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Imaging processor for different spaceborne SAR imaging modes
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Up to now, multiple innovative spaceborne synthetic aperture radar (SAR) imaging schemes have been demonstrated for high resolution or/and wide swath coverage. Different imaging modes usually require different imaging processors to focus their raw data. However, presented is a novel full-aperture imaging processor for different imaging modes. According to echo properties of different SAR imaging modes, a preprocessing step and a post-processing step are added to a modified accurate range migration algorithm processor. In addition to the advantage of being suitable for different imaging modes, this imaging processor is very efficient, since it avoids the large azimuth data extension to resolve the aliasing problem. Imaging results on simulated raw date validate the proposed imaging processor.
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Wei Xu, Yunkai Deng and Robert Wang
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Fig. 1 Planar rectilinear imaging geometries of different modes
where vg is the footprint velocity without taking account of azimuth beam steering, and r is the slant range. Then, the closest slant range rrot from the rotation centre to the flight path can be expressed as: rrot =
r vg cos2 u0 =− vr 1−A
(2)
The instantaneous Doppler centroid varying rate krot and the total Doppler bandwidth are as follows: krot = −
2v2r cos3 u0 lrrot
Btot = |krot | T + Bf +
2vs Br sin u0 c
(3)
raw data H3 H1
azimuth pre-processing
2D FFT
(5)
where Tf is the synthetic aperture time in the stripmap mode. According to (4) and (5), besides accurately implementing the range cell migration correction (RCMC), the azimuth aliasing problem both in the Doppler domain and in the time domain may be required to be overcome. Implementation of proposed imaging processor: The proposed imaging processor as shown in Fig. 2 mainly includes three important processing steps: azimuth preprocessing, the modified range migration algorithm (RMA) processor and azimuth post-filtering.
ELECTRONICS LETTERS 15th March 2012 Vol. 48
modified Stolt mapping range IFFT
azimuth Mosaic H4 range variant Doppler filtering HF
H5 azimuth IFFT
azimuth samples decreasing H2
H6 azimuth IFFT H7
azimuth FFT
focused image
Fig. 2 Block diagram of proposed imaging processor
The total Doppler bandwidth might span over several pulse repetition frequency (PRF) intervals due to azimuth beam steering during the whole acquisition interval. To resolve the aliased Doppler spectrum, an azimuth convolution between the raw data and a selected chirp signal is introduced, and the selected chirp signal can be expressed as [1, 2, 4]: H1 = exp(−j2pfdc × i × Dt) exp 2v2 (i × Dt)2 × jp r cos3 u0 , i = −I/2, ..., I/2 − 1 lrrot
(6)
where fdc is the Doppler centroid of the raw data, I is the number of original azimuth samples, and D t ¼ 1/PRF is the azimuth sampling interval. The azimuth convolution can be efficiently implemented by two complex function multiplications and an azimuth Fourier transform. The second multiplied function is: 2v2 (n × Dt ′ )2 H2 = j p r cos3 u0 , lrrot (7) n = −N /2, ..., N /2 − 1
(4)
where T is the whole acquisition interval, Bf is the azimuth beam bandwidth, Br is the transmitted pulse bandwidth, l is the wavelength, c is the light speed, vr and vs are the effective radar velocity and the satellite velocity, respectively. Furthermore, the minimal requirement of the azimuth output extension to avoid azimuth compressed data wrapping is Tout = A (T + Tf /2)
Stripmap or ScanSAR in subswath Sliding spotlight or mosaic mode in subswath Spotlight Inverse sliding spotlight or TOPS mode in subswath
azimuth post-filtering
Imaging geometry: To obtain high resolution or/and wide swath coverage in the spaceborne SAR systems, different imaging modes have been demonstrated for multiple SAR missions. For a low satellite orbit, the curved imaging geometries for different modes could be related to the rectilinear geometries as shown in Fig. 1. Furthermore, all imaging modes could be characterised by a squinted angle u0 and a constant azimuth beam rotation rate vr. The constant azimuth beam rotation rate introduces a fixed rotation centre and an azimuth steering factor A. Assuming that the direction from aft to fore is positive, the azimuth steering factor A is vr r (1) A(r) = 1 + vg cos2 u0
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RMA processor
Introduction: High resolution and wide swath coverage are two of the most important aims for spaceborne synthetic aperture radar (SAR) systems. Different innovative imaging modes have been proposed and demonstrated, such as spotlight and sliding spotlight SAR for high resolution [1, 2], ScanSAR and Terrain Observation by Progressive Scans (TOPS) for wide swath coverage [3, 4], Mosaic mode for the trade-off of high resolution and wide swath [5]. Different modes usually require different imaging processors to focus their raw data to accommodate their echo properties, and multiple imaging algorithms have been proposed in recent years [6]. This Letter presents a novel imaging processor to focus the raw data of different imaging modes. Imaging results on simulated raw data validate the proposed imaging processor.
where N is the number of output azimuth samples after azimuth convolution. It must be noted that the azimuth data sampling frequency 1/Dt′ in (7) is larger than Btot in (4) to resolve the aliased Doppler spectrum [3]. According to (4), the Doppler spectrum after azimuth deramping may be still aliased due to the squinted angle. To resolve the aliased Doppler spectrum caused by the squinted angle, multiple copies of azimuth data are combined together. Afterwards, the following range frequency f dependent Doppler filter is carried out to obtain the desired two-dimensional (2D) spectrum: ⎧ PRF 2( f + fc ) ⎨ 1, with fa − sin u0 , (8) HF ( f , fa ) = c 2 ⎩ 0, otherwise where fc is the carrier frequency, and fa is the Doppler frequency. After the azimuth preprocessing step for upsampling, the transfer function for the reference function multiply (RFM) implemented in the 2D frequency
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Table 1: Simulation parameters
= exp j
4prref c
c2 f 2 pf 2 pf 2 ( f c + f )2 − 2 a + j −j a 4vr (rref ) kr krot
Parameters Carrier frequency Antenna length Transmitted bandwidth Pulse duration
(9)
where rref is the reference range, vr (rref ) indicates the effective velocity at the reference range, and kr is the transmitted pulse modulation rate. Compared with the nominal Stolt mapping method [6], the modified Stolt mapping method in this Letter is: c2 f 2 c2 f 2 f1 = ( fc + f )2 − 2 a − fc2 − 2 a (10) 4vr (rref ) 4vr (rref )
Sampling frequency 200 MHz PRF 2320 Hz Slant range 600 km Effective radar velocity 7200 m/s
c =6
00
H5 ( fa ) = exp [jp (n × Dfa )2 /kx ]
(12)
10m
The residual azimuth data compression is carried out via the following transfer function: 4p(r − rref ) 2 c2 f 2 fc − 2 a H4 (r, fa ) = exp j 4vr (rref ) c
vr (rref ) 2 lrref fa2 (11) × exp jp 1 − 2v2r (rref ) vr (r) fdc × exp j2pfa tc − j2pfa krot
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The first exponential term in (11) is multiplied for the residual azimuth data compression. As the Stolt mapping is with the assumption that the effective velocity is independent with the slant range, the second exponential term is multiplied for different azimuth data compression accommodated to the variation of vr. The last exponential term is essential for avoiding a time shift caused by the squinted angle. Based on the same principle as that to resolve the aliased Doppler spectrum, we introduce an azimuth convolution in the Doppler domain to unfold the aliased SAR image in azimuth. The selected chirp signal is as follows:
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Fig. 3 Imaging experiment on designed scene a b c d e f
Designed scene Imaging result in Imaging result in Imaging result in Imaging result in Imaging result in
stripmap mode sliding spotlight mode spotlight mode ScanSAR TOPS
Conclusion: Presented is a novel SAR imaging processor for different modes. The modified RMA achieves the accurate range cell migration correction, while the preprocessing step and the post-processing step can resolve the azimuth aliasing problem and avoid the large azimuth data extension. Imaging results on simulated raw data validated the proposed imaging processor.
with kx =
1 − A 2v2r cos3 u0 × A lr
Dfa = 1/(N × Dt ′ )
(13) (14)
After the azimuth inverse Fourier transform, the following transfer function is multiplied to implement the azimuth convolution in the Doppler domain: H6 ( fa ) = exp [jp (n × Dfa′ )2 /kx ]
(15)
# The Institution of Engineering and Technology 2012 28 November 2011 doi: 10.1049/el.2011.3732 One or more of the Figures in this Letter are available in colour online. Wei Xu, Yunkai Deng and Robert Wang (Institute of Electronics, Chinese Academy of Science, Lab 6, No. 19, West Bei-Si-Huan Road, Hai Dian District, Beijing, 100190, People’s Republic of China) E-mail:
[email protected] References
with Dfa′ =
|kx | = |kx | × Dt ′ N × Dfa
(16)
After the final azimuth inverse Fourier transform is performed, the azimuth data is compressed and unfolded. If phase preserving SAR images are desired, a following quadratic phase term is applied to compensate a residual phase error caused by the post-filtering step: H7 (t) = exp [jpkx (n × Dt ′′ )2 ]
(17)
with Dt ′′ =
1 N × Dfa′
(18)
Simulation experiment: To validate the proposed processor, imaging experiments on simulated raw data were carried out, and simulation parameters are listed in Table 1. The obtained azimuth resolutions of different modes as shown in Figs. 3b – f are approximately 3, 1.5, 1, 7.5 and 7.5 m, respectively. All imaging results in Fig. 3 clearly indicate the arrangement of the five simulated point targets.
1 Lanari, R., Tesauro, M., Sansosti, E., and Fornaro, G.: ‘Spotlight SAR data focusing based on a two-step processing approach’, IEEE Trans. Geosci. Remote Sens., 2001, 39, (9), pp. 1993– 2004 2 Lanari, R., Zoffoli, S., Sansosti, E., Fornaro, G., and Serafino, F.: ‘New approach for hybrid strip-map/spotlight SAR data focusing’, IEE Proc., Radar Sonar Navig., 2001, 148, (6), pp. 363–372 3 De Zan, F., and Monti Guarnieri, A.: ‘TOPSAR: terrain observation by progressive scans’, IEEE Trans. Geosci. Remote Sens., 2006, 44, (6), pp. 2352–2360 4 Xu, W., Huang, P., and Deng, Y.: ‘An efficient imaging approach with scaling factors for TOPS mode SAR data focusing’, IEEE Geosci. Remote Sens. Lett., 2011, 8, (5), pp. 929– 933 5 Naftay, U., and Nathansonhn, R.: ‘Overview of the TESAR satellite hardware and Mosaic mode’, IEEE Geosci. Remote Sens. Lett., 2008, 5, (3), pp. 423–426 6 Cumming, I.G., and Wong, F.H.: ‘Digital processing of synthetic aperture radar data: algorithms and implementation’ (Artech House, Norwood, MA, 2005)
ELECTRONICS LETTERS 15th March 2012 Vol. 48 No. 6
