Novel Expressions for Ricean Sum Distributions and Densities

This letter provides exact expressions for the sum statistics of independent and identically distributed Ricean random variables. More precisely, we derive new compact, fast, and manageable solutions for both the probability density function and the cumulative distribution function of the considered sum. Numerical results verified the validity of our expressions. In particular, our solutions present a faster and efficient way to evaluate the exact Ricean sum, overcoming the traditional multi-fold Brennan’s integral approach. In order to show the wide applicability of our expressions, we evaluate the performance of an
$N$
-branch equal-gain combining diversity system over Ricean fading channels. More specifically, we derive
exact
and closed-form asymptotic expressions for the outage probability.