Copula Function Parameter Regions in Analyzing Wireless Communications Performances

Abstract: Copula functions have been widely employed in wireless communication analysis to model dependence structures and evaluate system performance. However, existing studies generally express performance metrics in terms of copula dependence parameters without explicitly characterizing their admissible regions. This letter introduces the concept of copula dependence parameter regions and investigates its significance in wireless communications. Considering a two-user wireless multiple access channel (MAC) with correlated Rayleigh fading modeled by the bivariate Farlie--Gumbel--Morgenstern (FGM) copula, explicit parameter regions are derived from communication-theoretic and probabilistic perspectives using outage probability and Pearson correlation coefficient (PCC) constraints. The results show that practical communication and statistical requirements can significantly shrink the classical copula admissible interval, rendering some theoretically admissible dependence structures infeasible. Numerical examples illustrate the proposed concept and its practical implications.