A 3-D Correlated Blockage Model for Satellite Networks

Integrating Low Earth Orbit (LEO) satellite Internet into the 6G system to realize ubiquitous global coverage is a key objective of this imminent system. Due to the inherent randomness of satellite locations, stochastic geometry has emerged as a popular analytical methodology to provide an efficient alternative to network simulations for deriving statistical performance metrics. Although satellites or ground users are modeled as random processes, the majority of papers in literature have employed propagation channels based on general shadowing or independent blockage situations for urban or suburban areas. Consequently, the impacts of blockage spatial correlation, induced by the physical dimensions (e.g., height, width, and thickness) on satellite link performance remain poorly understood. In this paper, we propose a novel three-dimensional (3D) cascade blockage structure and a functional framework to tackle this issue. Under the virtual satellite association strategy, two iterative functional equations in both azimuth and elevation domains are proposed to evaluate coverage performance in 3D correlated environments. For the real satellite association, a location index matrix is introduced to determine the serving node with minimum elevation angle in the orbital sphere. Then, a set of iterative functional equations are proposed to derive the association and coverage probabilities. Numerical simulations validate our analytical framework and quantify the impact of spatial correlation on coverage performance. This study provides guidelines for deploying future dense LEO constellations in correlated blockage environments for both satellite-only and hybrid networks.