Research on Bistatic SAR Imaging - UBC ECE
Research on Bistatic SAR Imaging Zhu Zhenbo , Tang Ziyue and Jiang Xingzhou
Abstract—For reasons of stealth and other operational advantages, more attention has recently been focused on bistatic SAR. Bistatic SAR uses separated transmitter and receiver flying on different platforms, and has the ability of the exploitation of additional information contained in the bistatic reflectivity of targets. Besides of technical problems - like the synchronization of the oscillators - the processing of bistatic raw data imaging is not well studied theoretically all the same, which is a major area in bistatic SAR. This paper firstly describes the special case of equal velocity vectors and parallel flight paths of transmitter and receiver, and then makes detailed and mathematical study on the approximate bistatic-to-monostatic application (BTMA). Based on the BTMA, the bistatic imaging can be processed with a Standard SAR Processor. Index Terms—Bistatic, imaging, Synthetic Aperture Radar (SAR).
direction and the same velocity V0 in the ideal condition. In the following, H T and H R refers the height of the transmitter and receiver respectively. A point scatterer Pn is placed at the position [ X n , Yn , 0] within the intersection, RT 0 and R R 0 is the initiatory range from point scatterer Pn to the platform track of transmitter and receiver, R R (t ) and RT ( t ) denotes the range from the receiver and transmitter to the point scatterer Pn at time t respectively. ϕ R and ϕT means the squint angle from receiver and transmitter to the target. Z Y
ϕT
Multiple image formation processes have been developed for monostatic SAR, the mathematically ideal method for image formation is matched filtering. Bistatic SAR systems, in contrast, have seen much less development in the area of image formation, at least in the open literature[1]-[3]. The difficulties to evaluate a bistatic processor is mainly due to the fact, that we have to handle a sum of two different terms with square roots in the denominator instead of one such term as in the monostatic case. The types of processors which can be used for the different geometrical situation are different, and the SAR image properties depend on them, too. This paper firstly describes the special case of equal velocity vectors and parallel flight paths of transmitter and receiver, and then makes detailed and mathematical study on the approximate bistatic-to-monostatic application. Based on the bistatic-to-monostatic application (BTMA), the bistatic imaging can be processed with a Standard SAR Processor, and then the conventional CS, ECS and omega-k algorithm are also applicable to the bistatic imaging, which are all testified by the simulation in the paper. II. MODELING THE PROBLEM Bistatic Geometry
The tandem bistatic geometry applied to the problem is shown in Fig.1. The transmitter and receiver coordinated [0, V0t , H T ] and [ X R 0 , V0t , H R ] respectively, which move at the same
Receiver
RT (t )
I. INTRODUCTION
A
Transmitter
HT
ϕR
RR (t )
HR X O
X R0
Pn ( X n , Yn , Z n )
Fig 1 The bistatic geometry and Target Moving Modeling On the assumption that the transmitter transmits chirp pulse signal with the chirp rate K ,then the received signal can be written as
Sr (τ , t ; RT 0 , RR 0 ) =
2 2 R ( t ; RT 0 , RR 0 ) (1) A ⋅ exp − jπ K τ − c 2π ⋅ exp − j R(t ; RT 0 , RR 0 ) λ c represents the velocity of light, and K represents the chirp rate of the transmitting signal. In addition, t represents slow-time, and τ represents fast-time.
B
Bistatic SAR Imaging
As the transmitter moves along its flight path, the radiating antenna periodically transmits pulses of energy in the direction of the scene center. Each transmitted pulse travels from the transmitter to the scene of interest, where it is reflected by scatterer within the area of illumination. This reflected energy disperses in all directions, and some of this energy is observed
0-7803-9510-7/06/$20.00 (c) 2006 IEEE
by the receive. We assume that the travel time of the pulse from the transmitter to a scatterer to the receiver is sufficiently short, with respect to the pulse duration, that any platform movement within that time period may be neglected. Multiple image formation processes have been developed for monostatic SAR, the mathematically ideal method for image formation is matched filtering. Bistatic SAR systems, in contrast, have seen much less development in the area of image formation, at least in the open literature. The difficulties to evaluate a bistatic processor is mainly due to the fact, that we have to handle a sum of two different terms with square roots in the denominator instead of one such term as in the monostatic case. The types of processors which can be used for the different geometrical situation are different, and the SAR image properties depend on them, too. The followings of the paper mainly talks about the imaging algorithm for side-looking mode and squint mode, witch is based on the BTMA and in special case of equal velocity vectors and parallel flight paths of transmitter and receiver.
Side-Looking Mode
In the special bistatic geometry as shown in Fig.1, with the transmitter and receiver working at side-looking mode, the bistatic imaging can be processed with a Standard SAR Processor based on the BTMA. The bistatic-to-monostatic equivalent is shown as the following. The monostatic SAR range model can be written as: R ( t ; Rc ) = R + Vm ⋅ t 2 c
2
(2) As shown in Fig.1, the bistatic SAR range model can be written as: R ( t ; RT 0 , RR 0 ) = RT20 + V02 ⋅ t 2 + RR20 + V02 ⋅ t 2
1+
where
r
t
ref
s
t
c
t
ref
(7)
Rc
(8)
(3)
(9)
4π fτ ⋅ exp j ⋅ Rref ⋅ Cs ( ft ) c (3) The cross compression factor 2 λ f 4π ⋅ Rc ⋅ 1 − 1 − t H c ( f t ; Rc ) = exp j 2V0 λ ⋅ exp { j Θ1 ( f t ; Rc )}
(10)
where Θ1 ( f t ; Rc ) =
4π ⋅ K r ( f t ; Rc ) ⋅ 1 + Cs ( f t ) ⋅ Cs ( f t ) ⋅ ( Rc − Rref c2
)
2
t → ft
H CS τ → fτ
Hr fτ → τ
Hc ft → t
Based on Equ. (3), in the first step of the linear chirp scaling algorithm, the chirp scaling factor can be expressed as 2 2 (5) H (τ , f ; R ) = exp − jπ K ( f ; R ) ⋅ C ( f ) ⋅ τ − R ( f ; R ) ref
3
= Rc [1 + Cs ( f t )] 2 λ ft 1− 2V0 where Rref means the reference slant range. (2) The range compression factor R ( ft ; Rc ) =
(1) The chirp scaling factor
t
(6)
2
λ f 2 2 1 − t 2V0 1 Cs ( ft ) = −1 2 λ ft 1− 2V0
the bistatic-to-monostatic application can be fulfilled by RT 0 + RR 0 Rc = 2 (4) RT 0 + RR 0 Vm = V0 2 RT 0 ⋅ RR 0 Based on the above BTMA, the bistatic imaging can be processed with a Standard SAR Processor, and then the conventional CS algorithm is also applicable to the bistatic imaging[4][7]. The monostatic chirp scaling algorithm relies on the direct proportionality of the range cell migration in range-Doppler domain with the slant range, which is not fulfilled in the analyzed bistatic scenario. The block diagram of the chirp scaling algorithm is presented in figure 2
CS
2λ KRc ⋅ c2
λ ft 2V0
π fτ2 H r ( fτ ; f t ; Rref ) = exp − j K r ( ft ; Rref ) ⋅ 1 + C s ( ft )
. BISTATIC SAR IMAGING ALGORITHM A
K
K r ( f t ; Rc ) =
Fig2 The block diagram of the chirp scaling algorithm
0-7803-9510-7/06/$20.00 (c) 2006 IEEE
(11)
B
Squint Mode
2 2 H ECS (τ , f t ; Rref ) = exp − jπK r ( f t ; Rref ) ⋅ Cs ( f t ) ⋅ τ − R ( f t ; Rref ) c
In the special bistatic geometry as shown in Fig.3, with the where transmitter and receiver working at squint mode, K K r ( f t ; Rc ) = α T and α R represent the squint angle of the transmitter and 2 λ ft receiver respectively. The bistatic imaging also can be 2V0 2λ KRc cos α processed with a Standard SAR Processor based on the BTMA. 1+ ⋅ 3 The bistatic-to-monostatic equivalent is shown as the c2 2 2 λ f following. 1 − t 2V0 V V 0
0
Cs ( ft ) =
−1 2 λ ft 1− 2V0 Rc cos α R ( ft ; Rc ) = = Rc [1 + Cs ( f t )] 2 λ ft 1− 2V0
Pn RT 0
αR
RR 0
αT
X
Transmitter
cos α
Receiver
(15)
(16)
(17)
(18)
where Rref means the reference slant range. Fig.3 Geometrical Configuration of Squint Mode Bistatic SAR
t → ft
The monostatic SAR range model can be written as: R ( t ; Rc ) = R + Vm ⋅ t − 2Rc ⋅ (Vm t ) ⋅ sin α m 2 c
2
2
H ECS
(12)
τ → fτ
As shown in Fig.3, the bistatic SAR range model can be written as: R ( t ; RT 0 , RR 0 ) = RT20 + V02 ⋅ t 2 − 2 RT 0 ⋅ (V0 t ) ⋅ sin α T + RR2 0 + V0 2 ⋅ t 2 − 2RR 0 ⋅ (V0t ) ⋅ sin α R
(13)
the bistatic-to-monostatic application can be fulfilled by RT 0 + RR 0 R0 = 2 2 2 ( RT 0 + RR 0 ) − ( RT 0 ⋅ sin α R + RR 0 ⋅ sin α T ) vs = V0 2 RT 0 ⋅ RR 0 (14) sin α R + sin αT sin α = 2 −1 ( R + R ) 2 − ( R ⋅ sin α + R ⋅ sin α ) 2 T 0 R 0 T 0 R R 0 T ∗ 2 RT 0 ⋅ RR 0 Based on the above BTMA, the bistatic imaging can be processed with a Standard SAR Processor, and then the conventional ECS algorithm is also applicable to the bistatic imaging[5][6][8]. The block diagram of the chirp scaling algorithm is presented in figure 4,the main process steps are given as the following (1) The ECS chirp scaling factor Based on Equ. (3), in the first step of the ECS algorithm, chirp scaling factor can be expressed as
H r _ ECS
the
fτ → τ
H c _ ECS ft → t
Fig4 The block diagram of the ECS algorithm (2) The range compression factor πfτ2 H r _ ECS ( fτ ; f t ; Rref ) = exp − j K r ( f t ; Rref ) ⋅ 1 + Cs ( f t ) (19) 4πfτ ⋅ exp j ⋅ Rref ⋅ Cs ( f t ) c (3) The cross compression factor 2 λ f 4π ⋅ Rc ⋅ 1 − 1 − t H c _ ECS ( f t ; Rc ) = exp j 2V0 λ
{
}
⋅ exp j Θ1 ( ft ; Rc ) + Θ2 ( ft ; Rc )
0-7803-9510-7/06/$20.00 (c) 2006 IEEE
(20)
where Θ1 ( f t ; Rc ) and Θ 2 ( f t ; Rc ) denote the residue phase after ECS application, and the expressions can be specified as 2 4π (21) Θ1 ( f t ; Rc ) = ⋅ K r ( f t ; Rc ) ⋅ 1 + Cs ( f t ) ⋅ Cs ( f t ) ⋅ ( Rc − Rref ) c2
Θ2 ( f t ; Rc ) =
Ⅳ.
2πf t Rc ⋅ sin α V0
(22)
SIMULATION AND EXPERIMENTAL RESULTS
The list of its systematic parameters is presented as follows: the carrier frequency is 9.6GHz, the sampling frequency is 150MHz, the pulse frequency is 200Hz, and the forward velocity of platform V0 = 80ms −1 . Meanwhile, the transmitter height H T = 6km and the receiver height H T = 4km , the target is assumed located at RT 0 = 40km and RR 0 = 10km . The pulse duration τ = 5µ s , and frequency band width B = 100MHz .
Given that the transmitter and receiver has the same constant velocity without motion error, and the bistatic configuration is shown as Fig1. Fig.5 shows ground plane image formed in the global (x; y) coordinate with CS algorithm at the side-looking mode. In squint mode, given that the squint angle of receiver is 10o, the imaging result of a point target is shown in Fig.6. The performance indexes of Impulse response in side-looking and squint mode are s in table 1. Table.1 Typical Impulse response for simulated point target data Squint Angle
Algor -ithm
ISLR (dB)
PSLR (dB)
SSLR (dB)
0o
CS
-17.05
-42.23
-45.35
10o
ECS
-17.05
-42.23
-45.35
Resolution (m) 2.5(range) 1.44(azimuth) 2.5(range) 1.44(azimuth)
CONCLUSIONS In this paper, the imaging algorithm for bistatic SAR, in the special bistatic geometry with the transmitter and receiver moving at the same, is studied. Based on the BTMA, the bistatic imaging can be processed with a Standard SAR Processor, and then the conventional CS, ECS algorithm are also applicable to the bistatic imaging, which are all testified by the simulation in the paper.
REFERENCE:
Fig. 5. Ground plane image formed in the global (x; y) coordinate with CS in side-looking mode.
[1]. Tang Ziyue, Zhang Shourong: Bistatic SAR system theory, Science Publishing House, 2003.6 [2]. Braun H.M., Hartl P., “Bistatic radar in space: a new dimension in imaging radar”, P roc. of IGARSS’89, pp. 2261–2264, 1989. [3]. M.Soumekh: Wide-bandwidth continuous-wave monostatic /bistatic synthetic aperture radar imaging. International Conference on Image Processing, Oct 1998, pp 361 - 365. [4]. Bao Zheng, et al.: Synthetic aperture radar imaging technology, Electronics Industry Publishing House, 2005.4. [5]. Liu Guangyan, Lei Wanming, Huang Shunji. The Extended CS algorithm of squint mode SAR imaging. Vol.18,No.4,2002.8. [6]. Sanz J., Prats, P., Mallorqui, J.J.: Platform and mode independent SAR data processor based on the Extended Chirp Scaling Algorithm. IGARSS proceedings, 2003. [7]. R. Keith Raney, H. Runge, R. Bamler, Ian Cumming, and Frank Wong, Precision SAR Processing Using Chirp Scaling, IEEE TGRS 32, pp. 786-799, 1994. [8]. A. Moreira, R. Scheiber, and J. Mittermayer, Extended Chirp Scaling Algorithm for Air- and Spaceborne SAR Data Processing in Stripmap and ScanSAR Imaging Modes, IEEE TGRS 34, pp. 1123-1136, 1996.
Fig. 6. Ground plane image formed in the global (x; y) coordinate with ECS in squint mode.
0-7803-9510-7/06/$20.00 (c) 2006 IEEE
Abstract—For reasons of stealth and other operational advantages, more attention has recently been focused on bistatic SAR. Bistatic SAR uses separated transmitter and receiver flying on different platforms, and has the ability of the exploitation of additional information contained in the bistatic reflectivity of targets. Besides of technical problems - like the synchronization of the oscillators - the processing of bistatic raw data imaging is not well studied theoretically all the same, which is a major area in bistatic SAR. This paper firstly describes the special case of equal velocity vectors and parallel flight paths of transmitter and receiver, and then makes detailed and mathematical study on the approximate bistatic-to-monostatic application (BTMA). Based on the BTMA, the bistatic imaging can be processed with a Standard SAR Processor. Index Terms—Bistatic, imaging, Synthetic Aperture Radar (SAR).
direction and the same velocity V0 in the ideal condition. In the following, H T and H R refers the height of the transmitter and receiver respectively. A point scatterer Pn is placed at the position [ X n , Yn , 0] within the intersection, RT 0 and R R 0 is the initiatory range from point scatterer Pn to the platform track of transmitter and receiver, R R (t ) and RT ( t ) denotes the range from the receiver and transmitter to the point scatterer Pn at time t respectively. ϕ R and ϕT means the squint angle from receiver and transmitter to the target. Z Y
ϕT
Multiple image formation processes have been developed for monostatic SAR, the mathematically ideal method for image formation is matched filtering. Bistatic SAR systems, in contrast, have seen much less development in the area of image formation, at least in the open literature[1]-[3]. The difficulties to evaluate a bistatic processor is mainly due to the fact, that we have to handle a sum of two different terms with square roots in the denominator instead of one such term as in the monostatic case. The types of processors which can be used for the different geometrical situation are different, and the SAR image properties depend on them, too. This paper firstly describes the special case of equal velocity vectors and parallel flight paths of transmitter and receiver, and then makes detailed and mathematical study on the approximate bistatic-to-monostatic application. Based on the bistatic-to-monostatic application (BTMA), the bistatic imaging can be processed with a Standard SAR Processor, and then the conventional CS, ECS and omega-k algorithm are also applicable to the bistatic imaging, which are all testified by the simulation in the paper. II. MODELING THE PROBLEM Bistatic Geometry
The tandem bistatic geometry applied to the problem is shown in Fig.1. The transmitter and receiver coordinated [0, V0t , H T ] and [ X R 0 , V0t , H R ] respectively, which move at the same
Receiver
RT (t )
I. INTRODUCTION
A
Transmitter
HT
ϕR
RR (t )
HR X O
X R0
Pn ( X n , Yn , Z n )
Fig 1 The bistatic geometry and Target Moving Modeling On the assumption that the transmitter transmits chirp pulse signal with the chirp rate K ,then the received signal can be written as
Sr (τ , t ; RT 0 , RR 0 ) =
2 2 R ( t ; RT 0 , RR 0 ) (1) A ⋅ exp − jπ K τ − c 2π ⋅ exp − j R(t ; RT 0 , RR 0 ) λ c represents the velocity of light, and K represents the chirp rate of the transmitting signal. In addition, t represents slow-time, and τ represents fast-time.
B
Bistatic SAR Imaging
As the transmitter moves along its flight path, the radiating antenna periodically transmits pulses of energy in the direction of the scene center. Each transmitted pulse travels from the transmitter to the scene of interest, where it is reflected by scatterer within the area of illumination. This reflected energy disperses in all directions, and some of this energy is observed
0-7803-9510-7/06/$20.00 (c) 2006 IEEE
by the receive. We assume that the travel time of the pulse from the transmitter to a scatterer to the receiver is sufficiently short, with respect to the pulse duration, that any platform movement within that time period may be neglected. Multiple image formation processes have been developed for monostatic SAR, the mathematically ideal method for image formation is matched filtering. Bistatic SAR systems, in contrast, have seen much less development in the area of image formation, at least in the open literature. The difficulties to evaluate a bistatic processor is mainly due to the fact, that we have to handle a sum of two different terms with square roots in the denominator instead of one such term as in the monostatic case. The types of processors which can be used for the different geometrical situation are different, and the SAR image properties depend on them, too. The followings of the paper mainly talks about the imaging algorithm for side-looking mode and squint mode, witch is based on the BTMA and in special case of equal velocity vectors and parallel flight paths of transmitter and receiver.
Side-Looking Mode
In the special bistatic geometry as shown in Fig.1, with the transmitter and receiver working at side-looking mode, the bistatic imaging can be processed with a Standard SAR Processor based on the BTMA. The bistatic-to-monostatic equivalent is shown as the following. The monostatic SAR range model can be written as: R ( t ; Rc ) = R + Vm ⋅ t 2 c
2
(2) As shown in Fig.1, the bistatic SAR range model can be written as: R ( t ; RT 0 , RR 0 ) = RT20 + V02 ⋅ t 2 + RR20 + V02 ⋅ t 2
1+
where
r
t
ref
s
t
c
t
ref
(7)
Rc
(8)
(3)
(9)
4π fτ ⋅ exp j ⋅ Rref ⋅ Cs ( ft ) c (3) The cross compression factor 2 λ f 4π ⋅ Rc ⋅ 1 − 1 − t H c ( f t ; Rc ) = exp j 2V0 λ ⋅ exp { j Θ1 ( f t ; Rc )}
(10)
where Θ1 ( f t ; Rc ) =
4π ⋅ K r ( f t ; Rc ) ⋅ 1 + Cs ( f t ) ⋅ Cs ( f t ) ⋅ ( Rc − Rref c2
)
2
t → ft
H CS τ → fτ
Hr fτ → τ
Hc ft → t
Based on Equ. (3), in the first step of the linear chirp scaling algorithm, the chirp scaling factor can be expressed as 2 2 (5) H (τ , f ; R ) = exp − jπ K ( f ; R ) ⋅ C ( f ) ⋅ τ − R ( f ; R ) ref
3
= Rc [1 + Cs ( f t )] 2 λ ft 1− 2V0 where Rref means the reference slant range. (2) The range compression factor R ( ft ; Rc ) =
(1) The chirp scaling factor
t
(6)
2
λ f 2 2 1 − t 2V0 1 Cs ( ft ) = −1 2 λ ft 1− 2V0
the bistatic-to-monostatic application can be fulfilled by RT 0 + RR 0 Rc = 2 (4) RT 0 + RR 0 Vm = V0 2 RT 0 ⋅ RR 0 Based on the above BTMA, the bistatic imaging can be processed with a Standard SAR Processor, and then the conventional CS algorithm is also applicable to the bistatic imaging[4][7]. The monostatic chirp scaling algorithm relies on the direct proportionality of the range cell migration in range-Doppler domain with the slant range, which is not fulfilled in the analyzed bistatic scenario. The block diagram of the chirp scaling algorithm is presented in figure 2
CS
2λ KRc ⋅ c2
λ ft 2V0
π fτ2 H r ( fτ ; f t ; Rref ) = exp − j K r ( ft ; Rref ) ⋅ 1 + C s ( ft )
. BISTATIC SAR IMAGING ALGORITHM A
K
K r ( f t ; Rc ) =
Fig2 The block diagram of the chirp scaling algorithm
0-7803-9510-7/06/$20.00 (c) 2006 IEEE
(11)
B
Squint Mode
2 2 H ECS (τ , f t ; Rref ) = exp − jπK r ( f t ; Rref ) ⋅ Cs ( f t ) ⋅ τ − R ( f t ; Rref ) c
In the special bistatic geometry as shown in Fig.3, with the where transmitter and receiver working at squint mode, K K r ( f t ; Rc ) = α T and α R represent the squint angle of the transmitter and 2 λ ft receiver respectively. The bistatic imaging also can be 2V0 2λ KRc cos α processed with a Standard SAR Processor based on the BTMA. 1+ ⋅ 3 The bistatic-to-monostatic equivalent is shown as the c2 2 2 λ f following. 1 − t 2V0 V V 0
0
Cs ( ft ) =
−1 2 λ ft 1− 2V0 Rc cos α R ( ft ; Rc ) = = Rc [1 + Cs ( f t )] 2 λ ft 1− 2V0
Pn RT 0
αR
RR 0
αT
X
Transmitter
cos α
Receiver
(15)
(16)
(17)
(18)
where Rref means the reference slant range. Fig.3 Geometrical Configuration of Squint Mode Bistatic SAR
t → ft
The monostatic SAR range model can be written as: R ( t ; Rc ) = R + Vm ⋅ t − 2Rc ⋅ (Vm t ) ⋅ sin α m 2 c
2
2
H ECS
(12)
τ → fτ
As shown in Fig.3, the bistatic SAR range model can be written as: R ( t ; RT 0 , RR 0 ) = RT20 + V02 ⋅ t 2 − 2 RT 0 ⋅ (V0 t ) ⋅ sin α T + RR2 0 + V0 2 ⋅ t 2 − 2RR 0 ⋅ (V0t ) ⋅ sin α R
(13)
the bistatic-to-monostatic application can be fulfilled by RT 0 + RR 0 R0 = 2 2 2 ( RT 0 + RR 0 ) − ( RT 0 ⋅ sin α R + RR 0 ⋅ sin α T ) vs = V0 2 RT 0 ⋅ RR 0 (14) sin α R + sin αT sin α = 2 −1 ( R + R ) 2 − ( R ⋅ sin α + R ⋅ sin α ) 2 T 0 R 0 T 0 R R 0 T ∗ 2 RT 0 ⋅ RR 0 Based on the above BTMA, the bistatic imaging can be processed with a Standard SAR Processor, and then the conventional ECS algorithm is also applicable to the bistatic imaging[5][6][8]. The block diagram of the chirp scaling algorithm is presented in figure 4,the main process steps are given as the following (1) The ECS chirp scaling factor Based on Equ. (3), in the first step of the ECS algorithm, chirp scaling factor can be expressed as
H r _ ECS
the
fτ → τ
H c _ ECS ft → t
Fig4 The block diagram of the ECS algorithm (2) The range compression factor πfτ2 H r _ ECS ( fτ ; f t ; Rref ) = exp − j K r ( f t ; Rref ) ⋅ 1 + Cs ( f t ) (19) 4πfτ ⋅ exp j ⋅ Rref ⋅ Cs ( f t ) c (3) The cross compression factor 2 λ f 4π ⋅ Rc ⋅ 1 − 1 − t H c _ ECS ( f t ; Rc ) = exp j 2V0 λ
{
}
⋅ exp j Θ1 ( ft ; Rc ) + Θ2 ( ft ; Rc )
0-7803-9510-7/06/$20.00 (c) 2006 IEEE
(20)
where Θ1 ( f t ; Rc ) and Θ 2 ( f t ; Rc ) denote the residue phase after ECS application, and the expressions can be specified as 2 4π (21) Θ1 ( f t ; Rc ) = ⋅ K r ( f t ; Rc ) ⋅ 1 + Cs ( f t ) ⋅ Cs ( f t ) ⋅ ( Rc − Rref ) c2
Θ2 ( f t ; Rc ) =
Ⅳ.
2πf t Rc ⋅ sin α V0
(22)
SIMULATION AND EXPERIMENTAL RESULTS
The list of its systematic parameters is presented as follows: the carrier frequency is 9.6GHz, the sampling frequency is 150MHz, the pulse frequency is 200Hz, and the forward velocity of platform V0 = 80ms −1 . Meanwhile, the transmitter height H T = 6km and the receiver height H T = 4km , the target is assumed located at RT 0 = 40km and RR 0 = 10km . The pulse duration τ = 5µ s , and frequency band width B = 100MHz .
Given that the transmitter and receiver has the same constant velocity without motion error, and the bistatic configuration is shown as Fig1. Fig.5 shows ground plane image formed in the global (x; y) coordinate with CS algorithm at the side-looking mode. In squint mode, given that the squint angle of receiver is 10o, the imaging result of a point target is shown in Fig.6. The performance indexes of Impulse response in side-looking and squint mode are s in table 1. Table.1 Typical Impulse response for simulated point target data Squint Angle
Algor -ithm
ISLR (dB)
PSLR (dB)
SSLR (dB)
0o
CS
-17.05
-42.23
-45.35
10o
ECS
-17.05
-42.23
-45.35
Resolution (m) 2.5(range) 1.44(azimuth) 2.5(range) 1.44(azimuth)
CONCLUSIONS In this paper, the imaging algorithm for bistatic SAR, in the special bistatic geometry with the transmitter and receiver moving at the same, is studied. Based on the BTMA, the bistatic imaging can be processed with a Standard SAR Processor, and then the conventional CS, ECS algorithm are also applicable to the bistatic imaging, which are all testified by the simulation in the paper.
REFERENCE:
Fig. 5. Ground plane image formed in the global (x; y) coordinate with CS in side-looking mode.
[1]. Tang Ziyue, Zhang Shourong: Bistatic SAR system theory, Science Publishing House, 2003.6 [2]. Braun H.M., Hartl P., “Bistatic radar in space: a new dimension in imaging radar”, P roc. of IGARSS’89, pp. 2261–2264, 1989. [3]. M.Soumekh: Wide-bandwidth continuous-wave monostatic /bistatic synthetic aperture radar imaging. International Conference on Image Processing, Oct 1998, pp 361 - 365. [4]. Bao Zheng, et al.: Synthetic aperture radar imaging technology, Electronics Industry Publishing House, 2005.4. [5]. Liu Guangyan, Lei Wanming, Huang Shunji. The Extended CS algorithm of squint mode SAR imaging. Vol.18,No.4,2002.8. [6]. Sanz J., Prats, P., Mallorqui, J.J.: Platform and mode independent SAR data processor based on the Extended Chirp Scaling Algorithm. IGARSS proceedings, 2003. [7]. R. Keith Raney, H. Runge, R. Bamler, Ian Cumming, and Frank Wong, Precision SAR Processing Using Chirp Scaling, IEEE TGRS 32, pp. 786-799, 1994. [8]. A. Moreira, R. Scheiber, and J. Mittermayer, Extended Chirp Scaling Algorithm for Air- and Spaceborne SAR Data Processing in Stripmap and ScanSAR Imaging Modes, IEEE TGRS 34, pp. 1123-1136, 1996.
Fig. 6. Ground plane image formed in the global (x; y) coordinate with ECS in squint mode.
0-7803-9510-7/06/$20.00 (c) 2006 IEEE
