To model existing or future low Earth orbit (LEO) satellite networks leveraging multiple constellations, we propose a simple analytical approach to represent the clustering of satellites on orbits. 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. Conditionally on the orbit process, satellites situated on these orbits are modeled as linear Poisson point processes, thereby forming a Cox point process. For this model, we derive useful statistics, including the distribution of the distance from the typical user to its nearest visible satellite, the outage probability, the Laplace functional of the proposed Cox satellite point process, and the Laplace transform of the interference power from the Cox-distributed satellites under general fading. The derived statistics enable the evaluation of the performance of such LEO satellite communication systems as functions of network parameters.

翻译：为建模利用多个星座的现有或未来低地球轨道（LEO）卫星网络，我们提出一种简单的解析方法来表征卫星在轨道上的聚类特性。具体而言，我们构建了一种可变高度的泊松轨道过程，该过程有效捕捉了卫星始终定位于轨道且轨道高度可变的几何事实。在给定轨道过程的条件下，位于这些轨道上的卫星被建模为线性泊松点过程，从而形成Cox点过程。针对该模型，我们推导了若干重要统计量，包括典型用户到其最近可见卫星的距离分布、中断概率、所提Cox卫星点过程的拉普拉斯泛函，以及一般衰落条件下Cox分布卫星产生干扰功率的拉普拉斯变换。这些推导的统计量使得此类LEO卫星通信系统的性能评估可表示为网络参数的函数。