# An Efficient Imaging Method for Medium-Earth-Orbit Multichannel SAR-GMTI Systems
###### Abstract  
Medium-Earth-orbit (MEO) synthetic aperture radar (SAR) has the advantages of short revisit time and wide coverage, and thus is a potential tool for implementing ground moving target indication (GMTI) tasks. In the paper, aiming at MEO SAR's problems of low signal-to-noise ratio and limited computation resource, an efficient imaging method is proposed for MEO multichannel SAR-GMTI systems with relatively low resolution. The proposed imaging method is designed with the consideration of both static scenes and ground moving targets, and it can simultaneously correct the range cell migrations of static scenes and multiple moving targets of no Doppler ambiguity. It needs only four Fourier transforms and twice phase multiplications, and thus is computationally efficient. Moreover, moving targets' signal characteristics, including the azimuth and range displacements and  
SAR, the high orbital altitude makes it suffer the problems of low signal-to-noise ratio (SNR) and limited computation resource. Therefore, it is essential to propose an imaging method with high computational efficiency for MEO SAR-GMTI systems to improve their performance. However, the existing imaging methods of MEO SAR [17; 18; 19] are designed only for the stationary scene and thus may not be suitable for SAR-GMTI systems. For example, [19] proposed an imaging algorithm based on a novel coordinate system. Since the imaging coordinate used in this algorithm depends on the Doppler parameters of the stationary scene, it cannot accurately correct the range cell migrations (RCMs) of moving targets.  
In this paper, we propose an efficient imaging method suitable for the MEO SAR-GMTI system. This method is designed with the consideration of both the stationary scene and ground moving targets. It utilizes the fact that, in a 2-D frequency domain, the couplings between the range and azimuth of static targets and the moving targets of no Doppler ambiguity are approximately identical, and thus the RCMs of these targets can be corrected simultaneously via a phase multiplication. The proposed imaging method is very efficient because it needs only four Fourier transforms (FTs) and twice phase multiplications. Thus, the proposed imaging method is very suitable for MEO SAR, which suffers the problem of limited energy and computation resources.  
The analysis and understanding of moving targets' signal characteristics in the image domain are very important for the development of the GMTI method [23], e.g., the clutter suppression and motion parameter estimation methods. Therefore, one other objective of this paper is to reveal moving targets' signal characteristics in the SAR image obtained by the proposed imaging method. Specifically, in the paper, the analytical expressions for the azimuth and range displacements and the along-track interferometric (ATI) phase of the target are derived, and their variation with the target's parameters are investigated.  
Note that the MEO SAR-GMTI system in this paper is assumed to have a relatively low resolution. The considerations are as follows: (1) A relatively low resolution can improve the SNR and reduce the data volume. This is important for MEO SAR, which suffers limited energy and computation resources and relatively high system complexity because of the increased orbital altitude; (2) For GMTI, a relatively low resolution can reduce the probability of Doppler ambiguity of moving targets.  
The remainder of this paper is organized as follows. In Section 2, the target's range equation model and 2-D spectrum for MEO multichannel SAR are derived. The proposed method is introduced in Section 3. The signal characteristics of the target in SAR image are analyzed in Section 4. In Section 5, experimental results are presented to verify the work of this paper. In Section 6, some discussions are presented. Finally, the paper is concluded in Section 7.