This work develops an analytical framework for downlink Low Earth Orbit (LEO) satellite communications, leveraging tools from stochastic geometry. We propose a tractable approach to the analysis of such satellite communication systems, accounting for the fact that satellites are located on circular orbits. We accurately incorporate this geometric property of LEO satellite constellations by developing a Cox point process model that jointly produces orbits and satellites on these orbits. Our work contrasts with previous modeling studies that presumed satellite locations to be entirely random, thereby overlooking the fundamental fact that satellites are exclusively positioned on orbits. Employing this new Cox model, we analyze the network performance experienced by users anywhere on Earth. Specifically, we evaluate the no-satellite probability of the proposed network and the signal-to-interference-plus-noise ratio (SINR) distribution, or the coverage probability. By presenting fundamental network performance as functions of network key parameters, this work allows one to assess the statistical properties of downlink LEO satellite communications and can thus be used as a system-level design tool to operate, design, and optimize forthcoming complex LEO satellite networks.

翻译：本文利用随机几何工具，提出了一种面向低轨卫星下行链路通信的分析框架。我们建立了一种可处理的卫星通信系统分析方法，充分考虑了卫星位于圆形轨道上的几何特性。通过构建能够联合生成轨道及其上卫星的Cox点过程模型，我们精确地刻画了低轨卫星星座的这一几何特征。与以往将卫星位置视为完全随机、从而忽略卫星仅位于轨道上这一基本事实的建模研究不同，本文采用这一新型Cox模型，分析了地球上任意位置用户的网络性能。具体而言，我们评估了所提网络的无卫星概率、信号干扰加噪声比（SINR）分布即覆盖概率。通过将基础网络性能表示为网络关键参数的函数，本文能够评估低轨卫星下行链路通信的统计特性，可作为系统级设计工具，用于运营、设计和优化未来复杂的低轨卫星网络。