improved secondary range compression focusing method in geo sar
IMPROVED SECONDARY RANGE COMPRESSION FOCUSING METHOD IN GEO SAR Zhipeng Liu, Cheng Hu, Tao Zeng
Radar Research Lab, department of electric engineering, Beijing Institute of Technology Beijing 100081, China ABSTRACT The paper firstly analyses the error caused by the linear trajectory model and the Fresnel approximation because of the long synthetic aperture time in Geosynchronous Synthetic Aperture Radar (GEO SAR), and then proposes an improved Secondary Range Compression (SRC) focusing algorithm to overcome the effect of linear trajectory model and the Fresnel approximation. The improved focusing algorithm adopts the curved trajectory model on basis of Norm operator to remove the error caused by the linear trajectory, derives and compensates the third order phase in two-dimensional frequency domain to overcome the large range migration. Finally, imaging results verify the improved focusing algorithm. Index Terms— GEO, SAR, SRC, Linear trajectory, Fresnel approximation 1. INTRODUCTION With the application development of synthetic aperture radar (SAR), low earth orbit (LEO) SAR becomes more and more difficult to meet the application requirement. Thus, geosynchronous synthetic aperture radar (GEO SAR) system was proposed by K.Tomiyas u in 1978 [1]. In 1983, K.Tomiyasu discussed the GEO SAR system in detail [2]. However, since imaging algorithms and the hardware technologies were immature at that time, the idea got into quiet for a long time. With the coming of the 21st century, the GEO SAR turns into a hot topic in accordance with the fast development of relevant technology and the maturity of LEO SAR imaging algorithms. The most representative organizations are Jet Propulsion Laboratory (JPL) and Cranfield University which both went deeply into studying the system [3]~[5]. The advantages of the GEO SAR are obvious, such as the huge coverage, the fine temporal sampling and the short interference period and so on. The above advantageous conditions make the tremendous potentiality of the GEO SAR in forecasting the earthquake and volcano, the hydrological cycle and monitoring vegetation changes etc [4][6]. However there is a fact which is not neglected with the increase of the satellite orbit height, namely that an atmosphere impact on the SAR focusing
978-1-4577-0539-7/11/$26.00 ©2011 IEEE
1373
needs to be taken into consideration. Reference [7] and [8] analyzed the impacts on focusing from ionosphere and troposphere. Imaging is an important aspect of GEO SAR. Reference [9], [10] and [11] studied imaging algorithms of GEO SAR, and reference [12] analyzed the resolution of GEO SAR, and reference [13] focused on the attitude control. According to the analysis of the above literatures, we can know many differences exist between LEO SAR and GEO SAR, such as the longer synthetic aperture time and the more complex attitude control in GEO SAR etc.; furthermore LEO SAR imaging algorithms cannot be directly used in GEO SAR. Therefore, the main emphasis of the paper is placed on the imaging algorithms at equator. A great error will appear if the classical imaging algorithms are used at equator; in addition, some factors that can be neglected in the classical imaging algorithms will not be neglected in GEO SAR. The paper modifies the secondary range compression (SRC) algorithm [14] which is popular in LEO SAR, and verifies the correctness of the improved SRC algorithm. This paper is organized as follow. Section 2 presents and analyzes the problem which is caused by the linear trajectory model and the Fresnel approximation. Section 3 proposes the improved SRC. Section 4 presents the simulation results of the SRC algorithm proposed, and makes a comparison with the results of the classical SRC. Finally, the conclusion is drawn. 2. ANALYSIS OF THE LINEAR TRAJECTORY MODEL AND THE FRESNEL APPROXIMATION Many algorithms are available in LEO SAR, including the familiar SRC [14], the chirp scaling (CS) [15] algorithm, the range migration algorithm (RMA) [16] as well as various extended algorithms. Those algorithms are derived under some model assumption or mathematical approximation, such as the linear trajectory model and the Fresnel approximation. The trajectory of the satellite in LEO is considered as the rectangular line (red line in Figure 1). This consideration is proper in processing the LEO SAR imaging, but the situation is of difference when it comes to GEO SAR due to thousands of kilometers of synthetic aperture length, for example, the error caused by the linear trajectory at the center of the scene at equator is up to 0.16 meter
ICASSP 2011
(wavelength order). The simulated results of error caused by the linear trajectory model and the Fresnel approximation are shown in Figure 2. The parameters of the satellite orbit are: the orbit inclination 53 degrees, the argument of perigee 270 degrees, and the right of ascend nod 265 degrees.
z
the curved trajectory
satellite
Gx Rsn
the linear trajectory
V
T
G
G
where RK K represents the range history, Rsn , Rgn respectively represent the positions of satellite and the target, and K denotes the azimuth time. Based on the geometry configuration of GEO SAR system, the echo can be written as, s K , t V aK K ar t 2 RK K c (1) 2 exp ª« j π D t 2 RK K c º» exp j 4 π RK K λ ¬
¼
where t is the range time, V stands for the backward scattering coefficient, aK and ar denote the envelope R0
o
functions of the azimuth and the range respectively. D denotes the range FM rate, λ is the wavelength and c is the speed of light. The first step is the range Fourier transform, and the range-frequency expression of echo can be given as s K , f r V aK K Ar f r exp j π f r2 D (2) exp ¬ª j 4 S RK K f r f 0 c ¼º
y G Rgn
target
x Figure 1. T he geometrical configuration of the linear trajectory and the curved trajectory
where Ar is the frequency expression of the range 1
0.8
0.8
envelope, f r is the range frequency and f 0 is the center
0.6
0.6 0.4
0.2
Unit,rad
0.2 Unit,rad
frequency of the transmitted pulse. Next, the range compression will be implemented, and the reference function can be written as H1 exp j π f r 2 D (3)
0.4
0 -0.2
0 -0.2
-0.4 -0.4
-0.6 -0.6
-0.8 -1 -20
-15
-10
-5
0
Time,s
5
10
15
20
-0.8 -20
-15
-10
-5
0
5
10
15
The following processing of classical SRC algorithm is to transform the echo of range compression into the twodimensional frequency domain, where the range RK K in (2)
20
Time,s
(a) T he error of the (b) T he error of the Fresnel approximation linear trajectory model Figure 2. T he error of models at the center of scene at equator
is regarded as the linear trajectory, we have
According to Figure 2, we can find that the model error cannot be neglected. For this reason, the error must be removed and some filtering functions need to be modified. This paper modifies the SRC algorithm and validates the improved SRC by the simulation results. The main processing method is as follow. Firstly, the error caused by the linear trajectory model will be compensated before the beginning of the SRC algorithm, and the error compensation function is processed in the range-Doppler domain. Secondly, because of the effect of earth rotation and long synthetic aperture time, we find that the range migration is so large that the high order phase neglected in LEO SAR imaging must be considered in GEO SAR. Furthermore, the high order phase error and range migration correction will be detailedly analyzed and compensated in two-dimensional frequency domain. 3. IMPROVED SRC ALGORITHMS According to Figure 1, the curved trajectory can be G G expressed via Norm operator, namely RK K Rsn Rgn
1374
RK K
R02 V K 2 R0 V K sin T 2
(4)
where V is the satellite velocity , T is the squint angle, and R0 is the range between the beam center and the central target of scene. V , T and R0 can be obtained via the curve fitting, which can satisfy the focusing demand in LEO SAR, while in GEO SAR, the error of curve fitting is very large, especially at equator. Thus, we need to compensate a phase to eliminate the effects of the curving fitting error before the azimuth FFT, and the phase compensation function can be written as H 2 exp ª¬ j 4 π f r f 0 'R0 c º¼ (5) where
G G 2 'R0 Rsn Rg 0 R0 2 V K 2 R0 V K sin T G here Rg 0 denotes the target coordinate of the scene centre. The next step is transforming the echo data into the two-dimensional frequency domain, and then twodimensional spectrum is obtained. In consequence, the range migration correction will be implemented and the third order phase frequently neglected in LEO SAR imaging will
also be compensated. In addition, the SRC function can be expressed as (6) H 3 exp j π f r 2 D src The range migration correction function can be shown as
exp j 4 π R0 c a fK f r
H4
(7)
The third order phase compensation function can be written as ½ j π R0 cos T λ 4 fK 2 ° ° (8) H 5 exp ® 2.5 ¾ 2 ° 2 c3 V 2 ª1 λ fK 2 V º ° ¬« ¼» ¿ ¯ where
a fK
D src
1 λ fK
cos T
2 V
2
where the range profile and the azimuth profile are respectively shown in Figure 6-a and Figure 6-b. Compared with the asymmetric side-lobes of the classical SRC algorithm, the symmetric side-lobes of the improved SRC algorithm are presented in Figure 5-b. Figure 6-c and Figure 6-d are the range profiles and the azimuth profiles. Peak sidelobe ratio (PSLR) and integrated side-lobe ratio (ISLR) results are listed in TABLE 1. By these simulated results, we can find that the improved SRC algorithm can achieve the focusing requirement, while the classical SRC algorithm can't meet the focusing requirement in GEO SAR.
1
2 · § ¨ 1 λ fK 2 V ¸ ¹ 2 V 2 c2 © R0 cos T λ 3 fK 2
3
here fK denotes the azimuth time. (a) T he classical SRC
The last step is the azimuth matching filtering which will be carried out in the Range-Doppler domain, and the azimuth reference function can be written as 2 ª § ·º § λ fK · ¸ » (9) H 6 exp « j 4 π R λ ¨ cos T 1 ¨ 1 ¸ « ¨ ¸» V 2 © ¹ © ¹ ¼» ¬« A fine focusing can be achieved after the azimuth IFFT. The basic processing flow-chart is shown in Figure 3.
System echo
Range FFT
Error compenstion function of the line trajectory model
Third phase function
u
Azimuth FFT
u
u
Range IFFT
(b) T he improved SRC Figure 4. T argets array imaging results
SRC function and Range migration rectified function
Range compression function
Focusing image
Azimuth IFFT
Azimuth compression function
Figure 3. Flow-chart of the improved SRC algorithm (a) T he classical SRC (b) T he improved SRC Figure 5.T he two-dimensional contour comparison of the center of the scene
The simulated parameters are as follow: the radar wavelength is 0.09375m, the bandwidth is 10MHz, the transmitted pulse width is 20 P s , the pulse repeat frequency is 100MHz and
1375
-10 -20 -20 Magnitude(dB)
the sampling frequency is 12MHz. The imaging scene size is 5 kilometers u 5 kilometers shown in Figure 4; nine targets are uniformly distributed into the scene in range direction and azimuth direction. Synthetic aperture time is assumed to be 40 seconds. Figure 5 compares the contour of the classical SRC algorithm with that of the improved SRC algorithm. It's quite obvious that the asymmetry side-lobes appear in both the range direction and the azimuth direction in Figure 5-a,
0
0
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Magnitude(dB)
4. SIMULATION RESULTS
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(a) T he range profile with the classical SRC algorithm
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100
200
300
400 Azimuth
500
600
700
800
(b) T he azimuth profile with the classical SRC algorithm
0
This work was supported by the National Natural Sciences Foundation of China (Grant Nos. 61032009, 60890073).
0 -10
-10
-20
Magnitude(dB)
Magnitude(dB)
-20
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7. REFERENCES
-40 -50
[1] Kiyo Tomiyasu, “Synthetic aperture radar in geosynchronous
-60
-50 -70
-60
0
100
200
300 Range
400
500
600
-80
0
100
200
300
400 Azimuth
500
600
700
800
(c) T he range profile (d) T he azimuth profile with the improved SRC algorithm with the improved SRC algorithm Figure 6. T he range and azimuth profile comparison of the center of the scene
TABLE 1 The evaluation results of imaging results with the improve SRC algorithm Target Position (0,0,0) (2.5km,2.5km,0) (-2.5km,2.5km,0) (2.5km,-2.5km,0) (-2.5km,-2.5km,0)
PS LR Range( Azimut dB) h(dB) -13.24 -13.29 -13.18 -13.18 -13.11 -13.20 -13.05 -13.20 -13.26 -13.24
IS LR Range( Azimut dB) h(dB) -10.36 -10.99 -10.20 -10.93 -10.01 -10.96 -9.97 -10.94 -10.34 -10.92
The improvement of imaging results obtained by the proposed SRC algorithm is apparent compared with the imaging results obtained by the classical SRC algorithm, furthermore the imaging scene reaches the 5 kilometers under 40 seconds synthetic aperture time. However, the imaging scene is still small in GEO SAR, and will decrease when the synthetic aperture time increases. Thus, the imaging algorithm used for large scene is the main research work in future. 5. CONCLUSION The paper analyses the error caused by the linear trajectory model and the Fresnel approximation, and it is found that the third order phase error can reach up to 0.7 rad under the 40 seconds synthetic aperture time, which results in the asymmetrical side lobes and thus it is necessary to be compensated. The paper proposes an improved SRC algorithm to overcome the curved trajectory, and verifies the correctness of improved algorithm as well via the simulation results. As an excellent imaging algorithm to deal with the range-variance, CS algorithm has been widely applied in LEO SAR. Via combining the method proposed by the paper, CS algorithm may solve the imaging for large scene under the long synthetic aperture time. Therefore, CS algorithm need to be further studied. 6. ACKNOWLEDGEMENT
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orbit,” IEEE Antennas and Propagation Symp. U.M aryland, pp.4245, 1978. [2] Kiyo Tomiyasu, Jean L.Pacelli, “Synthetic Aperture Radar Imaging from an Inclined Geosynchronous Orbit,” IEEE Transactions on Geoscience and Remote Sensing, vol.21, pp.324329, 1983. [3] “Global Earthquake Satellite System: A 20-Year Plan to Enable Earthquake Prediction,” JPL Document, pp.50-65, 2003.(http://www.jpl.nasa.gov) [4] Wendy Edelstein, Soren M adsen, Alina M oussessian and Curtis Chen, “Concepts and technologies for Synthetic Aperture Radar from M EO and Geosynchronous orbits,” SPIE International Asia-Pacific Symposium, Remote Sensing of the Atmosphere, Environment, and Space, Honolulu, Hawaii USA, pp.195-203, 2004. [5] S.E. Hobbs, “GeoSAR Summary of the Group Design Project, M Sc in Astronautics and Space Engineering 2005/06,” Cranfield University, pp.1-20, 2006. [6] S.N. M adsen Wendy Edelstein, Leo D. DiDomenico and John LaBrecque, “A Geosynchronous Synthetic Aperture Radar; for Tectonic M apping, Disaster M anagement and M easurements of Vegetation and Soil M oisture,” GeoScience and Remote Sensing Symposium, pp.1-3, 2001. [7] Stephen E. Hobbs and Davide Bruno, “Radar Imaging from GEO: Challenges and Applications,” Remote Sensing and Photogrammetry Society Annual Conference, pp.1-6, 2007. [8] Davide Bruno and Stephen E.Hobbs, “Radar Imaging From Geosynchronous orbit: Temporal Decorrelation Aspects,” IEEE Transactions on Geoscience and Remote Sensing, pp.1-6, 2010 [9] Wenfu Yang, Yu Zhu, Feifeng Liu, Cheng Hu, and Zegang Ding, “M odified Range M igration Algorithm in GEO SAR system,” The 8th European Conference on Synthetic Aperture Radar, pp.708-711, 2010. [10] Cheng Hu, Feifeng Liu, Wenfu Yang. “M odification of slant range model and imaging processing in GEO SAR,” Proc.IEEE IGARSS, Hawaii, pp.1-4, Jul.2010. [11] Feifeng Liu, Cheng Hu, Tao Zeng, “A novel range migration algorithm of GEO SAR echo data,” Proc.IEEE IGARSS, Hawaii, pp.1-4, Jul.2010. [12] Cheng Hu, Tao Zeng, Yu Zhu, and Zegang Ding, “The accurate resolution analysis in Geosynchronous SAR,” The 8th European Conference on Synthetic Aperture Radar, pp.925-928, 2010. [13] Teng Long, Xichao Dong, Cheng Hu, “A method of zero Doppler centroid control in GEO SAR,” IEEE Geoscience and Remote Sensing Letters, vol.PP, pp.511-515, 2010. [14] M .J. Jin, C. Wu, “A SAR Correlation Algorithm which Accommodates Large-Range M igration,” IEEE Transcation on Geoscience and Remote Sensing, vol.22, no.6, pp.592-597, 1984. [15] R.Keith Raney et al, “Precision SAR Processing Using Chirp Scaling,” IEEE Transcation on Geoscience and Remote Sensing, vol.32, no.4, pp.786-799, July 1994. [16] C. Cafforio, C. Pratic, and F. Rocca, “SAR Data Focusing Using Seismic M igration Techniques, ” IEEE Transactions on Aerospace and Electronic Systems, vol.27, no.2, pp. 194~206, 1991.
Radar Research Lab, department of electric engineering, Beijing Institute of Technology Beijing 100081, China ABSTRACT The paper firstly analyses the error caused by the linear trajectory model and the Fresnel approximation because of the long synthetic aperture time in Geosynchronous Synthetic Aperture Radar (GEO SAR), and then proposes an improved Secondary Range Compression (SRC) focusing algorithm to overcome the effect of linear trajectory model and the Fresnel approximation. The improved focusing algorithm adopts the curved trajectory model on basis of Norm operator to remove the error caused by the linear trajectory, derives and compensates the third order phase in two-dimensional frequency domain to overcome the large range migration. Finally, imaging results verify the improved focusing algorithm. Index Terms— GEO, SAR, SRC, Linear trajectory, Fresnel approximation 1. INTRODUCTION With the application development of synthetic aperture radar (SAR), low earth orbit (LEO) SAR becomes more and more difficult to meet the application requirement. Thus, geosynchronous synthetic aperture radar (GEO SAR) system was proposed by K.Tomiyas u in 1978 [1]. In 1983, K.Tomiyasu discussed the GEO SAR system in detail [2]. However, since imaging algorithms and the hardware technologies were immature at that time, the idea got into quiet for a long time. With the coming of the 21st century, the GEO SAR turns into a hot topic in accordance with the fast development of relevant technology and the maturity of LEO SAR imaging algorithms. The most representative organizations are Jet Propulsion Laboratory (JPL) and Cranfield University which both went deeply into studying the system [3]~[5]. The advantages of the GEO SAR are obvious, such as the huge coverage, the fine temporal sampling and the short interference period and so on. The above advantageous conditions make the tremendous potentiality of the GEO SAR in forecasting the earthquake and volcano, the hydrological cycle and monitoring vegetation changes etc [4][6]. However there is a fact which is not neglected with the increase of the satellite orbit height, namely that an atmosphere impact on the SAR focusing
978-1-4577-0539-7/11/$26.00 ©2011 IEEE
1373
needs to be taken into consideration. Reference [7] and [8] analyzed the impacts on focusing from ionosphere and troposphere. Imaging is an important aspect of GEO SAR. Reference [9], [10] and [11] studied imaging algorithms of GEO SAR, and reference [12] analyzed the resolution of GEO SAR, and reference [13] focused on the attitude control. According to the analysis of the above literatures, we can know many differences exist between LEO SAR and GEO SAR, such as the longer synthetic aperture time and the more complex attitude control in GEO SAR etc.; furthermore LEO SAR imaging algorithms cannot be directly used in GEO SAR. Therefore, the main emphasis of the paper is placed on the imaging algorithms at equator. A great error will appear if the classical imaging algorithms are used at equator; in addition, some factors that can be neglected in the classical imaging algorithms will not be neglected in GEO SAR. The paper modifies the secondary range compression (SRC) algorithm [14] which is popular in LEO SAR, and verifies the correctness of the improved SRC algorithm. This paper is organized as follow. Section 2 presents and analyzes the problem which is caused by the linear trajectory model and the Fresnel approximation. Section 3 proposes the improved SRC. Section 4 presents the simulation results of the SRC algorithm proposed, and makes a comparison with the results of the classical SRC. Finally, the conclusion is drawn. 2. ANALYSIS OF THE LINEAR TRAJECTORY MODEL AND THE FRESNEL APPROXIMATION Many algorithms are available in LEO SAR, including the familiar SRC [14], the chirp scaling (CS) [15] algorithm, the range migration algorithm (RMA) [16] as well as various extended algorithms. Those algorithms are derived under some model assumption or mathematical approximation, such as the linear trajectory model and the Fresnel approximation. The trajectory of the satellite in LEO is considered as the rectangular line (red line in Figure 1). This consideration is proper in processing the LEO SAR imaging, but the situation is of difference when it comes to GEO SAR due to thousands of kilometers of synthetic aperture length, for example, the error caused by the linear trajectory at the center of the scene at equator is up to 0.16 meter
ICASSP 2011
(wavelength order). The simulated results of error caused by the linear trajectory model and the Fresnel approximation are shown in Figure 2. The parameters of the satellite orbit are: the orbit inclination 53 degrees, the argument of perigee 270 degrees, and the right of ascend nod 265 degrees.
z
the curved trajectory
satellite
Gx Rsn
the linear trajectory
V
T
G
G
where RK K represents the range history, Rsn , Rgn respectively represent the positions of satellite and the target, and K denotes the azimuth time. Based on the geometry configuration of GEO SAR system, the echo can be written as, s K , t V aK K ar t 2 RK K c (1) 2 exp ª« j π D t 2 RK K c º» exp j 4 π RK K λ ¬
¼
where t is the range time, V stands for the backward scattering coefficient, aK and ar denote the envelope R0
o
functions of the azimuth and the range respectively. D denotes the range FM rate, λ is the wavelength and c is the speed of light. The first step is the range Fourier transform, and the range-frequency expression of echo can be given as s K , f r V aK K Ar f r exp j π f r2 D (2) exp ¬ª j 4 S RK K f r f 0 c ¼º
y G Rgn
target
x Figure 1. T he geometrical configuration of the linear trajectory and the curved trajectory
where Ar is the frequency expression of the range 1
0.8
0.8
envelope, f r is the range frequency and f 0 is the center
0.6
0.6 0.4
0.2
Unit,rad
0.2 Unit,rad
frequency of the transmitted pulse. Next, the range compression will be implemented, and the reference function can be written as H1 exp j π f r 2 D (3)
0.4
0 -0.2
0 -0.2
-0.4 -0.4
-0.6 -0.6
-0.8 -1 -20
-15
-10
-5
0
Time,s
5
10
15
20
-0.8 -20
-15
-10
-5
0
5
10
15
The following processing of classical SRC algorithm is to transform the echo of range compression into the twodimensional frequency domain, where the range RK K in (2)
20
Time,s
(a) T he error of the (b) T he error of the Fresnel approximation linear trajectory model Figure 2. T he error of models at the center of scene at equator
is regarded as the linear trajectory, we have
According to Figure 2, we can find that the model error cannot be neglected. For this reason, the error must be removed and some filtering functions need to be modified. This paper modifies the SRC algorithm and validates the improved SRC by the simulation results. The main processing method is as follow. Firstly, the error caused by the linear trajectory model will be compensated before the beginning of the SRC algorithm, and the error compensation function is processed in the range-Doppler domain. Secondly, because of the effect of earth rotation and long synthetic aperture time, we find that the range migration is so large that the high order phase neglected in LEO SAR imaging must be considered in GEO SAR. Furthermore, the high order phase error and range migration correction will be detailedly analyzed and compensated in two-dimensional frequency domain. 3. IMPROVED SRC ALGORITHMS According to Figure 1, the curved trajectory can be G G expressed via Norm operator, namely RK K Rsn Rgn
1374
RK K
R02 V K 2 R0 V K sin T 2
(4)
where V is the satellite velocity , T is the squint angle, and R0 is the range between the beam center and the central target of scene. V , T and R0 can be obtained via the curve fitting, which can satisfy the focusing demand in LEO SAR, while in GEO SAR, the error of curve fitting is very large, especially at equator. Thus, we need to compensate a phase to eliminate the effects of the curving fitting error before the azimuth FFT, and the phase compensation function can be written as H 2 exp ª¬ j 4 π f r f 0 'R0 c º¼ (5) where
G G 2 'R0 Rsn Rg 0 R0 2 V K 2 R0 V K sin T G here Rg 0 denotes the target coordinate of the scene centre. The next step is transforming the echo data into the two-dimensional frequency domain, and then twodimensional spectrum is obtained. In consequence, the range migration correction will be implemented and the third order phase frequently neglected in LEO SAR imaging will
also be compensated. In addition, the SRC function can be expressed as (6) H 3 exp j π f r 2 D src The range migration correction function can be shown as
exp j 4 π R0 c a fK f r
H4
(7)
The third order phase compensation function can be written as ½ j π R0 cos T λ 4 fK 2 ° ° (8) H 5 exp ® 2.5 ¾ 2 ° 2 c3 V 2 ª1 λ fK 2 V º ° ¬« ¼» ¿ ¯ where
a fK
D src
1 λ fK
cos T
2 V
2
where the range profile and the azimuth profile are respectively shown in Figure 6-a and Figure 6-b. Compared with the asymmetric side-lobes of the classical SRC algorithm, the symmetric side-lobes of the improved SRC algorithm are presented in Figure 5-b. Figure 6-c and Figure 6-d are the range profiles and the azimuth profiles. Peak sidelobe ratio (PSLR) and integrated side-lobe ratio (ISLR) results are listed in TABLE 1. By these simulated results, we can find that the improved SRC algorithm can achieve the focusing requirement, while the classical SRC algorithm can't meet the focusing requirement in GEO SAR.
1
2 · § ¨ 1 λ fK 2 V ¸ ¹ 2 V 2 c2 © R0 cos T λ 3 fK 2
3
here fK denotes the azimuth time. (a) T he classical SRC
The last step is the azimuth matching filtering which will be carried out in the Range-Doppler domain, and the azimuth reference function can be written as 2 ª § ·º § λ fK · ¸ » (9) H 6 exp « j 4 π R λ ¨ cos T 1 ¨ 1 ¸ « ¨ ¸» V 2 © ¹ © ¹ ¼» ¬« A fine focusing can be achieved after the azimuth IFFT. The basic processing flow-chart is shown in Figure 3.
System echo
Range FFT
Error compenstion function of the line trajectory model
Third phase function
u
Azimuth FFT
u
u
Range IFFT
(b) T he improved SRC Figure 4. T argets array imaging results
SRC function and Range migration rectified function
Range compression function
Focusing image
Azimuth IFFT
Azimuth compression function
Figure 3. Flow-chart of the improved SRC algorithm (a) T he classical SRC (b) T he improved SRC Figure 5.T he two-dimensional contour comparison of the center of the scene
The simulated parameters are as follow: the radar wavelength is 0.09375m, the bandwidth is 10MHz, the transmitted pulse width is 20 P s , the pulse repeat frequency is 100MHz and
1375
-10 -20 -20 Magnitude(dB)
the sampling frequency is 12MHz. The imaging scene size is 5 kilometers u 5 kilometers shown in Figure 4; nine targets are uniformly distributed into the scene in range direction and azimuth direction. Synthetic aperture time is assumed to be 40 seconds. Figure 5 compares the contour of the classical SRC algorithm with that of the improved SRC algorithm. It's quite obvious that the asymmetry side-lobes appear in both the range direction and the azimuth direction in Figure 5-a,
0
0
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Magnitude(dB)
4. SIMULATION RESULTS
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(a) T he range profile with the classical SRC algorithm
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100
200
300
400 Azimuth
500
600
700
800
(b) T he azimuth profile with the classical SRC algorithm
0
This work was supported by the National Natural Sciences Foundation of China (Grant Nos. 61032009, 60890073).
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Magnitude(dB)
Magnitude(dB)
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7. REFERENCES
-40 -50
[1] Kiyo Tomiyasu, “Synthetic aperture radar in geosynchronous
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-50 -70
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0
100
200
300 Range
400
500
600
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0
100
200
300
400 Azimuth
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600
700
800
(c) T he range profile (d) T he azimuth profile with the improved SRC algorithm with the improved SRC algorithm Figure 6. T he range and azimuth profile comparison of the center of the scene
TABLE 1 The evaluation results of imaging results with the improve SRC algorithm Target Position (0,0,0) (2.5km,2.5km,0) (-2.5km,2.5km,0) (2.5km,-2.5km,0) (-2.5km,-2.5km,0)
PS LR Range( Azimut dB) h(dB) -13.24 -13.29 -13.18 -13.18 -13.11 -13.20 -13.05 -13.20 -13.26 -13.24
IS LR Range( Azimut dB) h(dB) -10.36 -10.99 -10.20 -10.93 -10.01 -10.96 -9.97 -10.94 -10.34 -10.92
The improvement of imaging results obtained by the proposed SRC algorithm is apparent compared with the imaging results obtained by the classical SRC algorithm, furthermore the imaging scene reaches the 5 kilometers under 40 seconds synthetic aperture time. However, the imaging scene is still small in GEO SAR, and will decrease when the synthetic aperture time increases. Thus, the imaging algorithm used for large scene is the main research work in future. 5. CONCLUSION The paper analyses the error caused by the linear trajectory model and the Fresnel approximation, and it is found that the third order phase error can reach up to 0.7 rad under the 40 seconds synthetic aperture time, which results in the asymmetrical side lobes and thus it is necessary to be compensated. The paper proposes an improved SRC algorithm to overcome the curved trajectory, and verifies the correctness of improved algorithm as well via the simulation results. As an excellent imaging algorithm to deal with the range-variance, CS algorithm has been widely applied in LEO SAR. Via combining the method proposed by the paper, CS algorithm may solve the imaging for large scene under the long synthetic aperture time. Therefore, CS algorithm need to be further studied. 6. ACKNOWLEDGEMENT
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