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In this paper, accurate closed-form approximations for the distribution and density of a sum of Nakagami random variables are presented. The proposed approximations are then used to analyze the probability of error of a L-branch predetection equal gain combiner with different fading parameters. Coherent and noncoherent binary signaling as well as coherent M-ary signaling are considered. In addition, a closed-form expression for the outage probability of these systems is derived. These closed-form expressions permit rapid evaluation of the performance of equal gain combining diversity systems without resorting to numerical integration as required by previous solutions.