Uma Solução Exata Mais Eficiente para a Soma de Variáveis Aleatórias Nakagami-m e Aplicações

Sums of random variables (RVs) play a key role in the performance analysis of communication systems. In particular, sums of Nakagami-m RVs allow the performance characterization and evaluation of equal-gain combining (EGC) receivers, a classical diversity technique that has been explored in fifth-generation mobile networks. As the statistical characterization of sums of variables --- in terms of the probability density function (PDF) or the cumulative distribution function (CDF) --- involves an intricate mathematical treatment, the exact solutions available for the sum of Nakagami-m RVs are time-consuming, limited, or even unfeasible as the number of RVs in the sum increases. In this work, we obtain novel exact expressions for the PDF and CDF of the sum of Nakagami-m variates, in terms of infinite series. Compared with the state of the art, the new expressions reduce the computational cost (or, equivalently, the computation time) by more than 95%. To show the applicability of these expressions, we analyze the outage probability in EGC receivers. Monte-Carlo simulations corroborate our analytical results.