On the Linear Combination of Gamma Conditionally Gaussian Distributions with Application to Decode and Forward Cooperation

In this paper, exact statistics for the linear combination of gamma conditionally Gaussian random variables (CGRVs) are obtained. In particular, the probability density function (PDF), the cumulative distribution function (CDF) and the moment generating function (MGF) are derived. Closed form expressions are obtained for both integer and noninteger parameters, using the Mellin-Barnes integral representation of the extended Fox-(H) over cap function. The significance of these results is then explained by obtaining performance metrics for decode and forward (DF) cooperation in Nakagami-m fading