Distribution of the sum of K-distributed random variables and applications in free-space optical communications

Performance analysis of free-space optical (FSO) systems employing equal-gain combining (EGC) diversity technique over the K channels needs the probability density function (PDF) of the sum of K-distributed random variables (RVs), which is not available in an analytical closed form. In this study, the statistics of the sum of independent identically distributed K variates is investigated and novel exact closed-form expressions are provided for the PDF, cumulative density function and the nth-order moment of the sum of K-distributed RVs. To show the applications of the presented results, performance of subcarrier intensity-modulated FSO communication system employing EGC diversity technique is investigated over the K channel and bit error rate and outage performance are discussed.