Copulas for statistical signal processing (Part II): Simulation, optimal selection and practical applications

• Algorithms proposed for generating random variables for exponential/Rayleigh/Weibull, Nakagami-m and Rician copulas where any desired copula parameter(s) are allowed.
• Novel optimal copula selection is proposed, based on mutual information measurement between the copula and the corresponding bivariate distribution.
• Case studies are presented to validate the efficacy of copulas, including dual branch selection combining diversity in communication applications.

This paper presents algorithms for generating random variables for exponential/Rayleigh/Weibull, Nakagami-m and Rician copulas with any desired copula parameter(s), using the direct conditional cumulative distribution function method and the complex Gaussian distribution method. Moreover, a novel method for optimal copula selection is also proposed, based on the criterion that for a given series of copulas, the optimal copula will have its copula density based mutual information closest to the corresponding bivariate distribution based mutual information. The corresponding bivariate distribution is the bivariate distribution that is used to derive this copula. Akaike information criterion (AIC) and Bayes’ information criterion (BIC) are compared with the proposed mutual information based criterion for optimal copula selection. In addition, several case studies are also presented to further validate the effectiveness of the copulas, which include dual branch selection combining diversity using Nakagami-m, exponential/Rayleigh/Weibull and Rician copulas with different marginal distributions as in real applications.