To model existing or future Low Earth Orbit (LEO) satellite networks with multiple constellations, we propose a simple analytical approach to represent the clustering of LEO satellites on orbits, based on a Cox point process. More precisely, we develop a variable-altitude Poisson orbit process that effectively captures the geometric fact that satellites are always positioned on orbits, and these orbits may vary in altitude. Conditioned on the orbit process, satellites situated on these orbits are modeled as Poisson point processes, thereby forming a Cox point process. For this model, we derive useful statistics, including the distribution of the distance to the nearest visible satellite, the outage probability, the Laplace functional of the proposed Cox satellite point process, and the Laplace transform of the interference from the Cox-distributed satellites under general fading. The derived statistics enable the evaluation of the performance of LEO satellite communication systems as functions of network parameters.

翻译：为模拟现有或未来具有多个星座的低地球轨道（LEO）卫星网络，我们提出一种基于Cox点过程的简单分析方法，以表征LEO卫星在轨道上的聚类特性。具体而言，我们发展了一种可变高度的泊松轨道过程，有效捕捉了卫星始终位于轨道上且轨道高度可能变化的几何事实。在给定轨道过程的条件下，这些轨道上的卫星被建模为泊松点过程，从而构成一个Cox点过程。针对该模型，我们推导了若干重要统计量，包括最近可见卫星的距离分布、中断概率、所提出的Cox卫星点过程的拉普拉斯泛函，以及在一般衰落条件下Cox分布卫星干扰的拉普拉斯变换。所推导的统计量可用于评估LEO卫星通信系统性能随网络参数变化的函数关系。