An Imaging Method for Spaceborne Cooperative Multistatic SAR Formations With Nonzero Cross-Track Baselines

Spaceborne multistatic synthetic aperture radar (M-SAR) formations can deploy multiple spatially separated receiving phase centers along the along-track (AT) direction to achieve high-resolution wide-swath. However, the cross-track (XT) separation between the spacecraft is inevitable due to the formation design like orbital safety and application potential like the XT interferometry. In addition, the different motion vectors of two or more satellites caused by the Helix formation will lead to the difference of the Doppler parameters at the same range gate. Therefore, nonzero XT baselines and space-variant characteristics pose new challenges to the focusing and phase-preserving of the M-SAR imaging. To this end, an imaging method for spaceborne cooperative M-SAR formations with nonzero XT baselines is proposed in this article. Firstly, a spaceborne cooperative M-SAR formation is demonstrated. Afterward, the imaging method is described in detail. The motion compensation technology and the idea of partitioned equivalent velocity are adopted to solve the problems of nonzero XT baselines and space-variant characteristics, respectively. Finally, the simulations of point targets and distributed targets are carried out to verify the proposed method, and the results show that the precise focusing of spaceborne cooperative M-SAR with nonzero XT baselines can be achieved by the proposed imaging method.

characteristics that meet the application requirements of the next-generation spaceborne SAR system, such as highresolution wide-swath (HRWS) imaging, along-track (AT) interferometry, cross-track (XT) interferometry, and so on, so it has received extensive attention [3], [4], [5]. Another trend is adopting cheaper systems with the intention to shift the complexity from the space segment to software. Thus, small satellites which received echoes only can be deployed in the formation of M-SAR systems to provide equivalent or superior performance compared to the state-of-the-art SAR systems currently with a minor cost and higher robustness toward failure [6].
The processing methods of spaceborne M-SAR data have been studied by several scholars, and the main purpose is to use the M-SAR data to overcome the contradiction between the swath width and the azimuth resolution of the conventional SAR systems. The reconstruction method proposed in [7] can be used in the case of AT displaced receivers, and Sakar et al. proposed a reconstruction method for M-SAR formation with large AT baselines [8], [9]. In [10], a reconstruction scheme in the 2-D frequency domain is introduced, which is also aimed to the case of AT baselines. However, the XT separation between the spacecraft may be intentional when the spacecrafts are operating in cooperative formations, so that along-track drifts can be tolerated without increasing the collision risk. More importantly, it can form a single-pass XT interferometry system, which has broad application prospects. Unfortunately, a large difference of the slant range history between secondary satellites is produced due to XT baselines, so the existence of XT baselines will bring difficulties to the subsequent imaging processing. The most troublesome problem is that the additional azimuth modulation phase introduced by XT baselines will make the existing reconstruction methods used only for AT direction failure. Some scholars have put forward some ideas to solve this problem. Dogan et al. [11] provided a processing method in the case of nonzero XT baselines, but the derivation of the method is carried out under the assumption of flat earth. In [12], the errors introduced by XT baselines were modeled as channel mismatches, and a compensation method is proposed. However, the model established in [12] is based on the traditional monostatic multichannel system, i.e., receiving apertures are distributed in one platform, so the method proposed in [12] is only practicable for the case where XT baselines are very This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ small (less than 10 m). There are other efforts for the problem of nonzero XT baselines, which is mentioned in [10], [13], [14], but no complete solution is given.
For the imaging algorithm, since the cooperative M-SAR system also satisfies the quasi-stationary configuration, so many existing BiSAR imaging algorithms can be considered, such as Loffeld's bistatic formula (LBF) method [15], [16], extended LBF method [17], [18], series reversion [19], [20], and so on. However, there are still some problems. The different motion vectors of two or more satellites caused by the Helix satellite formation will lead to the difference of the closest slant range and Doppler characteristics at the same range gate. In more general terms, the azimuth modulations are unequal for the primary and secondary satellites due to the different slant ranges and velocities, which is described as the problem of space-variant characteristics in this article. However, the imaging algorithms mentioned above cannot solve the problem of space-variant characteristics well.
In this article, an imaging method for spaceborne cooperative M-SAR formations with nonzero XT baselines is proposed under the assumption that the error of elevation accuracy is zero, and the unambiguous recovery of the M-SAR data and the problem of space-variant characteristics are aimed to be solved. Firstly, remove the extra phase error in the echo data caused by nonzero XT baselines. Since nonzero XT baselines are similar to the motion error, so it is possible to consider applying Motion Compensation (MoCo) technology to compensate for the extra phase error introduced by XT baselines [21], [22]. After that, the case of nonzero XT baselines is converted to the case of zero XT baselines, and many mature reconstruction methods for the data of AT displacements can be used to obtain the unambiguous echo signal. Secondly, an imaging algorithm based on the idea of partitioned equivalent velocity instead of the hyperbolic range history framework is proposed, which refers to the quasi-monostatic method proposed by Bamler et al. [23], and the range-variant and azimuth-variant equivalent velocity is used to solve the problem of space-variant characteristics in the Bi/M-SAR imaging.
This article is arranged as follows. In Section II, a kind of spaceborne cooperative M-SAR formations with nonzero XT baselines is demonstrated, and the problem brought by nonzero XT baselines is discussed. An imaging method for spaceborne cooperative M-SAR formations with nonzero XT baselines is proposed in Section III. The simulations of point targets and distributed targets are carried out in Section IV to verify the proposed method. Finally, Section V concludes the article.

II. FORMATION AND PROBLEM
Although spaceborne cooperative M-SAR formation with nonzero XT baselines can provide many application potentials that cannot be ignored, it brings some difficulties of signal processing. Therefore, a kind of spaceborne cooperative M-SAR formation is demonstrated firstly, and the coverage capability of this formation is given. Then, the problem caused by nonzero XT baselines is also discussed.

A. Formation Configuration
A conceptual diagram of an M-SAR formation applied to multibaselines interferometry is given in Fig. 1. The formation consists of a primary satellite, which transmits radar signals and three secondary satellites which receive echo signals only. In the proposed M-SAR formation, the three secondary satellites follow the primary satellite in a cooperative formation, and the flexible baselines can be selected between them. In addition, the inherent system limitation of HRWS imaging is overcome by placing the receiving phase centers on separate small satellites. For the convenience of expression, Sat 0 is used to represent the primary satellite, and Sat n (n = 1, 2, 3) is used to denote the nth secondary satellite.
The Helix formation can be adopted in the proposed formation, which uses the double-Helix formation of TanDEM-X for [24]. The coverage capability of the proposed formation is analyzed in Fig. 2. The specific configurations of the low-latitude formation are taken as an example, and the six orbital elements of the proposed M-SAR formation are shown in Table I. Three sets of configurations are formed by the coordination of baselines between the Sat 0 and Sat n , and they are represented by the lines of three colors in Fig. 2.

B. Problem
Usually, the control in XT baselines has to take into account the topographic variations within the footprint, since topography  imposes an inherent model mismatch in the reconstruction process. Thus, the XT baseline must be strictly controlled to obtain the high-quality M-SAR image, which was analyzed in detail in [25]. The requirement on the orbital tube for the constellation can be approximated as follows [25]: where ε φ (AASR, N rx ) 1 is the maximum phase excursion, which can be tolerated within the elements of the constellation, and the value of ε φ is a design parameter, which depends on the Azimuth-Ambiguity-to-Signal Ratio (AASR) value of the system specification and the number of satellites N rx in the formation; R 0 is the near slant range; θ i is the near incidence; δh refers to the maximum topographic variation within the scene. When the error introduced by the XT baseline is not compensated, the XT baseline b xt is needed to be strictly limited due to the topographic variation δh, the AASR, and the number of satellites N rx . The impact of the XT baseline as a function of the phase error is shown in Fig. 3. Fig. 3(a) shows the phase error ε φ changes with the topographic variation δh and the XT baseline b xt , and it is calculated assuming a formation of two satellites. The relation between the phase error and the AASR for different constellation sizes is illustrated in Fig. 3 More detailed analysis on the orbit control sensitivity of SAR systems in different frequency bands is given in [25], and the conclusion is that a threshold between 10λ and 20λ covering topographic variations up to 1-2 km is an acceptable compromise when the compensation of nonzero XT baselines is not considered, where λ is carrier wavelength. Otherwise, the azimuth ambiguity level of the reconstructed signal will raise dramatically. However, the applications potential of too short XT baselines (5 m in L-band and 0.6 m in X-band) is limited in the M-SAR system used for the multibaselines interferometry. Thus, the problem to be considered is how to compensate for the extra phase error introduced by XT baselines when they are further increased. For the proposed formation in this article, phase errors caused by the difference of the slant range history due to nonzero XT baselines are shown in Fig. 4. Obviously, larger XT baselines will produce nonnegligible phase errors, which causes the reconstruction process to fail. Therefore, the method proposed in this article can eliminate these phase errors to achieve fine focusing of spaceborne cooperative M-SAR formations with nonzero XT baselines.

III. DATA PROCESSING
In this section, an imaging method for spaceborne cooperative M-SAR formations with nonzero XT baselines is proposed, and the diagram of the data processing is shown in Fig. 5.

A. Preprocessing
Two tasks, i.e., synchronization phase error compensation and platform mismatch calibration, are needed to be completed in the preprocessing step.

1) Synchronization Phase Error Compensation:
The independent oscillators are used in the transmitter and receivers, and any deviation between the oscillators will cause a residual modulation of the recorded SAR raw data [27], [28]. An advanced noninterrupted synchronization scheme is adopted in the LuTan-1 (LT-1) mission [29], and the LT-1 is a spaceborne BiSAR mission. For the spaceborne cooperative M-SAR system, the synchronization scheme used in the current BiSAR system can be used for reference. Pulse compression is firstly performed to the synchronization signals and the peak phases are extracted in the compressed synchronization signals. Then, orbit parameters are used to correct the Doppler effects and the relativistic effect [30]. Afterward, the coarse-compensation phase can be calculated as follows [29]: whereφ 0,n andφ n,0 are the peak phases of the synchronization signals from the primary satellite and the nth secondary satellite, respectively; ϕ cal is the internal calibration phase. Further, the high-accuracy compensation phase ϕ syn,n can be obtained through the Kalman filter and interpolation [31]. Finally, compensate ϕ syn,n into the echo signals of the nth secondary satellite.

B. Platform Mismatch Calibration
The receiving links of different secondary satellites are also independent, and the platform mismatch error caused by the hardware link and atmosphere must be considered [32], [33]. A method called azimuth cross correlation can be used in calibration [34] and the excellent effect can be achieved. Assume that the echo signals of every secondary satellite after the synchronization phase error compensation is s n (η, τ ), and n = 1, 2, 3 in this article. Take the 1-th secondary satellite as the reference secondary satellite, and the relationship between the echo signals in the range frequency domain is given as follows [34]: where m refers to subscripts of other secondary satellites other than the reference secondary satellite, and m = 2, 3 in this article; η and τ are the range and azimuth time, respectively; f τ represents the range frequency; Δb AT,m is the phase center distance between the mth secondary satellite and the reference secondary satellite; v s,m is the velocity of the mth secondary satellite; ϕ m and Δτ m are the constant phase error and the range sampling time delay, respectively, which is the error that needs to be estimated and compensated. Perform the operation of azimuth cross correlation to the m echo signals, and the constant phase error ϕ m and the range sampling time delay Δτ m can be obtained as follows [34]: where E a [·] denotes averaging operation along the azimuth direction.

C. Nonzero XT Baselines Compensation
Nonzero XT baselines compensation based on MoCo technology is the core step of the proposed method. After the phase error caused by nonzero XT baselines in the echo signal is eliminated, the relevant azimuth reconstruction algorithm can be used to obtain the unambiguous echo signal.
1) Calculate Virtual-Zero-Cross (VZC) Positions: Firstly, calculate the VZC positions of all secondary satellites. The so-called VZC positions refer to the positions of the Sat n relative to the Sat 0 when there is no XT baseline, as shown in Fig. 6. Suppose coordinates of the Sat 0 and every Sat n are p Sat 0 (η) and p Sat n (η), respectively. Calculate the length of AT baselines from the every Sat n to the Sat 0 , and denote them aŝ B AT,n (η). It should be noted that the calculation of baselines may be deviated, and we will estimate this deviation and correct it in the subsequent step.
Then, the Range-Doppler (RD) geolocation algorithm [35] is used to obtain ground aiming point (GAP) coordinates and zero-Doppler (ZD) vectors of the Sat 0 . Assuming that GAP coordinates are represented as p η,k , where η indicates the η-th azimuth moment and k represents the kth ZD vector in this period. Thus, the ZD vector at the ηth azimuth moment corresponding to p η,k can be calculated as l ZD,η,k (η) = p Sat 0 (η) − p η,k . At any azimuth moment, the cross product of any two ZD vectors is performed to obtain the forward vector l f,0 (η) of the Sat 0 at this moment. Thus, the VZC positions of the every Sat n relative to the Sat 0 can be calculated as whereη indicates that there may be deviation in azimuth direction because the calculated VZC positions may deviate from the ideal case.
2) First-Order Error Compensation: The slant range error specific to the scene center between the every Sat n and the corresponding VZC position is compensated in the first-order error compensation. Assuming that the coordinate of the scene center is p 0 , and the slant range error can be calculated as Thus, first-order phase error compensation for the received echoes is performed as where s n (τ, η) is the echo signals after preprocessing. Then, the range resampling is performed as where c is speed of light; f τ represents the range frequency; FFT r [·] and IFFT r [·] refer to Fast Fourier Transform and Inverse Transform in range direction.

3) Second-Order Error Compensation:
The residual slant range error specific to all sampling points in the scene is compensated in the second-order error compensation. Firstly, pulse compression in range direction is performed using the matched filter H r (f η ) as follows: where K r is range frequency-modulated rate. Secondly, divide the range directions into K segments. Use the RD geolocation algorithm to calculate the GAP coordinates and ZD vectors in kth range segment of the Sat 0 in every azimuth moment in combination with Digital Elevation Model, where k = 1, 2, . . . , K. The slant range error between every Sat n and the corresponding VZC position relative to GAP coordinates p η,k can be calculated as Thus, the residual slant range error can be obtained as δR k,n (η) = ΔR k,n (η) − ΔR 0,n (η) .
Then, the interpolation along the range direction is carried out to obtain the residual slant range error δR n (η) of all sampling points in the scene, and phase error compensation is performed as follows: 4) Azimuth Resampling: As shown in Fig. 6, there may be deviations between calculated VZC positions and ideal VZC positions in azimuth direction, which is caused by the inaccurate calculation of AT baselinesB AT,n (η). These deviations can be estimated by an optimization problem. The coordinate of Sat 0 (precision), AT baselines (deviation), and XT baselines (deviation) are used to estimate the coordinates of Sat n , and the distance between the estimated and real coordinates of Sat n can be calculated. When the distance is small enough, it can be considered that the estimated coordinates of Sat n are precise enough, i.e., the estimated baselines are precise enough. Thus, we can letB n (η) = {B AT,n (η),B XT,n (η)} be the estimated baselines, and the distance D[B n (η)] between the estimated and real coordinates of Sat n is chosen as the criterion for optimization.
The forward vector l f,0 (η) of the Sat 0 and the forward vectors l f,n (η) of the Sat n are used to perform the cross product, and the vectors l ⊥,n (η) along the XT baselines direction can be obtained. Thus, the estimated coordinates of Sat n can be calculated as follows: p Sat n (η) = p VZC,n (η) + l ⊥,n (η) ·B XT,n (η) (15) where p VZC,n (η) can be obtained according to (6). Thus, the distance between the estimated and real coordinates of Sat n is given as follows: where · denotes the module of a vector. Therefore, the optimal estimation of baselines iŝ B n (η) = arg min Some optimal methods, such as steepest descent method and Newton method, have been studied to solve the unconstrained optimization problem in (17). The gradient descent method (GDM) is used here as an example. The optimal estimated baselinesB n,opt (η) are obtained when the last iteration is done. Based on GDM, the steps for the optimization problem are given as follows [36]: Step 1 (Initialization): Given initial values of baselinesB n,0 (η) Step 2: Calculate the search direction. ΔB n,j (η) = ∇D[B n,j (η)].
Step 3 (Linear search): Choose step size t via exact or backtracking line search.
Step 5: If the stopping criterion is satisfied, stop; otherwise, return to step2.
The ∇D[B n (η)] can be expressed as Thus, the deviations between the calculated and ideal VZC positions can be calculated as follows: whereB AT,n,opt (η) is obtained fromB n,opt (η). Thus, the sinc interpolation is used in azimuth resampling to compensate deviations of VZC positions in azimuth direction.

D. Reconstruction Processing
After eliminating the extra phase error introduced by the nonzero XT baseline, the physical meaning of signal acquisition is transformed into the case that acquires echoes along only the AT direction, and the spacing of the receiving phase centers is the length of AT baselines between the Sat n and the Sat 0 . Select the Sat 1 as the reference secondary satellite in this article, which is similar to the reference receive channel in the multichannel SAR system, and Sat m refers to other secondary satellites other than the reference secondary satellite. Thus, the traditional reconstruction method based on the filter bank [7] is adopted in this article.
The reconstruction filter P[f η ; Δx n (η)] is adopted as follows: where Δx n (η) represents the spacing between the Sat n and the Sat 1 . Besides, the elements in the prefilter H[f η ; Δx n (η)] can be expressed as follows [7]: where v s,n is the velocity of the nth secondary satellite; f η refers to the azimuth frequency.

E. Imaging Processing
After reconstruction processing, the unambiguous echo signal is obtained. Considering the approximation of the quasimonostatic configuration is still satisfied in the cooperative M-SAR formation; the imaging method proposed by Bamler et al. for BiSAR imaging can be used for [23]. Thus, the imaging geometry of the cooperative M-SAR formation can be considered as the geometry between the Sat 0 and the reference secondary satellite 2 Sat 1 .
The equivalent velocity v e is the most important parameter in the linear track case. For moderate bistatic configurations, the 2 It is necessary to ensure that the reference secondary satellite during the imaging processing is consistent with the reference secondary satellite during the reconstruction processing. slant range history can be approximated when some assumptions are satisfied [23] where R 0 is the closest slant range. For the sake of accommodating orbit curvature, a solution of the equivalent velocity is given as follows [37]: This solution is optimal for the center of the aperture but degenerates toward its boundaries. Thus, the best approximation is to use the least mean square error fit over the entire aperture time [23], [37]. In the imaging algorithm proposed in this article, the range-variant and azimuth-variant equivalent velocity, i.e., partitioned equivalent velocity, is adopted, so as to achieve fine focusing of the entire scene including edge points.
Thus, the slant range history of the reference secondary satellite Sat 1 corresponding to the reference point of the scene can be given by Using the approximation of quasi-monostatic, the history given in (24) can be expressed as where the subscript ref refers to "reference." Using the method of minimum mean square error to fit [R bi (η)/2] 2 , the closest slant range R 0,ref and the equivalent velocity v e,ref of the reference point of the scene can be obtained. The first step of the imaging processing is bulk range processing applied in 2-D frequency domain, which includes range cell migration correction (RCMC), secondary range compression (SRC), and the compensation of all higher-order phase terms for all points located at the reference range [23]. The transfer function is given as follows [23]: where f 0 is the carrier frequency. Afterward, the differential RCMC (DRCMC) is performed in the RD domain to correct the residual range cell migration (RCM) of targets at ranges of R 0,i = R 0,ref by sinc interpolation, as well as the space-variant correction in range direction [23] where ΔR(f η ; R 0,i , v e,i ) is the RCM at the ith range gate, which i = 1, 2, . . . , N r , and N r is the sampling numbers in range; is the RCM at the reference range gate; and the specific form is expressed as follows: where D(f η ; v e ) is the migration factor in the RD domain, and it is given by where v e,i represents the equivalent velocity corresponding to the ith range gate.
In the case of wide swath, the residual high-order phase errors caused by bulk range processing cannot be ignored. Further, the residual space-variant characteristics in range direction are considered in order to achieve the high phase-preserve imaging. Therefore, the signal of the RD domain after DRCMC is divided into N blocks along the range direction and transformed into 2-D frequency domain. Then, a range-variant transfer function is given by where Φ high refers to high-order residual phase; n = 1, 2, . . . , N; R 0,n and v e,n are the closest slant range and the equivalent velocity corresponding to each block of the signal. Use (30) to complete the compensation of each block of the signal in the 2-D frequency domain. Then, transform each block of the signal into the RD domain for splicing. It should be noted that the purpose of segmenting the signal in range direction is to compensate the residual phase error after the bulk range processing, and will not cause the difference in imaging quality of each block. After the above operation, the space-variant characteristic in range direction can be corrected through the range-variant equivalent velocity. Finally, the imaging processing is azimuth compression, which the space-variant characteristic correction in azimuth direction is also performed in this step. The signal in the RD domain is divided into M blocks along the azimuth direction, and the azimuth matched filter of each block is constructed according to the equivalent velocity v e,m and closest slant range R 0,m of the reference range gate corresponding to the each block where m = 1, 2, . . . , M. Use the azimuth matched filters of (31) to perform M times matched filtering on the overall signal in azimuth, i.e., multiple the signal and the matched filter in the RD domain and then transform them into the azimuth time domain to obtain all imaging results after matched filtering. In  the azimuth time domain, the images focused by each filters are extracted and spliced according to the segmentation strategy to obtain a complete focusing image. So far, the 2-D space-variant characteristics are compensated, and all pixels in the scene (including edge points) can achieve high phase-preserve fine focusing.

IV. SIMULATION
In order to demonstrate the validity of the proposed method, the simulations of point targets and distributed targets are carried out in this section. An array composed of nine point targets is adopted in the simulation, which are laid on a 100 km×100 km grid in ground range/azimuth directions, and the geometry of the designed scene is presented in Fig. 7. P5 is the center of the scene (which is also the reference point target). In order to evaluate the focusing effect of the imaging algorithm on the edge of aperture, point targets of P1, P5, and P9 are chosen for analyzing the imaging quality without loss of generality. Simulation parameters are listed in Table II, and the X-band SAR system is used to reflect the goal of HRWS. In addition, parameters of the satellite orbit are from the spaceborne M-SAR formation proposed in this article. A rectangular window is used in both the range and azimuth direction instead of a real antenna pattern, i.e., no weight is used, in order to facilitate the quantitative evaluation of imaging results.
The influence of nonzero XT baselines on the azimuth reconstruction algorithm can be observed from the azimuth spectrum of one point target, as shown in Fig. 8. It can be seen from   Fig. 8(a) and (c) that when the error introduced by nonzero XT baselines is not compensated, the reconstruction method fails completely. The spectrum is split into some segments in azimuth direction, which is obviously wrong. After performing compensation with the proposed method, the spectrum within the effective frequency band is well reconstructed as shown in Fig. 8(b) and (d).
The imaging results processed by the proposed method are presented in Fig. 11, and contour plots, azimuth profiles, and range profiles are given. It can be seen that the reference point (P5) and the edge points (P1 and P9) are all well focused, and the problem of space-variant characteristics, i.e., the defocusing of edge points, is solved well. The evaluation of imaging quality is given in Table III. The peak sidelobe ratio (PSLR), the integral sidelobe ratio (ISLR), and the pulse response width (IRW) in both directions are almost the same as those in theoretical values [38], and theoretical values are also given in Table III. Thus, according to the simulation results of point targets, the proposed imaging method shows the excellent focusing performance for the scenario where spaceborne M-SAR system is used to achieve high-resolution (below 1 m) and wide swath width (100 km).
In addition, it is necessary to verify whether the proposed method can achieve high phase-preserving. Commonly, the phase of the slant range R of the point target that needs to be retained after the imaging processing should be exp(j4πR/λ). The phase-preserving evaluation is to obtain the phase difference between the phase of the focused point target and the abovementioned phase that needs to be retained, and the evaluation results are also shown in Table III. Similarly, taking the P1, P5, and P9 as examples. Under the focusing of the proposed method, the phase-preserving accuracy of the whole scene is approximately 0.1 • , which is small enough.
The suppression effect of the proposed method on the azimuth ambiguity is shown in Fig. 9, and the nonbandlimited real antenna patterns in azimuth direction is considered here. Obvious ghosts appear in the simulated single satellite case due to the undersampling in azimuth direction, as shown in Fig. 9(a). The result processed by the proposed method after merging simulated three satellites' echoes is shown in Fig. 9(b). The performance of the azimuth ambiguity is greatly improved, and the intensity of ghosts is weakened by about −30 dB. In fact, the azimuth ambiguity is worse when the traditional filter bank method is used to deal with the case of large AT baselines. This problem is not the focus of this article, and the methods proposed in [8], [25] can be used to solve the reconstruction problem of large AT baselines.
Finally, the simulation of distributed targets is carried out to verify the performance of the proposed method, and a real SAR image that is extracted by GaoFen-3 is used as the target radar cross-sectional information for simulation purpose. The selected position is the coast along the northeast of China (42.16 • N 130.22 • E), and the imaging result of distributed targets  processed by the proposed method is shown in Fig. 10. The fine imaging of the M-SAR formation with nonzero XT baselines can be achieved by the proposed method, and the good suppression of the ambiguities is also achieved.

V. CONCLUSION
In the M-SAR formation, AT baselines are necessary to achieve the HRWS, and the XT separation may be existed due to orbital safety and application potentials. Thus, how to deal with the problem of nonzero XT baselines for the signal processing of M-SAR needs to be considered urgently. On the other hand, different motion vectors of multiple satellites caused by the Helix formation will lead to the difference of the closest slant range and Doppler characteristics at the same range gate. Thus, space-variant characteristics pose challenge to the focusing and phase-preserving of the Bi/M-SAR imaging, which needs to be solved in the imaging algorithm. Firstly, an M-SAR formation which consists of one transmitting primary satellite and three receiving only secondary satellites are demonstrated in this article. Afterward, an imaging method for spaceborne cooperative M-SAR formations with nonzero XT baselines is proposed, which is aimed to solve the extra error introduced by nonzero XT baselines and the problem of space-variant characteristics.
Finally, the simulations of point targets and distributed targets are carried out to verify the proposed method, and the results demonstrate the effectiveness of the proposed method.