On the Distribution of the Sum of Generalized Gamma Variates and Applications to Satellite Digital Communications

A versatile envelope distribution which may be useful for both terrestrial and satellite fading channel modelling is the generalized Gamma (GG) distribution. By considering the product of N GG random variables (RV)s, useful expressions for its moments-generating and cumulative distribution functions are obtained in closed-form. These expressions are used to derive closed-form union upper-bound for the distribution of the sum of GG distributed RVs. The proposed bound turns out to be an extremely convenient analytical tool for studying the performance of N-branch equal-gain combining receivers operating over GG fading channels. For such receivers, novel union upper-bounds for the outage and the average bit error probability are derived and evaluated in terms of the Meijer´s G-function. The tightness of the proposed bounds is verified by performing comparisons between numerical evaluation and computer simulations results