Cox Point Processes for Multi-Altitude LEO Satellite Networks

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.