A Novel Analytical Model for LEO Satellite Constellations Leveraging Cox Point Processes

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.