# Reconstruction of Rainfall Field Using Earth-Space Links Network: A Compressed Sensing Approach
## 1 Introduction
A corresponding ESL in the Ka band is better for retrieval of light rainfall because the microwave signal is more affected by the rainfall at higher frequencies, but it is also important not to ignore the effect of other factors in the atmosphere [15]. Furthermore, a large number of communication satellites are forming networks above the Earth with the rapid development of the satellite Internet of Things, such as the Starlink satellite constellation of SpaceX, which provides the opportunity to use multiple ESL de-networks to reconstruct the high-precision rainfall fields in the area [19; 20; 21; 22; 23]. In terms of the research on reconstructing rainfall fields with ESL networks, it is crucial to find an algorithm that enables the reconstruction of a rainfall field with high accuracy based on the actual distribution of ESL networks. Moreover, the CT technique, the IDW algorithm and Kriging interpolation have been successively used to reconstruct rainfall fields using multiple ESLs as verified by simulation experiments [19; 20; 23]. The results of these studies validate the feasibility of reconstructing rainfall fields by ESL networks and further demonstrate the great potential of the method for monitoring rainfall over large areas. Previous studies on reconstructing rainfall fields using multiple ESLs are mainly theoretical validations based on simulations and have not considered the effect of the density and structural distribution of the actual ESL [20; 23]. Moreover, the use of general spatial interpolation algorithms (e.g., IDW and Kriging interpolation) and CT techniques to reconstruct rainfall fields has high requirements regarding the density and topology of the links network. As a matter of fact, the distribution of satellite antennas on the ground, the sparsity of the links and the accuracy of the reconstruction results are all important and need to be taken into account when reconstructing rainfall fields using ESL networks. In view of the superior spatial reconstruction performance of the compressed sensing (CS) method in other fields in the case of sparse sampling [24; 25], we propose the use of CS to reconstruct high-precision rainfall fields based on the sparse density distribution of the ESL network in this paper. Firstly, the ESL networks with different densities conforming to the CS principle have been designed in Jiangning district, Nanjing, based on the spatial clustering algorithm. The real rainfall fields in the area are then reconstructed using the ESL networks with CS, and the reconstructed results are compared with those of the IDW algorithm, so as to validate the performance of the method. The major contributions in this article are as follows:  
1. The spatial clustering algorithm has been used to design the ESL network conforming to the CS principle, and the effect of the distribution of ESL on reconstructing the rainfall fields has been studied. 2. The CS technique has been used for reconstructing rainfall fields using an ESL network, and the results show that an ESL network with CS is able to reconstruct high-precision rainfall fields under sparse sampling. The rest of this paper is organized as follows. Section 2 describes the principles of retrieving rainfall by ESL and the methods for reconstructing rainfall fields using the ESL network with CS. Section 3 provides a simulated design for the ESL networks. The performance of reconstructing the real rainfall fields using the designed ESL networks with CS is presented in Section 4. Finally, the conclusions to the paper are given in Section 5.