Cox Point Processes for Multi-Altitude LEO Satellite Networks

We propose a simple analytical approach to describe the locations of low earth orbit (LEO) satellites based on a Cox point process. We develop a variable-altitude Poisson orbit process by accounting for the fact that satellites are always located on circular orbits and these orbits may have different altitudes. Then, the satellites on these orbits are modeled as the Poisson point processes conditionally on the orbit process. For this model, we derive the distribution of the distance to the nearest visible satellite, the outage probability, the Laplace functional of the proposed satellite Cox point process, and the Laplace transform of the interference under a general fading. The derived statistics allow one to evaluate the performance of such LEO satellite communication systems as functions of network parameters.