Although a significant number satellites are deemed essential for facilitating diverse applications of satellite networks, aerial platforms are emerging as excellent alternatives for enabling reliable communications with fewer satellites. In scenarios with sparse satellite networks, aerial platforms participate in downlink communications, serving effectively as relays and providing comparable or even superior coverage compared to a large number of satellites. This paper explores the role of aerial platforms in assisting downlink communications, emphasizing their potential as an alternative to dense satellite networks. Firstly, we account for the space-time interconnected movement of satellites in orbits by establishing a stochastic geometry framework based on an isotropic satellite Cox point process. Using this model, we evaluate space-and-time performance metrics such as the number of orbits, the number of communicable satellites, and the connectivity probability, primarily assessing the geometric impact of aerial platforms. Subsequently, we analyze signal-to-noise ratio (SNR) coverage probability, end-to-end throughput, and association delay. Through examination of these performance metrics, we explicitly demonstrate how aerial platforms enhance downlink communications by improving various key network performance metrics that would have been achieved only by many satellites, thereby assessing their potential as an excellent alternative to dense satellite networks.

翻译：尽管大量卫星被认为是实现卫星网络多样化应用的必要条件，但空中平台正逐渐成为在卫星数量较少情况下实现可靠通信的卓越替代方案。在稀疏卫星网络场景中，空中平台参与下行通信，有效充当中继节点，并能提供与大量卫星相当甚至更优的覆盖性能。本文探讨了空中平台在辅助下行通信中的作用，重点论证其作为密集卫星网络替代方案的潜力。首先，我们通过建立基于各向同性卫星考克斯点过程的随机几何框架，对卫星在轨道中的时空互联运动进行建模。利用该模型，我们评估了轨道数量、可通信卫星数量及连通概率等时空性能指标，重点分析了空中平台的几何影响。随后，我们分析了信噪比覆盖概率、端到端吞吐量及关联时延等通信性能。通过对这些性能指标的考察，我们明确论证了空中平台如何通过提升原本需大量卫星才能实现的各项关键网络性能指标来增强下行通信，从而评估其作为密集卫星网络优质替代方案的潜力。