TH1.R3.2
Processing High Squint FMCW SAR Data Using Extended Inverse Chirp-Z Transform Algorithm Yue Liu, Robert Wang, Yunkai Deng, Fengjun Zhao, Zhimin Zhang Spaceborne Microwave Remote Sensing System Department, Institute of Electronics, Chinese Academy of Sciences. email:
[email protected];
[email protected];
[email protected] Abstract –This paper proposes an Extended Inverse Chirp-Z Transform (EICZT) algorithm to handle the high squint FMCW SAR data, where the conventional Inverse Chirp-Z Transform (ICZT) cannot work due to the failure in dealing with the rangevariance of second- and higher- order range-azimuth coupling terms. A pre-processing operation is implemented in the azimuth-Doppler and range-time (Doppler-time) domain, where a perturbation function consisting of second-order and thirdorder range time variables is implemented to compensate the range variance of the second order range terms. Moreover, a new scaling factor is formulated to represent the Range Cell Migration (RCM), and further corrected by the presented EICZT approach. The proposed approach is analyzed and compared with the conventional ICZT. The simulated high squint FMCW SAR data from a scene with nine targets is well focused by the proposed approach and the quality is greatly improved with respect to the conventional ICZT.
I.
INTRODUCTION
Frequency-Modulated Continuous Wave (FMCW) Synthetic Aperture Radar (SAR) systems are gaining more interest in remote sensing field [1]. Dechirp-on-receive operation is commonly applied in FMCW SAR systems to reduce the sampling requirements and data rate. Which means the received FMCW SAR data is no longer in chirp modulation [1]-[2]. Inverse Chirp-Z Transform (ICZT) algorithm is suitable for processing FMCW SAR data, because it can handle non-chirp signal, without interpolation [1]-[4]. Nevertheless the earlier proposed ICZT algorithm [1] is limited to handling broadside configurations or low squint configurations because of ignoring the range variance of second- and higher- order range-azimuth coupling terms. In this paper, an Extended ICZT (EICZT) algorithm is proposed specially for FMCW SAR data, with a pre-processing operation in the azimuth-Doppler and range-time (Dopplertime) domain to compensate the range variance of the second order range terms, by using a perturbation function consisting of second-order and third-order range time variables. Furthermore, a new scaling factor is formulated and corrected by the Chirp-Z operation. Simultaneously, the proposed EICZT algorithm maintains the advantages of conventional ICZT, while is capable of handling high squint FMCW signal. Simulation experiments and analyses are carried out and validate that the proposed approach is feasible in high squint FMCW SAR configurations.
467
This paper is organized as follows. In Section II, the EICZT algorithm is proposed to process high squint FMCW SAR data. An airborne simulation experiment in high squint mode with a squint angle of 40°is designed, and the processing results of the simulated data is processed by both the EICZT and ICZT algorithms in Section IV. Finally, conclusions are reported in Section V. II.
SIGNAL PROCESSING PROCEDURE
The conventional ICZT is used to correct the Range Cell Migration (RCM) without interpolation, but neglects the range-variant effect of the second- and higher- order range terms, what is not acceptable in high squint FMCW SAR situations [1], [3]. To make the algorithm feasible in high squint FMCW configurations, a pre-processing operation is proposed to compensate the range-variance of second order range terms in the Doppler-time domain. Note that the proposed algorithm is based on the analytical two-dimensional spectrum contributed by Dr. Wang [2]. The signal processing procedure is shown as Fig.1 and the crucial steps are explained as follows. (1) The transmitted FMCW signal is defined as s ( t ) = exp ( jπ K r t 2 ) (1) where t represents the range time variable, Kr is the chirp rate. (2) In step 3, a matched filtering operation is carried out to compensate all the range-invariant terms in twodimensional frequency domain. (3) In step 5, A Perturbation Function Multiplication (PFM) is carried out in the Doppler-time domain to remove the range-variance of second order range terms, with a perturbation function consisting of second-order and third-order range time variables, which is expressed as
{⎣
}
H PFM ( fτ , t ) = exp j ⎡πγ ( fτ ) ( t − τ ref ) − 2πξ ( fτ ) ( t − τ ref ) ⎤ 2
3
⎦
(2)
γ ( fτ ) and ξ ( fτ ) are chosen to remove the rangevariance of the second- and third-order terms, which are described as
2013 Asia-Pacific Conference on Synthetic Aperture Radar (APSAR)
467
exp ( − jπβ f 2 )
(
exp jπβ f 2
)
exp ( − jπβ t 2 )
Fig. 1 Signal Processing Procedure.
cΦ 2 K m ref ⎧ ⎪γ ( fτ ) = 3r Φ Φ − cΦ ref 1 3 2 ⎪ ⎨ ⎛ 2 K mref − 1 ⎞ ⎪ξ f = r Φ Φ K 2 ( ) ⎜ 2 3 ref mref τ ⎪ ⎜ 3r Φ Φ − cΦ ⎟⎟ 2 ⎠ ⎝ ref 1 3 ⎩
(3)
where ⎛ cfτ ⎞ ⎟, ⎝ 2vf 0 ⎠
μ =⎜
D = 1− μ 2
(4)
1 ⎧ ⎪Φ1 ( fτ ) = D ⎪ 2 ⎪Φ ( f ) = − μ ⎪ 2 τ 2 f0 D3 ⎪ (5) μ2 ⎨ Φ = ， f ( ) τ 3 2 5 ⎪ 2 f0 D ⎪ Kr ⎪ ⎪ K mref = 4Φ 2 ( fτ ) rref K r ⎪ 1+ c ⎩ where f and fτ represent the range and azimuth frequency variables, respectively, f 0 is the carrier frequency, c is light speed. rref represents the reference range, which is generally chosen as the closest slant range from the scene center to the receiver. (4) In step 8, the new kernel for EICZT is expressed as K mref β =− (6) 2 2π D ⎡⎣ K mref + γ ( fτ ) ⎤⎦ The inverse Chirp-Z Transform can be carried out through one convolution and two multiplications, interpolation operation is not involved [1]. III.
SIMULATION EXPERIMENTS
A high-squint airborne simulation with a squint angle of 40° is carried out in this section to highlight the performance of
468
proposed algorithm. The designed scene consists of nine point targets, as shown in Fig.2. PT5 locates at the scene center, the near range and far range targets have a relative slant range of 200m and 200m. The distance between PT2 and PT5 is 100m in azimuth. For the ongoing simulations, we assume the window function of rectangular shape in both directions. The system parameters are shown in Table I. The theoretical azimuth resolution and range resolution are 0.42m and 0.3m, respectively.
Fig. 2 Scene geometry with nine point targets. TABLE I SYSTEM PARAMETERS Platform velocity
50 m/s
Azimuth antenna length Platform altitude Squint angle Depression angle Carrier frequency PRF Swath Width Range bandwidth
0.6m 1000 m 40° 45° 10 GHz 800 Hz 500 m 500MHz
2013 Asia-Pacific Conference on Synthetic Aperture Radar (APSAR)
468
The simulated data is processed by the proposed EICZT algorithm and ICZT algorithm, and the two-dimensional impulse response of PT1 is shown in Fig. 3 (a) and (b), respectively. To quantify the precision of processing, the Impulse Response Width (IRW), Peak Sidelobe Ratio (PSLR), and Integrated Sidelobe Ratio (ISLR) of PT 1 are used as criteria, as shown in Table II. TABLE II MEASUREMENT OF PT1
IRW PSLR ISLR
EICZT Azimuth Range 0. 43m 0.3m -13.28dB -13.26dB -9.70dB -9.69dB
ICZT Azimuth Range 0.54m 0.41m -15.69dB -16.01dB -7.97dB -7.65dB
The processing results show that the measurements by EICZT have a maximal broadening of 0.3% from the theoretical values, meaning they agree well with the theoretical values, while the measurements of ICZT derive more than 30% from the theoretical values. Therefore, the proposed EICZT shows much better performance in focusing high-squint FMCW SAR data.
IV.
The traditional ICZT can focus broadside or low squint FMCW SAR data well, but fails in high squint configurations due to the neglecting of range-variance of the second order range terms. The EICZT approach is proposed in this paper with a pre-processing operation in the Doppler-time domain by formulating a perturbation function to compensate the range-variance of second order range terms, which makes ICZT capable of working in high squint FMCW SAR configurations. The simulated high squint FMCW SAR targets are well focused by the proposed processing approach and show great improvement with respect to the ones focused by conventional ICZT. ACKNOWLEDGMENT This work reported herein was jointly supported by the Hundred Talents Program of The Chinese Academy of Sciences and the General Program of National Natural Science Foundation of China under Grant 61172122. REFERENCES [1].
Azimuth Time (Samples)
300
[2].
250 200
[3].
150
[4].
100 50
[5]. 50
100
150
200
250
300
Range Time (Samples)
[6].
(a) 500
[7].
AzimuthTime (Samples)
450 400
[8].
350 300
CONCLUSION
Y. Liu, Y. K. Deng, and R. Wang, “Focus Squint FMCW SAR Data Using Inverse Chirp-Z Transform Based on an Analytical Point Target Reference Spectrum”, IEEE Geoscience and Remote Sensing Letters, (b) Sep. 2012. vol. 9, no. 5, pp. 866-870, R. Wang, O. Loffeld, H. Nies, S. Knedlik, M. Hägelen, and H. Essen, “Focus FMCW SAR Data Using the Wavenumber Domain Algorithm”, IEEE Trans. Geosci. Remote Sens., vol.48, no.4, pp. 2109-2108, Apil. 2010. L. R. Rabiner, R. W. Schafer, and C. M. RADER, “The Chirp-Z Transform and Its Applications,” IEEE Trans. Audio. Electro., vol.17, no.2, pp. 86-92, Jun. 1969. I. G. Cumming and F. H. Wong, Digital Processing of Synthetic Aperture Radar Data Algorithms and Implementation. Norwood, MA: Artech House, 2005. Y. Tang, M. D. Xing, and Z. Bao, ‘The Polar Format Imaging Algorithm Based on Double Chirp-Z Transforms”, IEEE Geosci. Remote Sens. Lett., vol. 5, no.4, pp. 610-614, Oct. 2008. R. Lanari, S. Hensley, P.A. Rosen, “Chirp Z-Transform based SPECAN approach for phase-preserving ScanSAR image generation”, IEE Proc.-Radar, Sonar Navig., Vol. 145, No. 5, October 1998 R. Lanari, G. Fornaro, “A Short Discussion on the Exact Compensation of the SAR Range-Dependent Range Cell Migration Effect”, IEEE Trans. Geosci. Remote Sens., vol. 35, no. 6, pp.1446–1451, Nov. 1997. R. Lanari “A New Method for the Compensation of the SAR Range Cell Migration Based on the Chirp Z-Transform”, IEEE Trans. Geosci. Remote Sens., vol. 33, no. 5, pp.1296–1299, Sep. 1995.
250 200 150 100 50 100
200
300
400
500
Range Time (Samples)
(b) Fig. 3 Impulse response of PT1 (a) focused by the proposed algorithm; (b) focused by conventional ICZT.
469
2013 Asia-Pacific Conference on Synthetic Aperture Radar (APSAR)
469
