A closed-form solution for the distribution of the sum of Nakagami-m random phase vectors

The distribution of the modulus of the sum of random phase vectors, is of great practical importance in several applications which deal with sums of sinusoidal signals (wireless multipath transmissions, radars, optical communications, etc). In this letter, simple closed-form expressions are presented for the probability density function (PDF), the cumulative distribution function (CDF), the moment generating function (MGF) and the moments of the envelope distribution of the sum of L non-identical random Nakagami-m phase vectors with integer fading parameters. Moreover, the average over this distribution of the Gaussian Q-function and of the squared Q-function, are also presented in closed-form