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arXiv 2307.03343cs.ITcs.SYeess.SPeess.SYmath.IT
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具有随机高度的球面点过程:下行链路卫星网络建模与分析的新方法

Spherical Point Process with Random Heights: New Approach for Modeling and Analysis of Downlink Satellite Networks

Seyong Kim, Jinseok Choi, Namyoon Lee, François Baccelli, Jeonghun Park

AI总结:

本文提出基于三维泊松点过程的随机高度模型(RHM),通过在名义壳层引入随机径向位移来捕捉不同高度分布,推导了下行链路覆盖概率解析表达式,为分析大规模LEO立体星座网络性能提供了准确工具。

摘要:

低地球轨道(LEO)卫星产业正经历快速扩张,由于管辖轨道权利的先到先得原则,运营商竞相发射卫星。这促成了日益大规模的立体星座的形成,其中卫星在多种不同高度上运行。为了满足分析此类复杂网络的需求,本文利用三维泊松点过程(PPP)为 LEO 星座建立了一个新的分析框架。具体而言,我们引入了一个随机高度模型(RHM),通过对名义壳层上由均匀 PPP 生成的点应用随机径向位移,该模型能够捕捉各种高度分布。在此基础上,我们推导出了下行链路覆盖概率的解析表达式。为了论证我们的模型,我们展示了包括 Starlink 在内的几个主要卫星星座的高度分布与我们的模型假设相一致。随后,我们通过蒙特卡洛模拟证明,我们 RHM 的覆盖概率与这些现实世界网络的覆盖概率高度吻合。最后,我们通过证明解析表达式与模拟结果相一致,确认了解析表达式的准确性。因此,我们的工作为理解和预测卫星高度的统计分布如何影响网络性能提供了一个强大的工具。

英文摘要:

The Low Earth Orbit (LEO) satellite industry is undergoing rapid expansion, with operators competitively launching satellites due to the first-come, first-served principle governing orbital rights. This has led to the formation of increasingly large-scale, volumetric constellation where satellites operate across a diverse range of altitudes. To address the need for analyzing such complex networks, this paper establishes a new analytical framework for LEO constellations by leveraging a 3D Poisson point process (PPP). Specifically, we introduce a random height model (RHM) that can capture various altitude distributions by applying a random radial displacement to points generated by a homogeneous PPP on a nominal shell. Building on this, we derive an analytical expression for the downlink coverage probability. To motivate our model, we show that the altitude distributions of several leading satellite constellations, including Starlink, align with our model's assumptions. We then demonstrate through Monte Carlo simulations that the coverage probability of our RHM closely matches that of these real-world networks. Finally, we confirm the accuracy of our analytical expressions by showing their agreement with simulation results. Our work thereby provides a powerful tool for understanding and predict how the statistical distribution of satellite altitudes impacts network performance.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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