The Bivariate Generalized-K (KG) Distribution and its Application to Diversity Receivers

The correlated bivariate generalized-K (KG) distribution, with not necessarily identical shaping and scaling parameters, is introduced and studied. This composite distribution is convenient for modeling multipath/shadowing correlated fading environments when the correlations between the signal envelopes and their powers are different. Generic infinite series expressions are derived for the probability density function (PDF), the cumulative distribution function (CDF) and the joint moments. Assuming identical shaping parameters, simpler expressions for the PDF, CDF and the characteristic function (CF) are provided, while the joint moments are derived in closed form. Furthermore, the PDFs of the product and ratio of two correlated KG random variables are obtained. Capitalizing on these theoretical expressions for the statistical characteristics of the correlated KG distribution, the performance analysis of various diversity reception techniques, such as maximal ratio combining (MRC), equal gain combining (EGC) and selection diversity (SD), over bivariate KG fading channels is presented. For the SD, the outage probability is studied, while for the MRC and EGC the average bit error probability is obtained. The proposed analysis is accompanied by numerical results, clearly demonstrating the usefulness of the theoretical approach as well as the appropriateness of the KG distribution to model multipath/shadowing fading channels.