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Nonlinear Range Cell Migration (RCM) Nonlinear Range Cell Migration (RCM)

Compensation Method for Spaceborne/Airborne Forward-Compensation Method for Spaceborne/Airborne Forward-

Looking Bistatic SARLooking Bistatic SAR

Zhe Liu Zhe Liu ,, Jianyu Yang, Xiaoling Zhang Jianyu Yang, Xiaoling Zhang

School of Electronic Engineering, University of Electronic Science and School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, ChinaTechnology of China, Chengdu, 611731, China

Presentation byPresentation by Zhe LiuZhe Liu

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OutlineOutline

Introduction to the SA-FBSAR and its nonlinear RMC

Nonlinear RCM compensation method

Simulation results

Conclusions and further work

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IntroductionIntroduction－－ What is SA-FBSARWhat is SA-FBSAR

Spaceborne/Airborne Forward-Looking Bistatic SAR (SA-FBSAR)

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.

Target imaging scene: Target scene is along the receiver’s forward-looking direction

transmitter

receiver

Imaging scene

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IntroductionIntroduction－－ Emergence of SA-FBSAREmergence of SA-FBSAR

Monostatic Monostatic SARSAR

Bistatic/Bistatic/MultistaticMultistatic

SAR(B/M SAR)SAR(B/M SAR)

Spaceborne Spaceborne B/M SARB/M SAR

AirborneAirborneB/M SARB/M SAR

S-A B/MS-A B/MSARSAR

Commu.Commu.satellitesatellite

BroadcastBroadcastsatellitesatellite

RadarRadarsatellitesatellite

• Diversity of target information

• High immunity to attacks

• Low cost

• Wide coverage, high SNR

• Platform flexibility

• Power saving

• wide band

• repeated observation

SA-BSAR SA-BSAR with radarwith radarsatellitesatellite

SA-FBSAR SA-FBSAR • attractive potential for

aircraft landing and navigation

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IntroductionIntroduction－－ Emergence of SA-FBSAREmergence of SA-FBSAR

In Nov. 2009, FGAN (German Aerospace Center) launched the first experiment to test the feasibility of SA-FBSAR.

Fig.1 Imaging result of the first SA-FBSAR feasibility experiment in 2009

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IntroductionIntroduction －－ Challenges of SA-FBSAR imagingChallenges of SA-FBSAR imaging

·· Dramatic geometric differenceDramatic geometric difference

Satellite height：500-800km

Aircraft height： 1 - 5km

·· Essential velocity differenceEssential velocity differenceSatellite velocity： 7.4 -7.6km/s

Aircraft velocity： 100m/s

·· Different working mode Different working mode Satellite : side-looking

Aircraft : forward-looking

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IntroductionIntroduction－－ Challenges of SA-FBSAR imagingChallenges of SA-FBSAR imaging

·· Dramatic geometric differenceDramatic geometric difference

·· Essential velocity differenceEssential velocity difference

·· Different working modeDifferent working mode

Range cell migration (RCM) features are :

Vary with the target’s range and azimuth location

exhibits significant nonlinearity with target’s range location

Severe distortion and nonlinear misregistration will occur, if such RCM is not properly compensated

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IntroductionIntroduction－－ effect of nonlinear RCM on imaging resultseffect of nonlinear RCM on imaging results

Fig2. Imaging result of point targets

(a) original point scatterers (b) without RCM compensation

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x

y

(a) original area target (b) Without RCMC

IntroductionIntroduction－－ effect of nonlinear RCM on imaging resultseffect of nonlinear RCM on imaging results

Fig3. Imaging result of area targets

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IntroductionIntroduction－－ Our workOur work

Purpose: find a nonlinear two-dimensional RCM compensation method for SA-FBSAR in frequency domain

Main idea:

3. Set up SA-FBSAR response spectrum model

4. Deduce nonlinear RCM analytic formula

5. Propose SA-FBSAR nonlinear RCM compensation method

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Nonlinear RCM Compensation for SA-FBSARNonlinear RCM Compensation for SA-FBSAR－－ system geometric modelsystem geometric model

Fig.4 SA-FBSAR system geometry

Pξ0 0Pr

0A

A

0PzSξ

Pv

Sv0Sx

x

y

z

Imaging scene

S

P0 0Sr

xr

Sv T

0Pr

x

0Sr

( )( )

0 0

, : denote transmitter and receiver platforms, respectively

: reference point scatterer located at 0, ,0

: non-reference point scatterer located at , ,0

, : velocity of platforms

, : range and S P

S P

A y

A x y

v v

r T 0

0 0 0 0 0

0 0

0 0 0 0 0

0 0

azimuth time distance of A from

, : closest range from platforms to

, : closest range from platforms to

, : azimuth time when is closest to platforms

, : azimuth t

S P

S P

S P

S P

A

r r A

r r A

t t A

t t ime when is closest to platforms

, : the depression angles of platforms' antennaS P

A

ξ ξ

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( ) 220 0 0

2 200 0 0 0 0 0

2. Receiver closest range :

Due to its , targets along range direction are

. Sinc

sin

forward-looking

e sin

mode symmet

, we have . So t

rically

situated 2 he varsinS

P

P

P S

P P P S

r

r

r

r

r

r r r r

ξ

ξ ξ

= +

≈ + ⋅=

0

iance

of receiver's closest range on is . not linear but quadricPr r

( ) ( )

( )

2 2

0 0 0

2 2S 0 0

1. Transmitter closeset range:

Transmitter operates in , and it is asymmetrical with

targets along range direction, the condito

ctg

side-looking mode

ctn holds.

the

gξ2

vari n

a

S S S

S

r r r r

r r r r

ξ= + + ⋅

⋅ +=

0 0 0

ce of the is about proportional

with target'

transmi

s range

tter's closest a

position, i.e.

pproach linearly

.S Sr r r≈ +

.

Origin of nonlinear RCMOrigin of nonlinear RCM

0The , which is directly affected by ,

is also .

-variance of the range history in SA-FBSAR

nonlinearly variant with range locationPr r

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Nonlinear RCM Compensation for SA-FBSARNonlinear RCM Compensation for SA-FBSAR－－ system signal spectrum modelsystem signal spectrum model

( ) ( ) ( )( )

( )

' 2

''

The SA-FBSAR system response after range compression is

, ; ,, exp exp (1), ; ,

2 , ; ,

where is range freqency, is Doppler frequency,

is the range of the

dd d

d

d

f f r TH f f j drdTj f f r T

f f r T

f f

R t

φφ

φ

= −− ∫∫

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( )

0

2' ''

2

0 00 0 22

2 0

SA-FBSAR system about scatterer

2π, , ; ,

, ; , , , ; ,

, ; ,

b

b b

d d t t

d t t d t t

d Sb d S

dS

S

A

f ft R t f t f f r T t

c

t tf f r T f f r T

t tf r r

t f f r T t Tf f f

vc v

φ φ φ

φ φφ φ

=

= =

+ = + = ∂ ∂

= =∂ ∂

+= + −

+ −

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Nonlinear RCM Compensation for SA-FBSARNonlinear RCM Compensation for SA-FBSAR－ － nonlinear RCM analytic formulanonlinear RCM analytic formula

( ) ( )( )( )

After multiplying with conjugate of reference scatterer's spectrum, we get :

;, exp 2 (2)

;

where

RD d AD

d

AD d RD d

RD

ff r TH f f j drdT

Tf f r

α ϕπ

α ϕ

α

∆

+ ≈ − + +

∫∫

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( )( ) ( ) [ ]

2 21 2 1 2

01 1 22 2

22 20 0 0 00 0 0 00

2 2 3 2

0

; , ; (3)

1, , ,

2 sin

11, 1,

2 sin

d RD d RD d RD d RD d RD d

SRD d RD d RD d

S S Pf d

P S PP P SRD d AD AD

PZS Pf d PZ S

S

f r f r f r f r f r f r

f v Ff f f

vc F c r f

a t t va v r rff

c rc r f r v

fF v

c

α α ϕ ϕ ϕ

α ϕ αξ

ϕ α ϕξ

= ⋅ + ⋅ = ⋅ + ⋅⋅

≈ ≈ ≈⋅ ⋅ ⋅

− −− ⋅ ⋅≈ = + =

⋅⋅ ⋅ ⋅

= ( )

( )

2 22

2 2 0 00 0 0 0 0 0

22 20 0 0 0 0 0

, ,

,

d d SPf d P P S P

S S

PZ P P S P S P

f f rr f r v t t

v v F

r r v t t a v v

⋅− = + − − ⋅

= + − =

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Nonlinear RCM Compensation for SA-FBSARNonlinear RCM Compensation for SA-FBSAR－ － nonlinear RCM analytical formulanonlinear RCM analytical formula

2 2

In (2) (3), due to the forward-looking mode, the coefficients of

range-dependent terms and are significant

comparing with the linear terms. For example, in the SA-FBSAR sy

quad

stem of sim

r

u

ic RD RDα ϕlation system

when 300 , 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 va

r m=

ries 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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Nonlinear RCM Compensation for SA-FBSARNonlinear RCM Compensation for SA-FBSAR－ － nonlinear RCM compensation methodnonlinear RCM compensation method

Fig.5 flow chart of nonlinear RCM compensation method for SA-FBSAR

( )'RD

RAAD

T rϕα

=

( ) 0;RA RD d fdf rϕ ϕ ==

( )'0

;RD dRD fd

d

f r

f

ϕϕ =

∂=

∂

,

( ) ( )* *, ;0,0dH f f H fτ τ⋅

{ }exp ADj t fϕ ⋅ ⋅

ADa

imaging result

AD-RCMC

RD-RCMC

signal data from SA-FBSAR

1

dfSCFT −

, tFT FTτ

interpo-lation

1

dfFT −

1,t fFT FT −

( )( ) ( )

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2

RD d

RD d AD RA

a f ra f r T rτ

ϕ= ⋅ +

⋅ − ⋅

( )( ) ( )

2exp d RA

RA RA

j f T rj r T r

πϕ

⋅ ⋅ + ⋅ ⋅

modified two-step RCMC method

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Simulation 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 signal (GHz)

9.65

bandwidth of transmitting signal (MHz)

60

pulse repetition frequency(Hz) 2500

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Simulation Simulation － － Point scatterers

(a) original point scatterers (b) without RCM compensation

(d) with the proposed method(c) with RCMC Method in Ref[1]

Ref[1]: X.Qiu, D. Hu and C. Ding, IEEE Geosci. Remote Sens. Lett., 4, 735-739, 2008.

Fig.6 Imaging results of 15 point scatters

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Simulation Simulation － － Point scatterers

(a) error in range position (b) error in azimuth position

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Simulation Simulation － － area target

x

y

Fig. 7 Imaging results of area target

(a) original area target (b) Without RCMC (c) With the proposed RCM compensation

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16.4

16.4

16.4

16.8

16.8

16.8

17.2

17.2

17.2

17.6

17.6

17.6

1818

18

18.4

18.4

18.4

18.8

18.8

18.8

19.2

19.2

19.2

19.6

19.6

19.6

2020

20

20.4

20.4

20.4

20.8

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20.8

21.2

21.2

21.2

21.6

21.6

21.6

2222

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x /m

y/m

-500 -400 -300 -200 -100 0 100 200 300 400 500-100

-50

0

50

100

Fig.8 two-dimensional resolution performance

x/m

y/m

Ai=16.20m2

A=16.34m2

5 0 0

1 0 0

δr δ

a

x/m

y/m

Ai=18.72m2

A=19.55m2

0

0

δr δ

a

(a) Contour of ideal resolution cell’s area (unit: m2)

(b) target located at (500,100)

(c) target located at (0,0)

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SimulationSimulation

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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Conclusions & Further workConclusions & 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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Thank you