Copula Models for Wireless Fading and their Impact on Wireless Diversity Combining

Copulas are multivariate joint distributions of random variables with uniform marginal distributions. They have become increasingly important in statistical models in which the dependence structures cannot be simply described in terms of the classical Pearson correlation coefficient. In contrast to normal- copula fading, more general models can describe asymmetric and other nonlinear tail dependence. We introduce the concept of copula modeling to multivariate fading distribution theory. We use the Clayton copula to illustrate new fading dependence structures, still with Rayleigh or Nakagami marginals, that have strong dependence for small values. Not surprisingly, this results in a loss in performance as compared to classical fading models, even though both have the same correlation coefficient. Since most correlated fading models beyond the Rayleigh-Rice are presented without strong physical models, this suggests that wider class models are important. Copula-based models are the most general statistical models of multivariate data, and they are uniquely defined for any continuous multivariate random variable.