As the number of low Earth orbit (LEO) satellites rapidly increases, the consideration of frequency sharing or cooperation between geosynchronous Earth orbit (GEO) and LEO satellites is gaining attention. In this paper, we consider a hybrid GEO-LEO satellite network where GEO and LEO satellites are distributed according to independent Poisson point processes (PPPs) and share the same frequency resources. Based on the properties of PPPs, we first analyze satellite-visible probabilities, distance distributions, and association probabilities. Then, we derive an analytical expression for the network's coverage probability. Through Monte Carlo simulations, we verify the analytical results and demonstrate the impact of system parameters on coverage performance. The analytical results effectively estimate the coverage performance in scenarios where GEO and LEO satellites cooperate or share the same resource.

翻译：随着低地球轨道（LEO）卫星数量的快速增长，地球同步轨道（GEO）与LEO卫星之间的频谱共享或协同合作日益受到关注。本文研究一种混合GEO-LEO卫星网络，其中GEO与LEO卫星依据独立的泊松点过程（PPPs）分布，并共享相同频段资源。基于泊松点过程的性质，我们首先分析了卫星可见概率、距离分布及关联概率。随后，推导出网络覆盖概率的解析表达式。通过蒙特卡洛仿真，验证了理论分析结果，并展示了系统参数对覆盖性能的影响。该分析结果可有效评估GEO与LEO卫星协同合作或共享资源场景下的覆盖性能。