## 1 Introduction  
As a common weather phenomenon in the atmosphere, rainfall is closely related to human life [1]. When the distribution of rainfall in space and time is abnormal, natural disasters, such as floods and mudslides, can occur and cause life-threatening and significant economic losses to humans. In addition, the abnormal variation in rainfall reflects changes in climate [2]. Therefore, real-time and accurate monitoring of rainfall is of great significance to ensure the normal operation of society and to promote the research of atmospheric sounding science, especially the retrieval of spatial distribution of rainfall on a large scale with high accuracy and high spatial and temporal resolution [3, 4]. At present, the main instruments used to measure rainfall are rain gauges, weather radars and meteorological satellites [5]. The rainfall measured by the rain gauge represents the rainfall information of the meteorological station, which cannot reflect the rainfall information of other locations outside the station because of the uneven distribution of rainfall in space [6, 7]. Weather radar often obtains the echoes of cloud and parts of the precipitation in the atmosphere, which is significantly different from the rainfall on the surface [8]. Moreover, the meteorological rain satellite can retrieve the spatial distribution of a wide range of rainfall, but its spatial resolution is very low because of the long detection distance [9]. The use of a large number of rain gauges and weather radars to form a high-density meteorological observation network enables the acquisition on the distribution of rainfall over a large area with high precision and high temporal and spatial resolution [6; 10]. However, the current distribution of rain gauges and weather radars in different regions is uneven, limited by complex maintenance technology and high cost. In particular, the distribution is more sparse in remote areas [11]. Therefore, the proposal of advanced rainfall detection methods to supplement the existing detection instruments to obtain better rainfall information is still a widely undertaken research topic in recent years. With the rapid development of communication technology, a new method of retrieving rainfall by using the attenuation caused by rainfall on microwave communication links widely distributed in space has been proposed in recent years, and it has received widespread attention [12; 13; 14; 15]. Compared with traditional rainfall measurement methods, the denser distribution of microwave links promises to enable the retrieval of rainfall over large areas. Additionally, directly using the microwave links of the existing communication base stations for rainfall retrieval does not entail too much cost, so it has the advantage of low cost [16; 17]. First of all, [PERSON] et al. [12] conducted an experiment to retrieve rainfall using microwave links in commercial cellular networks in 2006. Additionally, the experimental results showed that the performance of microwave links for rainfall measurement was better than weather radar and showed the preliminary potential of using microwave links for rainfall measurement. Then, some scholars optimized the calculation model of retrieving rainfall through the accurate modeling of microwave propagation in the atmosphere, so as to further improve the accuracy of this method [17; 18; 19; 20]. Moreover, the technology of retrieving rainfall using microwave link is also applied to radar parameter calibration, precipitation classification and raindrop size distribution (DSD) inversion [21; 22]. In addition, with the rapid development of the internet of things technology and 5G communication networks, the distribution of microwave links is becoming denser and denser [19; 23]. A growing number of studies began to focus on using widely distributed horizontal microwave links (HMLs) to retrieve rainfall fields that represent the spatial distribution of rain rates in the area [24; 25].