Tractable Modeling and Performance Analysis of Low-Earth Orbit Satellite Constellations

In existing performance analysis of low-Earth orbit (LEO) satellite constellations, the poisson point process (PPP) is always used to model the satellite's distribution. However, in the actual LEO satellite constellations, satellites are incompletely random like PPP and exhibit a high degree of correlation with each other. In this article, to balance simplicity and accuracy, a tractable model based on spatial repulsion of LEO satellite constellations is derived to capture the correlation of satellites locations, which models a constraint angle $(\phi)$ for each satellite, and the coverage performance of the constellations is analyzed via stochastic geometry under shadowed-Rician fading. Specifically, the correlation between the location of satellites is modeled by a constraint angle to compensate for the performance mismatch based on the inherent nonrandom satellites distribution. Furthermore, the distance distribution of users to the satellite is derived under the spherical spatial repulsion model since the actual locations of satellites have a certain degree of regularity among them. In addition, the shadowed-Rician channel is used to model the propagation characteristics of satellite communication channels according to the shadowing condition of the signal on the propagation path. The results show that this model can closely capture the deployment of actual LEO satellite constellations, such as Walker-delta in terms of coverage probability. Overall, the work facilitates general performance analysis and planning of satellite constellations without network-specific orbital simulations and is time-consuming in space.