On the Correlated $K$ -Distribution With Arbitrary Fading Parameters

The correlated bivariate K-distribution with arbitrary and not necessarily identical parameters is introduced and analyzed. Novel infinite series expressions for the joint probability density function and moments are derived for the general case where the associated bivariate distributions, i.e., Rayleigh and gamma, are both arbitrary correlated. These expressions generalize previously known analytical results obtained for identical parameter cases. Furthermore, considering independent gamma distributions, the cumulative distribution and characteristic functions are analytically obtained. Although the derived expressions can be used in a wide range of applications, this letter focuses on the performance analysis of dual branch diversity receivers. Specifically, the outage performance of dual selection diversity receivers operating over correlated K fading/shadowing channels is analytically evaluated. Moreover, for low normalized outage threshold values, closed-form expressions are obtained.