In this paper, we investigate the performance of large-scale heterogeneous low Earth orbit (LEO) satellite networks in the context of three association schemes. In contrast to existing studies, where single-tier LEO satellite-based network deployments are considered, the developed framework captures the heterogeneous nature of real-world satellite network deployments. More specifically, we propose an analytical framework to evaluate the performance of multi-tier LEO satellite-based networks, where the locations of LEO satellites are approximated as points of independent Poisson point processes, with different density, transmit power, and altitude. We propose three association schemes for the considered network topology based on: 1) the Euclidean distance, 2) the average received power, and 3) a random selection. By using stochastic geometry tools, analytical expressions for the association probability, the downlink coverage probability, as well as the spectral efficiency are derived for each association scheme, where the interference is considered. Moreover, we assess the achieved network performance under several different fading environments, including low, typical, and severe fading conditions, namely non-fading, shadowed-Rician and Rayleigh fading channels, respectively. Our results reveal the impact of fading channels on the coverage probability, and illustrate that the average power-based association scheme outperforms in terms of achieved coverage and spectral efficiency performance against the other two association policies. Furthermore, we highlight the impact of the proposed association schemes and the network topology on the optimal number of LEO satellites, providing guidance for the planning of multi-tier LEO satellite-based networks in order to enhance network performance.

翻译：本文研究了三种关联方案下大规模异构低轨（LEO）卫星网络的性能。与现有研究仅考虑单层LEO卫星网络部署不同，本文提出的分析框架捕捉了真实卫星网络部署的异构特性。具体而言，我们建立了一个分析框架来评估多层LEO卫星网络的性能，其中LEO卫星的位置被近似为独立泊松点过程的点集，并具有不同的密度、发射功率和轨道高度。针对所考虑的拓扑结构，我们提出三种基于以下原则的关联方案：1）欧氏距离；2）平均接收功率；3）随机选择。利用随机几何工具，推导了每种关联方案在考虑干扰情况下的关联概率、下行覆盖概率及频谱效率的解析表达式。此外，我们评估了网络在多种衰落环境下的性能，包括低、典型和严重衰落条件，分别为无衰落、阴影莱斯衰落和瑞利衰落信道。研究结果揭示了衰落信道对覆盖概率的影响，并表明基于平均功率的关联方案在覆盖性能和频谱效率方面优于其他两种关联策略。进一步地，我们阐明了所提关联方案与网络拓扑对LEO卫星最优数量的影响，为增强网络性能的多层LEO卫星网络规划提供了指导。