A New Result for the Distribution of the Sum of Nakagami-m Random Variables

In this paper, we investigate the classical problem of finding the probability density function of the sum of Nakagami-m random variables. An exact infinite series formula is derived for the sum of three identically and independently distributed (i.i.d.) Nakagami-m random variables and subsquently it is extended to the sum of four and in general M number of random variables. A detailed discussion on the cumulative density function (cdf) of the sum of three Nakagami-m variables is also given. The newly derived probability density functions are used to analyze the performance of dual and triple predetection equal gain combining (EGC) receiver over Nakagami-m fading environment. Selected numerical plots are provided to compare the results with the approximate results available in the literature and to illustrate the validity of the results.