On the MGF and BER of Linear Diversity Schemes in Nakagami Fading Channels with Arbitrary Parameters

In this paper, we explore the relationship between the Lauricella hypergeometric functions (F_A, F_B, and F_D) and the performances of linear diversity combining schemes in Nakagami fading channels with arbitrary parameters. We consider maximal ratio combining, selection combining, and equal gain combining of an arbitrary number of independent Nakagami faded diversity branches. Specifically, we show that the moment generating function and the average bit error rate of these combining schemes can all be expressed in terms of the Lauricella hypergeometric functions.