Sum of correlated gamma variates with application to the performance of wireless systems over Nakagami channels

We extend the Moschopoulos representation for the probability density function (PDF) of the sum of independent gamma variates to the PDF of the sum of correlated gamma variates and provide an exact PDF-based approach for the performance analysis of many wireless communication systems over not necessarily independent identically distributed (i.i.d.) Nakagami fading channels. The key feature of this representation is that it is in the form of a single gamma series which implies that all the manipulations that can be performed for the i.i.d. case can now also be done for the non-i.i.d case. Aside from putting under the same umbrella many of the past results obtained via characteristic function (CF)-based approaches, the proposed PDF-based approach also allows the derivation of additional performance measures which are harder to analyze via CF-based approaches.