TOPS-Mode Raw Data Processing Using Chirp Scaling ... - IEEE Xplore

IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, VOL. 7, NO. 1, JANUARY 2014

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TOPS-Mode Raw Data Processing Using Chirp Scaling Algorithm Wei Xu, Pingping Huang, Robert Wang, Member, IEEE, Yunkai Deng, and Youchun Lu

Abstract—This paper presents four imaging approaches for terrain observation by progressive scans (TOPS)-mode SAR focusing, all of which take advantage of modified chirp scaling (CS) algorithms according to echo properties in TOPS. After adopting different azimuth preprocessing steps to resolve the aliased Doppler spectra, the resulting TOPS raw data can be handled by a classic CS processor. Unfortunately, the resulting images would appear back folding, if only a standard stripmap processor is adopted. To avoid or resolve azimuth back folding in the final focused TOPS SAR images, four modified CS algorithms are presented according to special properties of the slow time–frequency diagram in TOPS. Imaging results on point targets validate the presented imaging approaches. Index Terms—Aliasing, chirp scaling, spectrum analysis (SPECAN), synthetic aperture radar (SAR), terrain observation by progressive scans (TOPS).

I. INTRODUCTION

T

ERRAIN Observation by Progressive Scans (TOPS) [1] is a novel spaceborne wide-swath imaging scheme, which can obtain the same azimuth resolution and unambiguous swath width as conventional ScanSAR [2]. Moreover, it overcomes major drawbacks in azimuth varying ambiguity-to-signal ratio (ASR) and signal to noise ratio (SNR), as well as scalloping effect in ScanSAR by introducing azimuth beam steering during the whole acquisition interval [3]–[5]. The TOPS mode has been demonstrated by the TerraSAR-X, and it has been chosen as the default mode for its ultra-wide-swath interferometry [3]–[7]. Moreover, it is also selected as the operating mode for wideswath imaging for future Chinese spaceborne synthetic aperture radar (SAR) missions, and its corresponding airborne experiments have been performed [8]–[10]. In order to illuminate all targets with the complete azimuth antenna pattern (AAP) in the short burst duration to avoid the scalloping effect, a constant azimuth beam steering (either mechanically or electronically) is taken during the whole raw data

Manuscript received January 09, 2013; revised March 13, 2013; accepted April 02, 2013. Date of publication May 15, 2013; date of current version December 18, 2013. This work was supported in part by the Civil Aerospace Pre-research Project of State Administration of Science, Technology and Industry for National Defense for “Twelfth Five-Year” under Contract D040103. W. Xu, R. Wang, and Y. Deng are with the Institute of Electronics, Chinese Academy of Sciences (IECAS), Beijing 100190, China. (e-mail: [email protected]; [email protected]; [email protected]). P. Huang is with the College of Information Engineering, Inner Mongolia University of Technology, Hohhot 010051, China (e-mail: [email protected]). Y. Lu is with the China Center for Resources Satellite Data and Application, Beijing 100094, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTARS.2013.2260134

acquisition interval. As a result, the total Doppler bandwidth of a burst may span over multiple pulse repetition frequency (PRF) intervals. Moreover, azimuth beam rotation leads to different squinted angles for different targets, and a precise SAR processor is required to focus the wide-swath burst mode SAR data. Furthermore, the actual footprint velocity is several times faster than the SAR sensor to illuminate the large azimuth scene in the short burst duration in TOPS. Consequently, this imaging scheme causes the output SAR image wrapping, if the stripmap processor is directly adopted to focus the TOPS SAR data. Therefore, the opposite azimuth steering direction to the spotlight mode with a high rotation rate causes three major problems: the aliased Doppler spectra, different squinted angles for targets with different azimuth locations, and the focused image back folding in azimuth. Typically, stripmap processors can be modified to focus the raw data of any new imaging modes according to their echo properties. Several imaging algorithms and approaches for the TOPS mode have been proposed in recent years [1], [5], [9], [10], [32]–[35]. Classic chirp scaling (CS) algorithm [15], [25], [26] is an efficient SAR processor to focus raw data with the low squinted angle and/or the wide swath coverage without any interpolations. In this paper, four imaging approaches using different modified CS algorithms are presented. In particular, this paper focuses on processing the azimuth signal, since the only difference between the raw data in TOPS and in the other modes is its azimuth signal component. In additional to the precise imaging capability, the efficiency of the SAR processor should be considered. Therefore, the efficiencies of different algorithms are analyzed and compared in this paper. This paper is arranged as follows. Section II reviews the TOPS imaging geometry and analyzes the properties of its corresponding azimuth signal in detail. In order to resolve the first problem of the aliased Doppler spectra in TOPS, several solutions to overcome this insufficient sampling problem are first introduced in Section III. Afterwards, four imaging approaches using modified CS algorithms are presented in detail in Section IV. Section V shows simulation results on point targets to validate the presented imaging algorithms. Finally, some conclusions are reported in Section VI. II. TOPS MODE Different from the spotlight/sliding spotlight mode [11]–[14] for a higher azimuth resolution, the TOPS mode is proposed for wide swath coverage and overcoming the inherent problems in ScanSAR of azimuth varying imaging performances. This scheme is usually implemented by electronically steering azimuth beam form aft to fore opposite direction to the spotlight case. Moreover, different subswaths are illuminated periodically similar to ScanSAR, and fast azimuth beam steering

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IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, VOL. 7, NO. 1, JANUARY 2014

Fig. 1. Acquisition geometries of both the nominal and inverse TOPS modes in a subswath. (a) Nominal TOPS mode. (b) Inverse TOPS mode.

leads to a reduction in the target’s observation time for an impaired azimuth resolution. The same target’s observation time reduction can also be achieved by steering azimuth beam from fore to aft the same direction as in the spotlight mode as shown in Fig. 1(b), and this mode is named as the inverse TOPS mode [2], [3]. Compared with the nominal TOPS mode, it requires a higher rotation rate for the same desired azimuth resolution. Fig. 1 shows the acquisition geometries of both of the nominal and inverse TOPS modes. Similar to the spotlight/sliding spotlight mode, there is a fixed virtual rotation center in the acquisition geometry. However, the rotation center lies behind the sensor in the nominal TOPS mode, while it stays on the location between the sensor and the imaged swath for the inverse TOPS mode as shown in Fig. 1. The shrinking factor can be easily obtained from Fig. 1 and expressed as follows: (1)

Fig. 2. Raw data supports in the slow time/frequency domain. (a) Norminal TOPS. (b) Inverse TOPSTB.

and this neglect will not affect TOPS azimuth signal properties analysis just for the simplicity. By using the stationary phase method (SPM), the azimuth signal spectrum can be written as follows:

where is the slant range, represents the effective velocity of is the footprint velocity, is the distance the SAR sensor, from the virtual rotation center to the flight path. As a result, is obtained as follows: (2) only relates to the platform effective veRotation range locity and the azimuth beam rotation rate . This property is quite useful to TOPS SAR data focusing algorithms. Compared with echoes of conventional ScanSAR, the existing differences in TOPS are the shrunk azimuth antenna pattern and . Therefore, we just need to focus on the azimuth signal component, the azimuth component of radar echoes of point target with location can be written as

(3) with (4) and are the target dwell time and the burst durawhere tion, respectively. The higher order terms are neglected in (4),

(5) with (6) where is the point target Doppler bandwidth, is the limited squinted angle due to azimuth beam steering and can be even nein the glected (The maximum azimuth steering angle is TerraSAR-X satellite). The TOPS raw data supports in the azimuth time/frequency domain are shown in Fig. 2. and represent the burst output duration and the processed azimuth beam bandwidth, respectively, and are the beam-center time and zero-Doppler time, respectively, and is the Doppler bandwidth of the whole burst imaged scene. From Fig. 2, the properties of the azimuth signal in TOPS can be summarized as follows. 1) Both Doppler centroid and azimuth beam center time vary with the target azimuth location due to azimuth beam steering during the whole acquisition interval in TOPS. The target Doppler centroid varying with target azimuth location can be used to distinguish targets with

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different azimuth locations. Moreover, the instantaneous Doppler centroid varying rate is expressed as follows: (7) where is the initial squinted angle. It can be seen the Doppler centroid varying rate has no relation with target locations and only refers to the azimuth beam rotation rate. 2) Because of the opposite azimuth beam scanning to the spotlight case during the whole burst duration in TOPS, the Doppler bandwidth of point target is reduced, while the total Doppler bandwidth is seriously increased. They can be respectively expressed as follows:

Fig. 3. Azimuth up-sampling via zero padding.

where is the azimuth over sampling rate and usually about 1.1 1.4 [15]. Therefore, too many small azimuth blocks will be introduced, while is little more than 1 and remains a great value. This case will affect the efficiency and the quality of the TOPS SAR data imaging algorithms.

(8)

B. Zero Padding

(9)

Another effective approach to unfold the aliased Doppler spectra is azimuth up-sampling via the zero padding operation in the Doppler domain as shown in Fig. 3. Its main processing steps are summarized here. 1) Remove azimuth varying Doppler centroids via the deramping function given by

It can be seen that the imaged scene Doppler spectrum aliasing will exist in TOPS. This phenomenon will affect TOPS raw data focusing and should be resolved at first. 3) As the TOPS mode is a novel wide swath burst imaging scheme, the short burst duration is used to illuminate the imaged scene with a large azimuth extension. Consequently, the azimuth output extension is much greater than the burst duration . The azimuth back folding TOPS SAR image will be obtained, if the only traditional stripmap processor is adopted to handle the TOPS raw data. Therefore, three major problems, which are the aliased Doppler spectra, the large range cell migration due to the larger Doppler bandwidth, and the output image back folding in azimuth, should be resolved. Although several algorithms have been proposed for phase-preserving processing of burst mode data in recent years [26]–[31], these algorithms without some modifications may not be effectively fit for the TOPS SAR raw data due to its corresponding special echo properties in azimuth. In other words, some focusing algorithms suitable for conventional imaging modes can still be used to process the TOPS raw data but require some modifications. III. SOLUTIONS TO THE ALIASED SPECTRA The progressive azimuth beam steering during the whole acquisition in TOPS leads to the total Doppler bandwidth of a burst being several times greater than the system PRF. To resolve the aliased Doppler spectra, four approaches will be introduced here. A. Use of Subapertures In order to accommodate the large Doppler bandwidth of the burst imaged scene in TOPS, the use of subaperture is usually adopted, and the completed burst raw data is divided into several azimuth blocks [5], [11]. To avoid the Doppler spectral aliasing in each block, the size of each block should obey the following relationship: (10)

(11) where is the burst center time. After this deramping of the imaged operation, the Doppler bandwidth scene is the same as the point target. The new Doppler bandwidth is computed as follows: (12) It can be seen that the aliased Doppler spectra can be overcome after deramping. Afterwards, zero padding in the Doppler domain is applied to the ranges [ , ] and [ , ] after the azimuth fast Fourier transform (FFT). 2) Since range cell migration correction (RCMC) is usually performed in the Doppler domain and only depends on the instantaneous Doppler frequency [19], [20], [25], azimuth varying target Doppler centroids should be recovered by the reference function , which is the conjugated function of . After the final azimuth inverse FFT (IFFT) operation, the obtained TOPS SAR data is up-sampled with the high azimuth sampling frequency . Clearly, the aliased Doppler spectra are overcome at cost of the obviously increased azimuth samples, and the number of azimuth samples is up to . With the azimuth frequency scaling operation and the burst duration reduction presented in [12], the number of azimuth samples can be seriously reduced. However, the reduced burst duration will lead to the increased output image back folding in azimuth. C. Mosaic Approach Mosaic approach is an efficient way to unfold the aliased Doppler spectra originally proposed for the spotlight mode [16]. Its main steps are summarized here.

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D. Two-Step Focusing Technique The two-step focusing technique originally proposed for the spotlight case is an efficient way to resolve the aliased Doppler spectra. The key point of this technique is an azimuth prefiltering step implemented by an azimuth convolution between the selected chirp signal and the raw data, which allows a bulk azimuth data compression to overcome the aliased Doppler spectra [17], [18]. The selected chirp signal is assumed as follows: Fig. 4. Azimuth up-sampling via the mosaic approach.

(18)

1) Raw data are transformed into the range-Doppler domain, and the Doppler spectrum will be aliased as shown in Fig. 4(a). 2) Doppler domain mosaicing copies of the raw data to unfold the aliased Doppler spectrum as shown Fig. 4(b). can be computed as

where is the selected range and later discussed in detail. The convolution result between (3) and (18) in the discrete domain can be expressed as follows [17], [18]:

(13) where is the “rounding to the larger integer” operator. 3) Frequency deramping step in azimuth, which removes the azimuth varying beam center time as shown in Fig. 4(c), is taken. The deramping function is as follows: with (14) where is the instantaneous Doppler frequency, and is the Doppler centroid of the burst. Consequently, the new target dwell time and the Doppler modulation rate , respectively, become

(19)

where is the pixel number of the azimuth signal, is the pixel number of the output signal, is the raw data sampling interval, and is the output sampling interval. In order to use an efficient FFT implementation, is set to (20)

(15) (16)

To satisfy the Nyquist criterion, the output azimuth sampling interval should be (21)

4) Inverse Fourier transform the resulting TOPS raw data. To obtain the desired azimuth signal and reduce interference, low-pass filtering in the time domain and azimuth data resampling are taken via azimuth samples reduction. Afterwards, the number of azimuth samplers is decreased to , while the burst duration is reduced to . should be great than , the typical is selected as value of

Since the azimuth data acquisition scheme in TOPS is quite similar to the sliding spotlight case, the selected range is also chosen [10], [18] in TOPS. Moreover, is assumed, the number of pixels and the output signal duration can be computed as follows:

(17)

(22)

Compared with the up-sampling approach, the mosaic approach may seem to be less efficient because of . Actually, less azimuth samples could be obtained after the azimuth mosaic approach to unfold the aliased Doppler spectra, since the burst duration is obviously reduced in the final step of the mosaic approach.

(23) is It can be seen that the increase required to resolve the aliased Doppler spectra and the azimuth output signal duration is much shorter than the original burst duration.

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A. CS Algorithm With Postprocessing Steps As the azimuth extension of an imaged area should be observed in the short burst duration, the mere use of a stripmap processor to focus the TOPS raw data leads to the focused SAR image back folding in azimuth. The azimuth data extension in the time domain before azimuth data focusing is a simple way to avoid azimuth data back folding but at the cost of higher computational complexity. Another way to resolve this problem is postprocessing to unfold the aliased SAR image. The block diagram of CS algorithm with postprocessing steps is shown in Fig. 6. The two-step focusing technique is assumed to be adopted for azimuth data preprocessing. The steps of chirp scaling, RCMC, and range compression are carried out using transfer functions and , which can be found in [26]. The phase function for phase correction and azimuth data compression is as follows:

Fig. 5. Graphic explanation of different azimuth data focusing approaches.

IV. IMAGING APPROACHES Since the azimuth beam is steered in the whole acquisition time, a wider azimuth angular interval than the conventional stripmap mode is required. Fortunately, the maximum azimuth steering angle in TOPS is usually quite limited, i.e., in the TerraSAR-X and in the Sentinel-1. Therefore, an SAR imaging processor with the low squinted angle processing capacity is required to implement range cell migration correction (RCMC) in TOPS. Compared with other imaging algorithms [19]–[24], the classic CS algorithm [25], [26] is an efficient processor to focus raw data with a low squinted angel or/and a wide swath coverage without any interpolations. Therefore, it seems reasonable to modify classic CS processor to focus the resulting TOPS raw data. After resolving the aliased Doppler spectra and implementing RCMC, we focus on analyzing the positions for azimuth data focusing. Based on the special characteristics of the TOPS mode raw data support in the slow time/frequency domain as shown in Fig. 2, there are four major methods to record azimuth focused signal. In the time domain, the azimuth signal could be focused and recorded in the position of azimuth beam center time and zero Doppler time. Furthermore, the azimuth signal also could be recorded in the position of target Doppler centroid and burst center Doppler frequency in the Doppler frequency domain. The last imaging approach requires the further Doppler extension and consumes more computing time and resource. Fig. 5 shows four different imaging approaches for the TOPS raw data, and all imaging approaches are implemented by using chirp scaling algorithm. We call these imaging algorithms as CS algorithm with postprocessing steps, extended chirp scaling (ECS) algorithm with SPECAN, modified ECS (MECS) algorithm based on chirp- transform, and baseband azimuth scaling (BAS) algorithm, respectively.

(24) with (25) where is the residual phase term which can be found in [26]. The final phase term in (24) is multiplied to remove the phase error due to the azimuth preprocessing step to unfold the aliased Doppler spectra. After the azimuth IFFT, the focused TOPS SAR image presents some azimuth data wrapping as shown in Fig. 7(a). The solution to resolve the back-folding TOPS SAR image is similar to the above-mentioned mosaic approach [1], [9], [27] and is outlined in Fig. 7. The main steps are summarized here. 1) Azimuth time-domain mosaicing copies of the focused SAR image to unfold the aliased signal as shown Fig. 7(b). can be computed as (26) where is the slant range from the imaged scene center to the SAR sensor. 2) Deramp step in azimuth, which removes the azimuth varying Doppler centroid as shown in Fig. 7(c). The deramping function is as follows:

(27) 3) Fourier transform the resulting SAR image. To obtain the desired azimuth signal and reduce interference, low-pass filtering, and azimuth data resampling are performed via azimuth samples reduction as shown in Fig. 7(c). Afterwards, the azimuth data sampling frequency is reduced to (28)

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Fig. 6. Block diagram of different CS processors to focus the TOPS raw data.

Fig. 8. Graphic explanation of azimuth scaling.

Fig. 7. Graphic explanation of SAR image unfolding in azimuth.

4) After the final azimuth FFT operation, the phase function , which is a reference conjugate to , is multiplied to compensate the phase error. This imaging algorithm extends the focusing capability of the conventional CS processor for the stripmap mode to process the TOPS raw data. Only azimuth preprocessing steps to resolve the aliased Doppler spectrum and postprocessing steps to unwrap the back-folded SAR image are added to be fit for the TOPS mode. B. ECS Algorithm With Specan ECS algorithm with SPECAN operation [26], [28], [29] originally proposed for ScanSAR can focus SAR data with time

varying Doppler centroid [30]. According to the properties of the azimuth signal in TOPS, Fig. 8 shows the block diagram of the ECS processor to deal with the TOPS SAR raw data. In this imaging algorithm, the above-mentioned mosaic approach is assumed to unfold the aliased Doppler spectra. The phase function , which removes the hyperbolic phase history for all targets and introduces a constant azimuth modulation rate, is given by

(29) where is a selected scaling range for the final desired az. This function is used to remove the imuth sampling space hyperbolic azimuth phase history for all targets and introduce a

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constant linear frequency modulation for the whole subswath. The scaling reference range can be computed as follows:

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is a constant. The raw data transformed from the where range-Doppler domain into the two-dimensional (2-D) time domain is

(30) where is the velocity of the footprint, and is the number of the azimuth samples used for the FFT. Targets with different locations have different time shifts during the azimuth scaling as shown in Fig. 8. The azimuth filtering before azimuth scaling to remove the redundant Doppler bandwidth for those targets not illuminated by the complete AAP is to reduce the additional azimuth extension, since the higher Doppler bandwidth require a larger addition azimuth data extension. In the azimuth scaling operation in (29), the range variant azimuth data modulation rate is replaced by a constant rate at a selected scaling reference range , and the total azimuth time extension is (31) ECS algorithm with SPECAN seems to be less efficient for the TOPS SAR data than for the ScanSAR data, since the effective Doppler bandwidth in TOPS is much higher than the bandwidth in ScanSAR. The phase function compensating the linear frequency variation is

(36) is a constant and is the inverse Fourier where is multiplied to transform operator. The phase function compensate the linear frequency variation and is given by (37) If the conventional FFT is applied for the final azimuth compression, the focused TOPS mode SAR data can be expressed as follows:

(32) The azimuth signal is compressed after the final azimuth FFT. If the phase preserving focused SAR imaging is required, the residual phase error caused by the final SPECAN operation should be compensated via the following the phase function: (33)

C. Modified ECS Algorithm Based on Chirp -Transform The modified ECS algorithm based on chirp -transform was first proposed to process the ScanSAR data. The key point of this algorithm is that the final azimuth Fourier transform (FT) is replaced by the scaled Fourier transform (SCFT) using a selected scaled transform kernel to avoid the range-dependent azimuth distance sampling interval. To introduce a constant azimuth modulation rate, the following phase function is in (29): used instead of (34)

(38) where is a constant and is the Fourier transform operator. The obtained azimuth distance sampling interval is (39) is the azimuth time sampling interval. To where obtain a uniform azimuth distance sampling interval for each range bin, additional resampling for azimuth geometric correction is required. To avoid the range-dependent scaling of the azimuth pixel, the conventional Fourier transform is replaced by the scaled Fourier transform with the following transform kernel [31], [32]: (40) is the selected range for the final obtained sampling where interval. Afterwards, the raw data after the scaled Fourier transform is as follows:

Afterwards, the raw data in the range-Doppler domain can be expressed as follows:

(35)

(41)

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where is a constant and is the scaled Fourier transform operator. Afterwards, the uniform azimuth distance sampling interval for each range bin is obtained as

TABLE I SIMULATION PARAMETERS

(42) The scaled Fourier transform in the discrete domain is the chirp- transform, and it can be efficiently implemented by the efficient FFT code [31] as shown in Fig. 6. The phase functions and are expressed as follows: (43) (44) is final output Doppler sampling interval. where Compared with the above-mentioned ECS algorithm, the modified ECS algorithm based on chirp- transform seems to be more efficient, since it omits the large azimuth data extension to avoid wrapping. D. Baseband Azimuth Scaling (BAS) Algorithm The BAS algorithm is recently proposed to process the TOPS SAR raw data and sliding spotlight SAR data in [5], which is based on the de-rotation operation in azimuth to remove the azimuth-varying Doppler centroid [5], [33]. The BAS algorithm presented in this paper shown in Fig. 6 uses the same basic principle to focus the azimuth signal. However, an azimuth scaling factor corresponding to the slant range instead of is introduced, which is similar to a selected scaling range the constant range scaling factor in [26] for processing the highly squinted data. In this algorithm, the above-mentioned up-sampling technique via zero padding is assumed to resolve the aliased Doppler spectrum, and the phase function is adopted for removing the higher order terms and changing the Doppler centroid varying rate. is expressed as

Fig. 9. The designed imaged scene. (a) Arrangement of point targets. (b) Aliased Doppler spectrum.

The final azimuth matched filter for signal compression is expressed as (48)

(45) The azimuth scaling factor will be discussed later. The purpose of the presented azimuth scaling in (31) is to adjust the output azimuth distance sampling interval based on the fact that changing the Doppler modulation rate shifts the azimuth signal. Consequently, the new azimuth signal modulation rate for each target becomes

The azimuth distance sampling interval in the focused SAR image is given by

(49) To obtain the uniform azimuth distance sampling interval for each range bin, the scaling factor can be usually chosen as follows:

(46) (50) After inverse transforming the raw data to the 2-D time domain, the de-rotation is carried out via the transfer function as follows: (47)

is the azimuth scaling fact at referenced range . where Moreover, interpolations are avoided when multiple subswath images combining together, if an appropriate is chosen. For the phase-preserving focused SAR image, the data should be

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Fig. 10. Raw data in the range-Doppler domain after the azimuth preprocessing step. (a) Zero padding. (b) Mosaic approach. (c) Two-step technique.

Fig. 11. Imaging results of the designed imaged scene. (a) Before azimuth output unfolding. (b) After azimuth output unfolding.

compensated the phase error cause by the de-rotation processing step via the following phase function:

(51) The four imaging approaches presented for focusing the TOPS mode raw data are all based on the classic CS algorithm. The major difference between these algorithms is the strategy of azimuth signal compression according to the special properties of the azimuth signal component. Modified ECS and BAS algorithms should be more efficient than the other two, because they require fewer or no increased samples to avoid azimuth wrapping in the focused SAR image. V. SIMULATION EXPERIMENT Here, simulation experiments on point targets are carried out to validate the presented processing approaches for TOPS SAR data. The parameters in this simulation are listed in Table I. First, we validate the presented solutions to overcome the aliased Doppler spectrum in TOPS using a designed imaged scene as shown in Fig. 9(a), and its aliased Doppler spectrum is shown in Fig. 9(b). According to simulation parameters listed in Table I, the size of each subaperture should be less than 0.05 s. The unfolded Doppler spectrums via the presented methods of zero padding, azimuth data mosaicking, and the two-step tech-

nique are shown in Fig. 10. After these solutions to overcome the aliased spectrum, the number of azimuth samples is up to 7284, 2316, and 1853, respectively, while the original number of azimuth samples is 1668. Therefore, the two-step focusing technique seems to be the most efficient among three methods taking into account both the azimuth samples and the processing complexity. To demonstrate the focused SAR image back folding phenomenon in the CS algorithm with postprocessing steps, imaging results without and with postprocessing are given in Fig. 11. It can be seen that the postprocessing steps resolve the azimuth output folding problem. The final image in Fig. 11(b) clearly shows the arrangement of point targets. In addition to the imaging capability, the efficiency of the SAR processor should be considered. Therefore, the processing times of the presented four algorithms are compared. Since different azimuth preprocessing approaches (i.e., use of subaperture, zero padding, mosaic approach, and two-step focusing technique) to resolve the aliased Doppler spectra will affect the efficiency of the following imaging algorithm, the presented four imaging algorithms will adopt the two-step focusing technique to resolve the aliased Doppler spectrum. The processing times of the above-mentioned four algorithms to process the TOPS SAR data of the designed scene in Fig. 9 under the same condition are 94.73, 52.34, 35.52, and 40.27 s, respectively. To further validate the presented four imaging approaches in this paper, contour plots of impulse response of three simulated

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Fig. 12. Contour plots of point targets. Top to bottom: (a) P1 (CS); P1 (ECS); P1 (MECS); P1 (BAS); (b) P2 (CS); P2 (ECS); P2 (MECS); P2 (BAS); and (c) P3 (CS); P3 (ECS); P3 (MECS); P3 (BAS).

point targets P1, P2, and P3 with different locations are given. The relative coordinates (range azimuth) of P1, P2, and P3 are ( 10 km 7 km), (0 km 0 km) and (10 km 7 km), respectively. Since the azimuth beam is progressive steered during the whole acquisition time in TOPS, targets with different az-

imuth locations will be illuminated with different squinted angles. In order to distinguish these limited squinted angles, the transmitted pulse bandwidth and sampling rate increase to 150 and 200 MHz, respectively. The imaging results of three targets in each imaging algorithm are reported in Fig. 12, and their mea-

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TABLE II MEASURED IMAGING PARAMETERS

sured focusing parameters including resolution, peak sidelobe ration (PSLR), and integrated sidelobe ration (ISLR) in both range and azimuth are computed and listed in Table II. Sidelobe suppression in all presented imaging algorithms is better than 13.24 dB (no weighting), while ISLR is better than 9.84 dB. Both contour plots in Fig. 12 and measured focusing parameters listed in Table II show the well-focused features and validate the presented imaging algorithms. VI. CONCLUSION For TOPS SAR data focusing, three major problems, including the aliased Doppler spectra, the large range cell migration, and the output SAR image back-folding in azimuth must be resolved. In this paper, four imaging approaches based on the classic CS processor for the stripmap case are presented in this paper. First, different solutions to resolve the aliased Doppler spectra originally adopted for the spotlight case are reviewed and modified according to echo properties of the TOPS mode, and their corresponding advantages and drawbacks are compared and analyzed. Since the major difference between the echo signal of the TOPS mode and the stripmap case is its azimuth component, we focused on discussing the azimuth data focusing. According to the special properties of the TOPS SAR raw data, four imaging approaches based on the classic CS algorithm are presented in this paper. The major difference between these algorithms is that azimuth signal is focused and recorded in different positions. Furthermore, with the postprocessing steps via the mosaic approach, SPECAN and de-rotation operation, the focused SAR image back folding in azimuth can be overcome or avoided. All presented imaging algorithms in this paper have extended the focusing capacity of the classic CS algorithm. Simulation results on point targets validate the presented four imaging approaches.

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Dr. Xu was the recipient of the Special Prize of President Scholarship for Postgraduate Students from the Graduate University of Chinese Academy of Sciences in 2011.

Pingping Huang was born in Shandong, China, in 1978. He received the B.S. degree from the College of Information Engineering, Shandong University of Technology, Zibo, China, in 2003, the M.S. degree from the College of Information Engineering, Inner Mongolia University of Technology, Hohhot, China, in 2007, and the Ph.D. degree from the Institute of Electronics, Chinese Academy of Sciences, Beijing, China, in 2011. He is currently with College of Information Engineering, Inner Mongolia University of Technology, Hohhot, China. His current major research interests are signal processing, digital beamforming, polarimetric interferometry, and spaceborne synthetic aperture radar system design.

Robert Wang (M’07) received the B.S. degree in control engineering from the University of Henan, Kaifeng, China, in 2002, and the Dr. Eng. degree from the Graduate University, Chinese Academy of Sciences, Beijing, China, in 2007. In 2007, he joined the Center for Sensorsystems (ZESS), University of Siegen, Siegen, Germany, where he is currently involved with the hybrid bistatic experiment. He was also involved in some SAR projects for Fraunhofer-FHR. Since 2011, he has been a Research Fellow with the Spaceborne Microwave Remote Sensing System Department, Institute of Electronics, Chinese Academy of Sciences, Beijing, China, where he was currently funded by “100 Talents Programme of The Chinese Academy of Sciences. His current research interests include monostatic and bistatic SAR imaging, multibaseline for monostatic and bistatic SAR interferometry, high-resolution spaceborne SAR system and data processing, airborne SAR motion compensation, FMCW SAR system, and millimeter-wave SAR system. Dr. Wang has contributed to invited sessions on bistatic SAR at the European Conference on Synthetic Aperture Radar (EUSAR) 2008. He is the author of a tutorial entitled “Results and progresses of advanced bistatic SAR experiments” presented at the European Radar Conference 2009 and the coauthor of a tutorial entitled “Progress in bistatic SAR concepts and algorithms” presented at EUSAR2008.

Yunkai Deng received the M.S. degree in electrical engineering from Beijing Institute of Technology, Beijing, China, in 1993. In 1993, he joined the Institute of Electronics, Chinese Academy of Sciences (IECAS), Beijing, China, where he was involved with antenna design, microwave circuit design, and spaceborne/airborne SAR technology. He has been the leader of several spaceborne/airborne SAR programs and developed some key technologies of spaceborne/airborne SAR. Currently, he is a Research Scientist, a Member of the scientific board, and the Director of Spaceborne Microwave Remote Sensing System Department, IECAS. His current research interests include spaceborne/airborne SAR technology for advanced modes, multifunctional radar imaging, and microwave circuit design.

Youchun Lu received the M.S. degree from the University of Electronic Science and Technology, Chengdu, China, in 2006. He is currently with the China Center for Resources Satellite Data and Application, Beijing, China. His major research interests are SAR data focusing and SAR image processing.