# Spatial Baseline Optimization for Spaceborne Multistatic SAR Tomography Systems
## 1 Introduction  
[PERSON] proposed two azimuth-range two-dimensional synthetic aperture acquisition techniques--curve SAR (CurviLinear SAR, CLSAR) [1] and SAR tomography (TomoSAR) [2]--in 1994 and 1995, respectively. Compared with interferometric SAR (InSAR) [3], CLSAR and TomoSAR truly qualify as 3D imaging. In TomoSAR, the use of a stack of complex-valued images, by synthesizing apertures along the height direction, makes it possible to separate different scatterers in one range-azimuth resolution cell and achieves height resolution, so as to provide the full 3D scene reflectivity profile in azimuth, range, height, and average velocity deformation [4]. Since the first practical demonstration of TomoSAR [5], it has been successfully applied in many application contexts, such as forestry [6; 7], 3D urban reconstruction [8; 9], and glaciers [10]. TomoSAR consists of resolving an inversion problem. To date, various spectral analysis methods have been developed for TomoSAR [11] to perform tomography inversion. These methods can be divided into three groups: (1) nonparametric spectral estimation [12; 13; 14], (2) parametric spectral estimation [15; 16; 17], and (3) compressive sensing (CS) [18; 19; 20; 21]. Each of the three groups of TomoSAR methods has itsrespective advantages and drawbacks. For instance, the nonparametric spectral estimators (e.g., beamforming [12; 13] and Capon [13; 14]) are robust to focusing artifacts but obtain a low height resolution. The parametric spectral estimators, such as the multiple signal classification (MUSIC) estimator [15], the maximum likelihood (ML) estimators [16], and the weighted subspace fitting (WSF) estimators [16; 17], can obtain a better height resolution than the nonparametric spectral estimators. On the other hand, in [22], the single-pass multi-baseline TomoSAR system has 3D resolution, including height-resolving ability in a single-pass platform because there are multiple channels in the cross-track direction. However, the Rayleigh resolution in the height direction is very limited due to the limited baseline length in a single-pass platform. To obtain larger baseline length for better height resolution, the concept of Multistatic SAR [23] was introduced to the TomoSAR research. Moreover, multistatic SAR systems have great application potential in high-resolution wide-swath imaging, moving target detection, interferometric altimetry, 3D/4D imaging, anti-interference, multi-level imaging, etc. Therefore, the concept of a spaceborne multistatic TomoSAR (SMS-TomoSAR) system was proposed. SMS-TomoSAR has multi-baseline, multi-temporal detection capabilities in spatial and temporal dimensions, which can further realize spatial resolution in the height direction, and small surface deformation measurement of the 3D ground scene (i.e., 3D/4D imaging). To date, very limited research has been reported on this aspect of SMS-TomoSAR. Further, a series of key technical issues, such as baseline optimization design, phase error compensation, and imaging processing, directly affect the performance of high-precision resolution imaging in the height direction of SMS-TomoSAR systems. In this paper, the multi-base multi-pass baselines of SMS-TomoSAR systems are considered equivalent to a group of multi-pass baselines of monostatic SAR. Secondly, the equivalent baselines are established as a symmetric-geometric model to characterize the non-uniform characteristics of baseline distribution. The model is centered on the main image, and baselines on both sides satisfy symmetric-geometric distribution. It is concluded that an approximately uniform baseline distribution has better SMS-TomoSAR imaging performance in the height direction. Further, a baseline design method under uniform-perturbation sampling with normal distribution error is proposed. The imaging performance of different levels of perturbation is compared, and the maximum baseline perturbation allowed by the system is given.