Low-earth orbit (LEO) satellite communication (SatCom) has emerged as a promising technology for improving wireless connectivity in global areas. Cell-free massive multiple-input multiple-output (CF-mMIMO), an architecture recently proposed for next-generation networks, has yet to be fully explored for LEO satellites. In this paper, we investigate the downlink performance of a CF-mMIMO LEO SatCom network, where many satellite access points (SAPs) simultaneously serve the corresponding ground user terminals (UTs). Using tools from stochastic geometry, we model the locations of SAPs and UTs on surfaces of concentric spheres using Poisson point processes (PPPs) and present expressions based on linear minimum-mean-square-error (LMMSE) channel estimation and conjugate beamforming. Then, we derive the coverage probabilities in both fading and non-fading scenarios, with significant system parameters such as the Nakagami fading parameter, number of UTs, number of SAPs, orbital altitude, and service range brought by the dome angle. Finally, the analytical model is verified by extensive Monte Carlo simulations. Simulation results show that stronger line-of-sight (LoS) effects and a more comprehensive service range of the UT bring higher coverage probability despite existing multi-user interference. Moreover, we found that there exist optimal numbers of UTs for different orbital altitudes and dome angles, which provides valuable system design insights.

翻译：低地球轨道（LEO）卫星通信已成为提升全球区域无线连接能力的前沿技术。大规模无蜂窝多输入多输出（CF-mMIMO）作为面向下一代网络提出的新型架构，其在LEO卫星场景中的应用潜力尚未得到充分探索。本文研究CF-mMIMO LEO卫星通信网络的下行链路性能，其中大量卫星接入点（SAP）协同服务对应的地面用户终端（UT）。基于随机几何理论，我们采用泊松点过程（PPP）对分布在同心球面上的SAP与UT位置进行建模，并给出基于线性最小均方误差（LMMSE）信道估计与共轭波束成形的解析表达式。随后，我们推导了衰落与非衰落场景下的覆盖概率，重点分析了Nakagami衰落参数、UT数量、SAP数量、轨道高度以及穹顶角所决定的服务范围等关键系统参数的影响。最终，通过大量蒙特卡洛仿真验证了理论模型的正确性。仿真结果表明：尽管存在多用户干扰，更强的视距（LoS）效应和更广的UT服务范围仍能带来更高的覆盖概率。此外，研究发现针对不同轨道高度与穹顶角存在最优UT数量，这为系统设计提供了重要参考依据。