Outage Analysis of LEO Satellite Association Schemes Using Stochastic Geometry

This paper investigates the outage performance of large-scale low-Earth-orbit (LEO) satellite constellations using a stochastic-geometry framework. The ground-projected satellite distribution is modeled as a Poisson point process (PPP) that captures finite visibility and beam-hopping activity. Analytical outage expressions and approximations are developed under shadowed-Rician (SR) fading for two representative user–satellite association schemes: the optimal best-association rule and the practical nearest-association rule. For the latter, an Equivalent Integration Point (EIP) approximation is developed, replacing the outer serving-distance integral with a single evaluation at a representative distance, providing accurate yet tractable performance evaluation. Monte Carlo simulation results confirm the accuracy of the EIP approximation and demonstrate that nearest association offers a practical trade-off between reliability and selection complexity by requiring only distance information rather than instantaneous signal-to-interference ratio (SIR) evaluation.