A Fine Grained Stochastic Geometry-Based Analysis on LEO Satellite Communication Systems

Recently, stochastic geometry has been applied to provide tractable performance analysis for low earth orbit (LEO) satellite networks. However, existing works mainly focus on analyzing the “coverage probability”, which provides limited information. To provide more insights, this letter provides a more fine grained analysis on LEO satellite networks modeled by a homogeneous Poisson point process (HPPP). Specifically, the distribution and moments of the conditional coverage probability given the point process are studied. The developed analytical results can provide characterizations on LEO satellite networks, which are not available in existing literature, such as “user fairness” and “what fraction of users can achieve a given transmission reliability”. Simulation results are provided to verify the developed analysis. Numerical results show that, in a dense satellite network, it is beneficial to deploy satellites at low altitude, for the sake of both coverage probability and user fairness.

I. Introduction

Recently, deploying low earth orbit (LEO) satellite constellations to provide ubiquitous global connectivity is becoming an important enabling technique for 6G wireless communications [1]. Because LEO satellite constellations require a dense deployment of satellites, performance evaluation using computer simulations can be time-consuming but yeild limited insight. To address this challenge, emerging research is exploring the use of tools from stochastic geometry [2] to evaluate the performance of LEO satellite networks theoretically and provide a better understanding of their properties [3], [4], [5], [6], [7]. It is worth noting that existing research in this area typically focuses on metrics that reveal the average performance of the entire network, such as “the coverage probability”. However, many important properties of satellite communication networks remain unclear. For example, we may ask: i) how does a satellite network perform in terms of user fairness? ii) what fraction of users in the network can achieve certain link reliability?