[Paper Review] Coverage Analysis of LEO Satellite Downlink Networks: Orbit Geometry Dependent Approach

Junse Lee, Song Noh+2 more|arXiv (Cornell University)|Jun 19, 2022

Satellite Communication Systems4 citations

TL;DR

This paper proposes a novel analytical framework for coverage probability in LEO satellite downlink networks by modeling satellite locations as a one-dimensional Poisson point process on circular orbits, deriving the nearest-neighbor distance distribution based on orbit geometry (altitude, inclination), and characterizing coverage probability under small- and large-scale fading. The key contribution is a tractable, geometry-aware model that quantifies how orbital parameters directly influence network performance, validated via simulations and extended to multi-orbit systems with synergistic gains.

ABSTRACT

The low-earth-orbit (LEO) satellite network with mega-constellations can provide global coverage while supporting the high-data rates. The coverage performance of such a network is highly dependent on orbit geometry parameters, including satellite altitude and inclination angle. Traditionally, simulation-based coverage analysis dominates because of the lack of analytical approaches. This paper presents a novel systematic analysis framework for the LEO satellite network by highlighting orbit geometric parameters. Specifically, we assume that satellite locations are placed on a circular orbit according to a one-dimensional Poisson point process. Then, we derive the distribution of the nearest distance between the satellite and a fixed user's location on the Earth in terms of the orbit-geometry parameters. Leveraging this distribution, we characterize the coverage probability of the single-orbit LEO network as a function of the network geometric parameters in conjunction with small and large-scale fading effects. Finally, we extend our coverage analysis to multi-orbit networks and verify the synergistic gain of harnessing multi-orbit satellite networks in terms of the coverage probability. Simulation results are provided to validate the mathematical derivations and the accuracy of the proposed model.

Motivation & Objective

• To address the lack of analytical tools for LEO satellite network coverage by focusing on orbit geometry parameters such as altitude and inclination.
• To develop a tractable framework that models satellite locations as a one-dimensional Poisson point process on circular orbits.
• To derive the distribution of the nearest satellite distance to a fixed user based on orbital geometry.
• To characterize coverage probability as a function of geometric parameters and fading effects in single- and multi-orbit networks.
• To validate the model through simulations and demonstrate synergistic gains in multi-orbit configurations.

Proposed method

• Model satellite locations on a circular orbit using a one-dimensional Poisson point process with intensity λ.
• Derive the length of the visible satellite trajectory on the orbit using geometric analysis involving the Earth’s radius, orbit radius R, and minimum elevation angle.
• Define the visibility probability based on the satellite’s orbital inclination (θₙ) and the user’s location, using the arccosine of a geometric function η(R, θₙ, Rₐ).
• Establish the distribution of the nearest distance from a user to a satellite by integrating over the visible arc length and applying stochastic geometry principles.
• Compute the coverage probability by incorporating small-scale fading (e.g., Rayleigh) and large-scale path loss, using the derived distance distribution.
• Extend the analysis to multi-orbit networks by combining visibility and distance distributions across multiple orbital planes.

Experimental results

Research questions

• RQ1 How does the orbital inclination and altitude of LEO satellites affect the distribution of the nearest satellite distance to a fixed user on Earth?
• RQ2 What is the analytical expression for the coverage probability in a single-orbit LEO downlink network, considering both geometric parameters and fading effects?
• RQ3 How does the visibility probability of a satellite depend on the user’s geographic location and the orbital plane’s orientation?
• RQ4 What is the coverage gain from combining multiple orbital planes in a multi-orbit LEO network, and how does it depend on orbital geometry?
• RQ5 To what extent does the proposed geometry-dependent model match simulation results, and how accurate is it across varying orbital configurations?

Key findings

• The length of the visible satellite trajectory on an orbit is maximized when the orbital plane passes directly overhead (θₙ = π/2), confirming intuitive geometric expectations.
• The visible trajectory length decreases with increasing minimum elevation angle ω_min, as larger elevation angles reduce the visible spherical cap.
• The nearest-neighbor distance distribution is derived in closed form as a function of orbit radius R, inclination θₙ, and Earth radius R_E, enabling analytical coverage evaluation.
• Coverage probability is shown to be highly sensitive to orbital geometry, with optimal performance when the satellite orbit is aligned with the user’s zenith.
• The multi-orbit extension demonstrates synergistic gains in coverage probability, particularly when orbital planes are spaced to minimize blind spots.
• Simulation results confirm the accuracy of the analytical model across various orbital configurations and fading conditions.