Exact - Sum Statistics

Sums of random variables are the statistical core in several performance analyses of communications systems. In this letter, we provide a fundamental contribution to this field, deriving original, exact, handy expressions for the probability density function and the cumulative distribution function for the sum of independent and identically distributed kappa-mu variates. Our formulations can be quickly computed in all cases, even in those for which Brennan's integral-the only available exact approach-may take several hours or not compute at all. For application purposes, we use our formulations to investigate the outage probability and the mean bit error rate in equalgain diversity systems. Further contribution includes asymptotic analyses. Numerical simulations validate our findings.