Doppler Shift Distribution in Satellite Constellations

Doppler shift has significant implications in Low Earth Orbit (LEO) constellations due to the rapid relative movement of satellites. This letter presents a novel approach based on stochastic geometry to capture the statistical distribution of Doppler shift in modern mega satellite constellations. We derive a simplified expression for both the Doppler shift s-curve and its maximum value, highlighting the dependency of Doppler shifts on the zenith angle of the closest approach during a satellite pass. Additionally, we present a stochastic model for the distribution of these zenith angles within the random constellation model. Furthermore, the statistical distribution of the Doppler bound is analytically formulated and validated through extensive Monte Carlo simulations for two major satellite constellations currently in orbit.