## 1 Introduction  
Understanding the role of clouds is of great importance in many areas such as numerical weather prediction and climate studies, as clouds are not only vital in the hydrological cycle, but also crucial for the Earth's radiation budget. Various instruments have been developed and deployed, such as microwave radiometers, cloud radars and lidars, to measure cloud liquid water content (LWC) on a fine scale [1]. However, due to the high cost and scarce distribution of such instruments, the real-time global seamless high-resolution observation of clouds is still a challenge. In this paper, we propose a novel cloud estimation approach as an auxiliary means to traditional methods, in which the attenuation of low Earth orbit (LEO) satellite microwave links is used to measure the LWC in clouds. Currently, the number of active LEO satellites in space is well above 1000, and several companies are pursuing the proposal for large constellations of LEO satellites to provide global broadband access, e.g., OneWeb's system with 720 LEO satellites for global coverage and SpaceX's system with more than 4000 LEO satellites [2]. Once this service is available to the public, it can be foreseen that millions of user terminals (ground receivers) will be deployed across the globe. Because of the high demand for bandwidth, Ku-band (12-18 GHz) and Ka-band (26.5-40 GHz) are usually used for downlink and uplink. These links are sensitive to the water content in the atmosphere. Essentially, the communication links between the satellites and the user terminals maintain a very large sensor network that could provide off-the-shelf attenuation data for the purpose of atmospheric observations. The hypothesis of using LEO satellite microwave links for atmospheric measurements was first proposed in 2016 [3], where moving microwave links were used to achieve rain field estimations. Similar to the motion of the signal source in computed tomography (CT) [4], the orbital motions of the LEO satellites make it possible to perform tomographic reconstruction of rain fields. Various investigations have been carried out recently. For example, it has been shown that vertical rain fields can be reconstructed from the received signal level measurements of multiple receivers [5]. Furthermore, the approach of using the estimated signal-to-noise ratio (SNR) at the ground receivers for LEO satellites to achieve three-dimensional (3-D) tomographic rain field reconstruction has been analyzed in detail [6]. The focus of this paper is on using LEO satellite-to-ground signal links for cloud measurements. The same system model used for rain field retrieval [6] is employed for retrieving the attenuation field caused by nonprecipitating clouds. Although the attenuation induced by clouds is usually considerably less than that induced by rain, it is still significant enough in signal power measurements. For instance, for a LWC of 1 g/m\({}^{3}\), the specific attenuation at 30 GHz is about 0.88 dB/km [7]. This indicates that accurate LWC measurements can be achieved through accurately measured signal attenuations. The first objective of this study is to confirm that the SNR estimations at the ground receivers, subject to noise and estimation errors, can be used to retrieve cloud LWC induced attenuation fields through tomographic techniques. The second objective is to extend and refine previous studies on rain field retrieval [6], by introducing different basis functions to define the target attenuation field. Moreover, to cope with the sky noise induced by rain or cloud LWC, a reduced-complexity method of post-processing with a piecewise linear function is proposed and compared with the existing iterative approach [6]. This study only addresses cloud liquid water, and solid particles such as ice crystals and snow are not considered as they have minimal effects on the attenuation of microwave signals around 30 GHz [8].