Modeling of joint rainfall rate and rain attenuation statistics using Archimedean Copula functions

In this paper the theory of Copula functions is used for the modeling of joint exceedance probability of rain rate on two points and rain attenuation on two links. Joint statistics of rain rate and rain attenuation are employed in order to evaluate and design site diversity systems operating at frequencies above 10 GHz. Copula functions are used in order to couple the single marginal distributions of dependent variables. In this paper, four Copula functions are investigated for the modeling of joint exceedance probability of rain attenuation and rain rate for different sites and various site separation distances. It is found that the error performance of these statistics shows that they are appropriate for modeling the joint exceedance probability of rain attenuation. However, for small separation distances, it seems that other Copulas shall be used such as the Gumbel-Hoogard. Finally, some useful conclusions are drawn.