Ergodic Capacity Analysis for Terrestrial-LEO-GEO Relay Systems With Stochastic Orbit Modeling

This paper investigates an uplink transmission from a terrestrial user to a geostationary Earth orbit (GEO) satellite, using multiple low Earth orbit (LEO) satellites as amplify-and-forward (AF) relays. We first model the altitudes of LEO spherical orbits as a one-dimensional stochastic point process, where multiple satellites are randomly and uniformly distributed along each orbit. Then, we derive an approximate expression for the ergodic capacity by introducing a novel stochastic geometry-based analytical approach, which effectively captures the impact of random satellite distributions on system performance. Using this approximation method, we also derive the ergodic capacity accounting for the one-dimensional Poisson point process (PPP) and the terrestrial-satellite channel modelled with Rician-shadowed fading. Finally, the accuracy of the derived expressions is validated through Monte Carlo simulations, and the results further confirm that the one-dimensional PPP can accurately approximate the delivery performance even when a reasonable minimum inter-orbit distance for LEO satellites is considered.