A Novel Analytical Model for LEO and MEO Satellite Networks based on Cox Point Processes

TL;DR

The paper develops an isotropic Cox point process to model LEO/MEO satellite networks by jointly generating orbits and satellites on those orbits, capturing essential orbital geometry with two parameters: the mean number of orbits $\lambda$ and the mean satellites per orbit $\mu$. It derives tractable expressions for the no-satellite probability, the distance to the nearest satellite, and the downlink coverage probability under Nakagami-$m$ fading, leveraging isotropy to obtain closed-form or semi-closed forms and validating them via simulation. The framework enables system-level design and optimization by relating performance metrics to deployment choices (orbit count, satellite density per orbit, altitude, and antenna gains) and can approximate forthcoming constellations through moment matching. The model also supports extensions to non-isotropic orbits and direct orbit representations for regularly spaced constellations, offering a flexible, analytically tractable tool for evaluating large-scale satellite networks.

Abstract

This work develops an analytical framework for downlink low Earth orbit (LEO) or medium Earth orbit (MEO) satellite communications, leveraging tools from stochastic geometry. We propose a tractable approach to the analysis of such satellite communication systems, accounting for the fact that satellites are located on circular orbits. We accurately incorporate this geometric property of LEO or MEO satellite constellations by developing a Cox point process model that jointly produces orbits and satellites on these orbits. Our work contrasts with previous modeling studies that presumed satellite locations to be entirely random, thereby overlooking the fundamental fact that satellites are jointly positioned on orbits. Employing this Cox model, we analyze the network performance experienced by users located on Earth. Specifically, we evaluate the no-satellite probability of the proposed network and the Laplace transform of the interference created by such a network. Using it, we compute its SIR (signal-to-interference) distribution, namely its coverage probability. By presenting fundamental network performance as functions of key parameters, this model allows one to assess the statistical properties of downlink LEO or MEO satellite communications and can thus be used as a system-level design tool to operate and optimize forthcoming complex LEO or MEO satellite networks.

Figures (15)

• Figure 1: Let $A$ be the ascending/descending point. The longitude $\theta$ is the angle that $\overline{OA}$ makes with the $x$-axis. The inclination $\phi$ is the angle that the orbital plane makes with the reference plane. $\omega$ is the angle that the $\overline{OX}$ makes with $\overline{OA}.$
• Figure 2: The proposed model with $\lambda = 30$, $\mu = 40$, and $r_s = 7000 \text{ km}$.
• Figure 3: The proposed model with $\lambda = 28$, $\mu = 120$, and $r_s = 7000 \text{ km}$.
• Figure 4: The no-satellite probability. The satellite altitude is $550$ km. Simulation results validates the derived formula.
• Figure 5: The no-satellite probability. The satellite altitude is $550$ km. Simulation results validates the derived formula.

Theorems & Definitions (11)

• Theorem 1
• Remark 1
• Lemma 1
• Remark 2
• Proposition 1
• Theorem 2
• Theorem 3
• Theorem 4
• Remark 3
• Corollary 1