## 1 Introduction  
Over the past 40 years, considerable attention has been paid to quantum key distribution (QKD) for its ability to realize unconditional secure communication between two legal users over insecure channels [1]. To date, QKD has been well explored in both theory and experiments in fiber links, and the time is ripe to begin transitioning toward a global quantum communications network [2]. However, point-to-point QKD via optical fiber succeeds only within a limited distance due to huge fiber losses, and the no-cloning theorem [3] leads to the inability to perfectly clone a quantum state. One solution to this problem is the use of quantum repeaters for a global network [4]. These repeaters divide the transmission path into several segments, where errors and losses are corrected using entanglement swapping and entanglement purification. Unfortunately, the realization of mature quantum repeaters remains a challenge due to factors such as quantum memory technology, the limited brightness of entanglement sources, and technological restrictions associated with distillation protocols. A promising solution with current technology is to build a satellite-mediated network, which connects widely separated ground stations using quantum satellites [5]. Although the quantum state suffers atmospheric attenuation, the feasibility of satellite-mediated QKD has been verified by several applications such as the _Micius_ quantum satellite in China [6]. This is because the layer around the Earth with a thickness of 20 km contains, on average, 95% of the total mass of the atmosphere, while above this layer is approximately a vacuum [7]. To date, most of the investigations into satellite-mediated QKD have been based on a discrete-variable (DV) protocol [8], which uses discrete quantum degrees of freedom to encode information, e.g., the polarization of a single photon. However, the entanglement of the DV protocol relies on probabilistic generation, which results in non-deterministic communication. Moreover, background noise due to sunlight presents a serious limitation for the achievable performance of the DV protocol, limiting most of the experiments obtained so far to nighttime [9]. Unlike the DV protocol, the continuous-variable (CV) protocol [10; 11; 12; 13], which can generate deterministic entanglement using off-the-shelf telecommunication components, offers effective resistance against background noise for all-day operation. This is because only the contribution of the background noise mode-matching with the local oscillator (LO) will survive in the output of the CV protocol [14; 15; 16; 17]. Additionally, the LO can be used as the frequency reference of the signal so that the CV protocol is not affected by the space-time curvature [18]. However, the achievable performance of the CV protocol is limited by finite entanglement [19], especially in a fading channel. To date, the longest transmission distance of fiber-based CV-QKD is 202.81 km [20], which is far from the goal of a global network. [PERSON] et al. discussed the evolution of bipartite Gaussian entanglement in a fading channel [21] and showed that Gaussian entanglement transmission is related to the probability distribution of transmittance (PDT). The transmittance fluctuation leads to the total arriving quantum state becoming a non-Gaussian mixture of Gaussian states. This non-Gaussian property introduces extra fading noise, which reduces the secret key rate. To suppress fading noise, [PERSON] et al. proposed a postselection method [22], which sets a transmittance threshold and then selects the data from the sub-channels above this threshold for data post-processing. Since the total state after postselection has high transmittance and a more Gaussian nature, the fading noise is reduced. The postselection method was extended to the satellite-mediated case in [23]; however, it needs to discard measurement data, which reduces the data size for parameter estimation and key generation.