On the Sum of Kappa Stochastic Variates and Applications to Equal-Gain Combining

In this paper we study the statistics of the sum of not necessarily identically distributed kappa, that is, K, random variables (RV)s. Assuming half-integer values for the shaping parameters, novel closed-form expressions for the probability density function (PDF) of the sum of independent K RVs are obtained, while for arbitrary values of the shaping parameters, a corresponding PDF expression is derived in terms of fast converging infinite series. Furthermore, an infinite series representation for the PDF of the sum of two arbitrarily correlated K RVs is derived. The proposed analysis is employed to the performance analysis of equal-gain combining (EGC) receivers operating over composite fading/shadowing channels modeled by the K distribution. More specifically, the outage and the average bit error probabilities, as well as the average channel capacity of EGC receivers operating over such composite environment are studied. Considering different channel fading/shadowing conditions and correlation effects, various numerical performance evaluation results are presented. These results are complemented by equivalent computer simulated ones that validate the accuracy of the proposed analysis.