Achieving seamless global coverage is one of the ultimate goals of space-air-ground integrated network, as a part of which High Altitude Platform (HAP) network can provide wide-area coverage. However, deploying a large number of HAPs will lead to severe congestion of existing frequency bands. Spectrum sharing improves spectrum utilization. The coverage performance improvement and interference caused by spectrum sharing need to be investigated. To this end, this paper analyzes the performance of spectrum sharing between HAP network and terrestrial network. We firstly generalize the Poisson Point Process (PPP) to curves, surfaces and manifolds to model the distribution of terrestrial Base Stations (BSs) and HAPs. Then, the closed-form expressions for coverage probability of HAP network and terrestrial network are derived based on differential geometry and stochastic geometry. We verify the accuracy of closed-form expressions by Monte Carlo simulation. The results show that HAP network has less interference to terrestrial network. Low height and suitable deployment density can improve the coverage probability and transmission capacity of HAP network.

翻译：实现无缝全球覆盖是空天地一体化网络的最终目标之一，其中高空平台（HAP）网络可提供广域覆盖。然而，部署大量HAP将导致现有频段的严重拥塞。频谱共享可提升频谱利用率，但需要研究频谱共享带来的覆盖性能提升与干扰问题。为此，本文分析了HAP网络与地面网络之间的频谱共享性能。我们首先将泊松点过程（PPP）推广至曲线、曲面和流形，以建模地面基站（BS）和HAP的分布。随后，基于微分几何与随机几何理论，推导了HAP网络与地面网络覆盖概率的闭式表达式。通过蒙特卡洛仿真验证了闭式表达的准确性。结果表明，HAP网络对地面网络的干扰较小。适当降低高度并优化部署密度，可提升HAP网络的覆盖概率与传输容量。