Cox Point Processes for Multi Altitude LEO Satellite Networks

TL;DR

This work addresses the challenge of modeling and analyzing multi-altitude LEO satellite networks with realistic orbital structure. It introduces an isotropic Cox point process formed by a Poisson orbit process on a radii cuboid, with satellites distributed as linear PPPs on each orbit; this yields tractable expressions for key metrics. The main contributions are closed-form-like characterizations of the distance to the nearest visible satellite, outage probability, the Laplace functional of the satellite process, and the Laplace transform of total interference under general fading, plus a Starlink 2A case study and comparisons to binomial models. The framework supports efficient evaluation of downlink performance and provides insights into how altitude distributions and constellation densities influence coverage in future multi-constellation LEO networks.

Abstract

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.

Figures (2)

• Figure 1: The proposed Cox satellite model with $r_a=7000$ km, $r_b=7050$ km. We use $\lambda=72$, $\mu=22$, and $\nu(\mathop{}\!\mathrm{d} \rho) = {\mathop{}\!\mathrm{d}\rho}/{(r_b-r_a)}$.
• Figure 2: The Cox-modeled satellite with $r_a=7000$ km and $r_b=7050$ km. We use $\lambda=25$, $\mu=100$, and $\nu(\mathop{}\!\mathrm{d} \rho) = {\mathop{}\!\mathrm{d}\rho}/{(r_b-r_a)}$.

Theorems & Definitions (4)

• Lemma 1
• Lemma 2
• Lemma 3
• Lemma 4