# Spaceborne Sparse SAR Imaging Mode Design: From Theory to Implementation
###### Abstract
To satisfy the requirements of different tasks, more and more advanced spaceborne SARs have adopted the above modes, such as TerraSAR [21], Sentinel [22], and Gaofen-3 [23]. Nowadays, several matching filtering (MF)-based methods have been proposed for processing data from different SAR imaging modes [24, 25, 26]. In 1996, [PERSON] et al. introduced an extended chirp scaling (ECS) method, which employs a spectral analysis technique to process ScanSAR data [27]. Building on ECS, [PERSON] et al. developed the ECS-baseband azimuth scaling (BAS) algorithm in 2010, which utilizes the subaperture technique to address the issue of Doppler spectrum aliasing [28]. While these methods process raw data computationally efficiently, they still face challenges in data acquisition, storage, and transmission, especially for high-resolution wide-swath imaging. In addition, they cannot be used to process echoes that do not satisfy the Shannon-Nyquist sampling theorem [29,30]. The developed sparse SAR imaging technology offers a solution to deal with the above problems. Compared with MF-based methods, sparse SAR imaging algorithms can achieve high-quality imaging with lower pulse repetition frequency (PRF) and obtain images with higher performance. The concept of sparse signal processing was introduced into SAR imaging in 2001 [31]. In 2006, [PERSON] et al. proposed compressive sensing (CS) [32], which challenges the traditional Shannon-Nyquist sampling theory [33] and enables the reconstruction of sparse signals from a reduced number of samples. In 2012, [PERSON] et al. proposed an approximated observation-based sparse SAR imaging method, which has lower computational complexity than conventional observation matrix-based algorithms, allowing large-scale sparse scene recovery [34]. In the following years, this technology has been further developed and applied to various SAR imaging modes, including Stripmap [35], Scan [36,37], Sliding Spotlight [38], and TOPS [39,40]. Owing to its advantage of wider swath width, sparse SAR imaging shows another option for high-resolution and wide-swath imaging. Motivated by the performance advantages of sparse SAR, this paper proposes a mode design scheme for spaceborne sparse SAR imaging. In the proposed scheme, we first design the beam positions of sparse imaging mode based on its corresponding traditional mode. Then, the basic system parameters of the designed sparse mode are calculated based on the radar equations. Subsequently, the AAP and system performance are analyzed to verify the superiority of the novel mode. Finally, the mixed-norm regularization-based sparse SAR imaging method is introduced to obtain a high-quality image with less azimuth ambiguity from the data collected by the designed sparse mode. The experimental results and performance analysis show that compared with the traditional mode, the corresponding sparse mode obtains a wider swath coverage by reducing PRF, without changing the existing on-board system's hardware conditions. In addition, it can suppress the effect of antenna beam scanning on system performance and has lower range ambiguity. Different from MF-based methods, the sparse imaging algorithm can obtain images with higher quality when the echo data used is downsampled, and it can achieve unambiguous recovery of large-scale surveillance areas with a higher image signal-to-clutter-noise ratio (SCNR). This paper is organized as follows: Section 2 introduces the traditional SAR imaging mode briefly, such as the observation geometry and signal characteristics. In Section 3, we demonstrate the design principle of the sparse imaging mode in detail, including beam position design, parameter calculation, AAP, system performance analysis, and the mixed-norm regularization-based sparse SAR imaging method. Experimental results are shown in Section 4 to verify the designed framework. Finally, conclusions are drawn in Section 5.