S  r0 S 0  r.
2. Receiver closest range : r0 P  r02P 0   r sin  S 
2
Due to its forward-looking mode, targets along range direction are symmetrically
.
situated. Since r sin  S r0 P 0 , we have r0 P  r0 P 0  r 2 2r0 P 0  sin 2  S . So the variance
of receiver's closest range r0 P on r is not linear but quadric.
The r -variance of the range history in SA-FBSAR, which is directly affected by r0 P ,
is also nonlinearly variant with range location .
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13. Nonlinear RCM Compensation for SA-FBSAR
－system signal spectrum model
The SA-FBSAR system response after range compression is
  ' 2  f , fd ; r,T  
H  f , f d    exp   j  f , f d ; r , T   exp   j ''
   drdT (1)
 2  f , f d ; r , T  
 
where f is range freqency, f d is Doppler frequency,
R  t  is the range of the SA-FBSAR system about scatterer A
 f  f0 
  t   2π  R  t   f d t  ,   f , f d ; r , T     t  t tb
 c 
  t   2  t 
 '  f , fd ; r, T   t  tb ,   f , f d ; r , T  
''
t  tb
t t 2
f d  r0 S 0  r 
tb  f , f d ; r , T   t 0 S 0  T 
2
2  f  f   fd 
2
vS  0  
 c   vS 

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14. Nonlinear RCM Compensation for SA-FBSAR
－ nonlinear RCM analytic formula
After multiplying with conjugate of reference scatterer's spectrum, we get :

  RD  f d ; r    ADT  f  

H   f , f d    exp  j 2    drdT (2)

   ADTf d   RD  f d ; r   
 
where  RD  f d ; r    RD1  f d   r   RD 2  f d   r 2 ,  RD  f d ; r    RD1  f d   r   RD 2  f d   r 2 (3)
f 0  vS F 1
 RD1  f d   ,  RD1  f d   ,  RD 2  f d   ,
c F
2
vS 2c  sin  S  rPf  f d 
2
f0  a  1 vP  r02P 0  r0 S 0
2
 a  1 t0 P 0  t0 S 0  vP
2
 RD 2  f d   ,  AD   1,  AD 
2c  sin  S  rPf  f d 
2
rPZ  vS
3 2
c  rPZ
2 2
 f0   fd  2  f r 
2
F  vS  c     , rPf  f d   r02P 0  vP  t0 S 0  t0 P 0  d 0 S 0  ,
   vS   vS  F 
rPZ  r02P 0  vP  t0 S 0  t0 P 0  , a  vS vP
2 2
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15. Nonlinear RCM Compensation for SA-FBSAR
－ nonlinear RCM analytical formula
In (2) (3), due to the forward-looking mode, the coefficients of
quadric range-dependent terms  RD 2 and RD 2 are significant
comparing with the linear terms. For example, in the SA-FBSAR system of simulation system
when r  300m , the ratio between the quadric term and linear term is almost 0.1.
SA-FBSAR, RCM not only depends on target's range location (RD-RCM)
and azimuth location (AD-RCM); but also varies with the range location nonlinearly.
The nonlinearity in RD-RCM is not just slight deviation from the linear part as the
monostatic spaceborne side-looking SAR; it exhibits evident nonlinear deviation in RCM trajectory.
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16. Nonlinear RCM Compensation for SA-FBSAR
－ nonlinear RCM compensation method
signal data from
SA-FBSAR imaging result
FTt , FT FT f1
d
H *  f , f d ;0, 0   H*  f 
 j 2  f d  TRA  r   
exp  
 j RA   r   TRA  r  
,
a AD SCFT f1
interpo-   aRD1  f d   r 
d lation aRD 2  f d   r 2   AD  TRA  r 
 RD
'
RD-RCMC TRA  r  
exp  j AD  t  f   AD
RD  f d ; r 
AD-RCMC RD 
'
fd  0
FTt , FT f1 f d
modified two-step RCMC method RA  RD  f d ; r  fd  0
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Fig.5 flow chart of nonlinear RCM compensation method for SA-FBSAR

17. Simulation － Parameters
Parameters Transmitter Receiver
Height (km) 514 3
velocity (m/s) 7600 100
azimuth beam width(degree) 0.33 2.9
maximum steering angle(degree) 0.75 15
depression angle (degree) 37 68
beam velocity(m/s) 2100 700
integration duration (s) 0.43
pulse width (μs) 2
central frequency of transmitting 9.65
signal (GHz)
bandwidth of transmitting signal 60
(MHz)
pulse repetition frequency(Hz) 2500
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18. Simulation － Point scatterers
(a) original point scatterers (b) without RCM compensation
(c) with RCMC Method in Ref[1] (d) with the proposed method18
Fig.6 Imaging results of 15 point scatters
Ref[1]: X.Qiu, D. Hu and C. Ding, IEEE Geosci. Remote Sens. Lett., 4, 735-739, 2008.

19. Simulation － Point scatterers
(a) error in range position (b) error in azimuth position
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20. Simulation － area target
y
x
(a) original area target (b) Without RCMC (c) With the proposed RCM
compensation
Fig. 7 Imaging results of area target
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21. 100
Ai=16.20m2
21.6
21.2
20.8
20.4
19.6
19.2
18.8
18.4
17.6
17.2
16.8
16.4
r A=16.34m2
22
20
18
a
y/m
100
50
y/m
21.6
21.2
20.8
20.4
19.6
19.2
18.8
18.4
17.6
17.2
16.8
16.4
0 500
22
20
18
x/m
(b) target located at (500,100)
Ai=18.72m2
-50 A=19.55m2
r
a
21.6
21.2
20.8
20.4
19.6
19.2
18.8
18.4
17.6
17.2
16.8
16.4
0
y/m
22
20
18
-100
-500 -400 -300 -200 -100 0 100 200 300 400 500
x /m
(a) Contour of ideal resolution cell’s area (unit: m2) 0
x/m
(c) target located at (0,0)
Fig.8 two-dimensional resolution performance 21

22. Simulation
From the above simulation results, we could find that:
Uncompensated RCM could deteriorate imaging result severely, cause
nonlinear distortion
RCM compensation method designed for other FBSAR system could not
compensate the nonlinear RCM, thus could not be applied to SA-FBSAR.
The proposed RCM compensation method could effectively compensate the
nonlinear RCM in SA-FBSAR, and all targets are arranged in their originally
correct positions.
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23. Conclusions & Further work
 RCM in SA-FBSAR not only depends on the target’s
two-dimensional space location, but also varies with its
range location nonlinearly. If not properly corrected, RCM
would cause nonlinear distortion in the image and greatly
degrade the imaging quality.
 We propose a two-dimensional nonlinear RCMC method
for SA-FBSAR. The validity of the proposed method is
verified.
 Further improvement on resolution performance is under
research
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24. Thank you
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