Series Expansions and Approximations of the Nakagami-m Sum Probability Density Function

The numerical evaluation of the pdf of a sum of Nakagami-m random variables is considered in this letter. Different methods are proposed to obtain this approximation: i) a power series expansion based on elementary properties of unilateral convolution of power signals; ii) a Laplace approximation stemming from Laplace's method for asymptotic integral approximations; and iii) a Gaussian series expansion capturing the deviation of the wanted pdf from the Gaussian with the same mean and variance. Numerical results are included for validation and comparison with the literature and a critical assessment of the different methods is provided.