Bivariate Rician Shadowed Fading Model

In this paper we present a bivariate Rician shadowed fading model where the shadowing is assumed to follow a Nakagami-m distribution. We derive exact expressions involving a single integral for both the joint probability density function (PDF) and the joint cumulative distribution function and we also derive an exact closed-form expression for the moment generating function. As a direct consequence we obtain a closed-form expression for the power correlation coefficient between Rician shadowed variables as a function of the correlation coefficient between the underlying variables of the model. Additionally, in the particular case of integer m we show that the PDF can be expressed in closed form in terms of a sum of m Meijer G-functions of two variables. Results are applied to analyze the outage probability of a dual-branch selection combiner in correlated Rician shadowed fading and the evaluation of the level crossing rate and average fade duration of a sampled Rician shadowed fading envelope.