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

Abstract

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.Index Terms-Copulas, site diversity, rain attenuation.

Measured and modeled spatial rain rate correlation to improve the prediction method for satellite site diversity

“…Craig [] deployed copula distributions for an analysis of clear‐air fading and enhancement on radio links and a recent paper by Kourogiorgas et al . [] actually tried some functions with interesting results.…”

“…One such approach seems to be what is called copula distributions, see, e.g., Schötzel and Friedrichs [2008] for an introduction. Craig [2007] deployed copula distributions for an analysis of clear-air fading and enhancement on radio links and a recent paper by Kourogiorgas et al [2014] actually tried some functions with interesting results.…”

Time diversity prediction modeling using Copula functions for satellite communication systems operating above 10GHz

“…Copula functions are used in order to couple the marginal distribution of dependent random variables aiming to model the joint statistics. Copula functions in propagation community have been very recently introduced in modeling the joint exceedance probability of rain attenuation for site diversity systems [15,16] with very successful results. More particularly, in [15], a primary investigation of the modeling of joint exceedance probability of rain rate and rain attenuation is conducted, showing the good accuracy of the use of copula functions, while in [16], a new model is proposed based on Copulas theory.…”

“…More particularly, in [15], a primary investigation of the modeling of joint exceedance probability of rain rate and rain attenuation is conducted, showing the good accuracy of the use of copula functions, while in [16], a new model is proposed based on Copulas theory. As pointed in [15,16], the advantage of Copulas theory, is that it does not make any assumption on a specific distribution for the first order statistics of rain attenuation and they can be described from the Copula function and the parameter, called dependence index, which quantifies the dependence between the random variables.…”

Μοντελοποίηση Καναλιού Και Αξιολόγηση Επίδοσης Ασύρματων Επίγειων Και Δορυφορικών Συστημάτων Επικοινωνιών Νέας Γενιάς Υψηλών Ταχυτήτων

“…The use of copula for modeling joint statistics of rain attenuation has been firstly used in [Kourogiorgas14a], [Livieratos14] for capturing the spatial dependence of rain attenuation and rain rate. Moreover, the study has been extended for temporal dependence and in particular for the joint statistics of rain attenuation for various time delays [Kourogriorgas14b].…”