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 paper 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, {\color{black}it is} beneficial to deploy satellites at low altitude, for the sake of both coverage probability and user fairness.

翻译：近期，随机几何被应用于低轨卫星网络的易处理性能分析。然而，现有研究主要关注“覆盖概率”的分析，所能提供的信息有限。为提供更深入的认识，本文对由齐次泊松点过程模型化的低轨卫星网络进行了更细粒度的分析。具体而言，研究了在给定点过程条件下条件覆盖概率的分布与矩。所提出的分析结果能够提供现有文献中尚未涉及的低轨卫星网络特性表征，例如“用户公平性”及“能够达到给定传输可靠性的用户比例”。为验证所提出的分析，提供了仿真结果。数值结果表明，在密集卫星网络中，为兼顾覆盖概率与用户公平性，将卫星部署于低轨道是有益的。