1. Introduction
High-resolution wide-swath (HRWS) synthetic aperture radar (SAR) imaging on ground moving target (GMTIm) has become increasingly important for homeland security and conflict control in real time over a vast area. The recent literature on SAR imaging indicates the feasibility of HRWS SAR imaging is in general constrained by the azimuth spectrum aliasing (ASA) and azimuth Doppler ambiguity (ADA) problems, which are inevitable as low pulse repetition frequency (PRF) is required for wide-swath SAR imaging. In this work, we explore the feasibility of using a suborbital spaceplane as platform to carry out SAR missions, and a rigorous SAR imaging approach is developed and verified by simulations.
A spaceplane orbiting near the top of atmosphere takes a vantage point for surveillance of cruising ships over a vast ocean area. To acquire images at fair spatial resolution over a wide swath [
1], low pulse repetition frequency is required to avoid range ambiguity. However, the effects of azimuth Doppler ambiguity (ADA) and azimuth spectrum aliasing (ASA) will emerge if the pulse repetition frequency is lower than the Doppler bandwidth of the backscattered signals from the targets [
2], resulting in multiple ghost targets and range error.
Wide Doppler spectrum implies a high azimuth resolution, but the spectrum will be wrapped into multiple segments in the azimuth baseband of , with an offset of for each segment, where is the pulse repetition frequency, and is the aliasing ambiguity number. This phenomenon is called azimuth spectrum aliasing (ASA). The radial velocity of a moving target induces a Doppler frequency shift , with the Doppler ambiguity number, which will arouse ambiguity between different targets at different along-track locations. This phenomenon is called azimuth Doppler ambiguity (ADA). Thus, the total Doppler frequency shift in each spectrum segment adds up to . If the ASA and ADA issues are not solved, the subsequent range-cell migration correction (RCMC) and phase compensation will not be properly implemented, resulting in artifacts such as ghost targets and range error.
Figure 1 shows the schematic of original azimuth spectrum before wrapping due to ASA and ADA. The baseband of Doppler frequency,
is labeled with
. The spectrum of received signals is wrapped into multiple segments of bandwidth
, each labeled with a different aliasing ambiguity number
. The
associated with any spectrum segment will be determined first, then the true Doppler frequency
will be determined from its baseband counterpart
after estimating the Doppler ambiguity number
. Many methods have been proposed to solve the ADA issue for SAR imaging of fast moving targets, but few of them considered the ASA issue which is crucial for HRWS applications. The ASA issue is more complicated than the ADA issue since a moving target is associated with only one
, but multiple spectrum segments are associated with multiple
’s.
The ASA issue has been tackled in [
1,
2]. In [
1], a deramp space-time adaptive process (STAP) was applied on a multi-channel SAR system, composed of one transmitter and an array of receivers, to tackle the ASA issue and coarsely focus the ground moving targets (GMTs) in a Doppler frequency-angle domain. The ambiguity number was then estimated by maximizing the signal-to-clutter-plus-noise ratio (SCNR) of GMTs in the image. However, prior knowledge of GMT along-track velocity was needed for the deramp function, otherwise the acquired image would be blurred. Performance between our proposed approach and the method in [
1] will be compared by future simulations. It will be shown that the SAR image generated with the method in [
1] maybe blurred if practical parameters for HRWS applications are imposed.
In [
2], a bistatic SAR system operated at PRF of 75 Hz for GMT imaging was composed of a GEO satellite-borne transmitter and an airborne multi-channel receiver. The signals from the multi-channel receiver were Fourier transformed to obtain a spatial spectrum, which was composed of multiple sinc functions separated at intervals of
, and a specific spectrum segment was extracted with a specific bandpass filter. However,
may not be commensurate with the baseband width of the spatial spectrum, causing additional wrapping of the spatial spectrum and inducing other artifacts. Although this method can focus SAR image, artifacts or ghost targets cannot be suppressed to an acceptable level, as will be shown later in the simulations. In this work, we propose a phase matching technique to tackle the ASA issue for acquiring images that meet the requirements of HRWS SAR on GMTim. By using a uniform array of receivers and exploiting the phase relation among the received signals, with proper receiver number
M and receiver spacing
d, the spectrum segment associated with specific
can be completely extracted.
Many techniques have been developed to acquire HRWS images. In [
3], multiple high-power beams with different azimuth phase centers were radiated from a satellite-borne HRWS SAR, around which three transponder-like MirrorSAR satellites orbited to configure multiple interferometric baselines in a single pass. The simulated resolution was 1.5 m and the swath width was 20 km. Significant trajectory curvature of spaceborne SAR is difficult to compensate for completely via signal processing, and the nested helix orbit of MirrorSAR in [
3] makes this issue even worse, leading to degraded resolution. Compared with practical HRWS applications, resolution of 1.5 m and swath width of 20 km seem to be insufficient. Take the simulation parameters in our work for example, where the resolution is 0.5 m and the swath width is 150 km.
At low PRF, the received signal over a single channel is not sufficient to estimate the Doppler centroid with conventional methods. In [
4], a multi-channel SAR approach was proposed to estimate the Doppler ambiguity number embedded in the backscattered signal from static objects by exploiting the range-variant feature of Doppler centroid, which was perturbed by ground moving targets.
Two types of method were mentioned in [
5] for removal of Doppler ambiguity. The first type utilizes a multiple-input multiple-output (MIMO) array to form several independent subapertures along track. The second type unwraps the Doppler spectrum by using multi-channel digital beamforming. Several identical linear frequency modulation (LFM) waveforms were emitted at tunable delays, making beams at different constituent frequencies point in different directions. The backscattered signals from a specific subswath could thus be extracted by using a band-pass filter. The range resolution was 0.75 m, compared with 0.25 m if the whole spectrum was radiated upon a fixed subswath. However, the benefit of solving range ambiguity other than Doppler ambiguity of HRWS SAR was not mentioned in [
5]. Based on the simulation results, a swath width of 100 km is not very wide considering the platform height of 600 km, and the range resolution of 0.75 m is not impressive with a signal bandwidth of 1200 MHz. As a comparison, our simulations can achieve a resolution of 0.5 m with signal bandwidth of 350 MHz.
In [
6], a ScanSAR was proposed by varying the elevation angle of a beam with slow time to cover a wide swath. The resolution became poorer as the illumination time on each subswath was curtailed. Since the strengths of backscattered signals from different subswaths were different, streak pattern was induced on the acquired image. Multiple subarrays were aligned along track, with tunable time delays between adjacent subarrays. The beams from different subarrays could be steered towards different directions, thus different frequency components of the LFM signals were emitted at different squint angles, achieving frequency-dependent along-track beam-steering to mitigate streak pattern and Doppler ambiguity. The swath width was about 400 km and the spatial resolution was about 5 m. Based on the simulation parameters in [
6], the resolution was improved from 20 m to 5 m, but is still not fine enough for practical HRWS applications, even for imaging a large target such as a ship.
Next, we will review some methods on imaging of ground moving targets. Taking steady images of ground moving targets (GMTs) is useful to many civic and military applications [
2,
7,
8,
9]. Some focusing techniques are required, especially when the aperture time is long or the target moves fast [
10,
11,
12]. Typical approaches to focus the image of a GMT require the estimation of its motion parameters from features embedded in its backscattered signal, such as Doppler centroid, modulation rates, and other higher-order parameters.
In [
13], an airborne SAR system, composed of one transceiver and multiple receivers, was proposed for GMT imaging, with the Doppler frequency and chirp rate estimated from an Lv distribution. Clearer images were acquired than those with Radon–Wigner transform (RWT) and fractional Fourier transform (FrFT), but were not clear enough for target identification. The method in [
13] may be suitable for moving target detection, but the image quality is not fine enough for identification purpose.
In [
14], an airborne SAR system, composed of one transceiver and multiple receivers, was used for GMT imaging. A third-order polynomial phase signal (PPS) model was used to focus the GMT of interest, with coefficients estimated using a minimum entropy method. Minimum entropy method may work on a point target, but may not work as well on more complex or large targets, which were not presented in [
14]. In addition, the method of [
14] could focus the image of one moving target at a time, but the other moving targets would appear blurred.
In [
15], a SAR system composed of an airborne transmitter and a companion airborne receiver was applied to acquire image of a ship at squint angle of
, with resolution of 1 m, which maybe sufficient for imaging large targets such as ships, as compared with our resolution of 0.5 m. Moreover, no real data processing was verified in [
15].
In [
16], a three-channel circular SAR was proposed to survey a specific area, at resolution of 2 m. The motion parameters of GMTs were estimated, but the image quality was not sufficient for target identification. Although circular SAR is a feasible method for imaging fixed point target, it cannot be extended for large area surveillance since the illuminated area is fixed.
In [
17], SAR imaging on ships over a vast ocean was studied. A squint minimization (SM) method was implemented for the compensation of third range compression, which was caused by ship translation. The squint angle was
, low PRF of 400 Hz was used to avoid range ambiguity, and the spatial resolution was 1 m, which may be sufficient for ship identification purpose. Moreover, no real data processing was verified in [
17] and the image quality may degrade in real applications.
In [
18], an azimuth multi-channel HRWS SAR was proposed to acquire images of moving ships, with swath width of 30 km and resolution of 3 m. With proper processing, the image is coarsely focused, then the Doppler parameters can be estimated and used in subsequent focusing process. However, resolution of 3 m maybe too large for identification purpose, only suitable for detecting large targets.
In [
7], the Doppler frequency was estimated by curve fitting the signal trace after range compression. A modified Keystone transform was then applied to compensate the linear range cell migration (RCM). However, signals from a real target are contributed by a bunch of scatterers, their signal traces are mingled and difficult to separate.
In [
19], a focusing method on maneuvering target was proposed by improving the Keystone transform with a coherently integrated cubic phase function (CICPF), but the acquired images were not well focused; maybe the CICPF was not accurate enough for compensating phase shift, or some higher-order phase term in the simulation data was too large.
In [
20], an airborne bistatic forward-looking SAR (BFL-SAR) was proposed. The received signals were processed with Keystone transform to compensate the linear RCM, followed by a mismatched compression in range to estimate the Doppler parameters of GMT. However, this technique might become laborious to focus image of large moving targets.
Compressive-sensing technique can be applied on the received signal matrix to minimize the rank of clutter signal matrix and the zero-norm of target signal matrix. In [
8], a robust principal component analysis (RPCA) was proposed for SAR imaging with a multi-channel airborne platform. The target signal matrix was further decomposed into three matrices, embedding the radial velocity, nearest range, number and echo strength, respectively, of the GMT. Images could thus be acquired under strong clutters, but the ignored along-track velocity could compromise the image quality.
An airborne SAR system for GMT imaging proposed in [
21] required no prior knowledge of motion parameters. The received signals after range compression, Keystone transform and RCMC were reversely processed in slow time, taken conjugate, and multiplied with its original version to eliminate the quadratic phase term in slow time. The peak in the resulting signals in fast-time and Doppler-frequency domain was used to estimate the closest range and radial velocity. However, the along-track velocity of GMT was ignored, which could compromise the image quality.
In an airborne SAR imaging method on GMTs [
22], RCMC was conducted by using a sequence of filters and Stolt interpolation after clutter removal. The best-fit of range and along-track velocity component were derived from the focused image. This method is basically a trial-and-error process, and the computational cost could be high.
In this work, we propose a multi-channel SAR on board a spaceplane orbiting near the top of atmosphere to acquire images of cruising ships. For surveillance over a vast ocean area, low pulse repetition frequency is required, inducing ADA and ASA issues. A modified azimuth spectrum reconstruction method on multi-channel signals is proposed. A compressive-sensing technique is applied to improve the estimation accuracy of the baseband Doppler frequency, with proper number and spacing of receivers, and a phase matching technique is proposed to determine the aliasing ambiguity number of each baseband spectrum segment. After all the spectrum segments are unwrapped, the Doppler ambiguity number is estimated from their slope.
The rest of this paper is organized as follows. The range model and signal model are presented in
Section 2. The estimation methods of motion parameters and ambiguities, along with simulations on a moving point target, are presented in
Section 3. The simulation results on five similar types of cruising ship are presented and discussed in
Section 4. Conclusions are drawn in
Section 5.