An Accurate, Fast Approximation for the Sum of Fading Random Variables via Expectation Maximization Applications to Diversity Systems

Sums of fading envelopes occur in several wireless communications applications. The exact mathematical solution to this statistic is, however, rather intricate. In this paper, we derive a novel closed-form approximation to the sum of not necessarily identically distributed Nakagami- m random variables. The necessary parameters of the approximate solution are estimated by using the well-known expectation maximization algorithm with a Nakagami- m mixture model. The proposed approximation finds applicability in obtaining important performance metrics of communications systems where sums of variates arise. More specifically, we apply the proposed method to derive a closed-form expression for average bit error probability (ABEP) of multibranch equal-gain combining receivers. The presented models are general and can be applied to any modulation scheme. Furthermore, simplified asymptotic closed-form expressions for the ABEP have been derived to examine the achievable diversity and coding gains. Finally, the performance of the proposed approach is verified by comparing itself against both the exact evaluation and the previous results in the literature.