Average Error Rates for Equal Gain Combining Schemes in Nakagami Fading Channels with Arbitrary Fading Parameters

Equal gain combining (EGC) is employed in many practical wireless communication systems to combat fading and interference due to its simplicity. However, although EGC is easy to implement, its performance is usually very difficult to evaluate. This difficulty stems from the fact that it is usually not easy to express the probability density function (pdf) of the sum of independent Nakagami-m distributed random variables in closed-form. In this paper, we derive an expression for the pdf of the sum of independent Nakagami random variables in terms of multivariate hypergeometric function. Consequently, we express the average error rate of several digital modulation schemes at the output of the EGC in terms of the well known multivariate Lauricella function.