On Rain Attenuation Time Series Generation: A New Simple Copula-based Channel Model for Satellite Slant Paths

The use of copulas decreases and almost vanishes the dependence of stochastic synthesizers from theoretical distributions, since empirical distributions can also be used. Therefore, in this correspondence, a novel rain attenuation time series synthesizer based on a Gaussian copula function is proposed. First, the Gaussian copula is tested for the modeling of joint exceedance probability of rain attenuation on a temporal domain with good results. Afterward, taking an advantage of the results from the previous tests, two expressions are proposed for the modeling of the Gaussian copula parameter as a function of time for the temperate and tropical regions. These expressions may be refined using more experimental beacon data in various climatic regions and for different satellite link characteristics. The synthesizer is based on the generation of time series from copula functions. It reproduces the first-order statistics and it is independent of the distribution that may describe well the rain attenuation used as input. The synthesizer is validated on the first-order statistics, for no time delay and with time delay and on the second-order statistics.