Space-Time Stochastic Rain Fading Channel for Multiple LEO or MEO Satellite Slant Paths

In this letter, a novel time series synthesizer of rain attenuation is proposed which incorporates the spatial correlation of rain attenuation for multiple Low Earth Orbit or Medium Earth Orbit (MEO) satellite links. The model is based on the multi-dimensional stochastic differential equations (SDEs) and it extends the well-known Maseng-Bakken model for multiple Earth-LEO or MEO satellite links. Analytical expressions, for the prediction of the joint exceedance probability of rain attenuation induced in LEO or MEO slant paths, are given. Moreover, multi-dimensional SDEs are proposed and the solution of the SDEs is used for the generation of time series of rain attenuation for spatially time-dependent correlated slant paths correlated in spatial domain. The synthesizer is validated with the theoretical expressions for the calculation of joint first order statistics of rain attenuation in various diversity schemes.