The Trivariate Weibull Distribution with Arbitrary Correlation

In this paper an analytical framework for analyzing the arbitrarily correlated trivariate Weibull distribution is introduced. For this distribution infinite series representations for the joint probability density function, the cumulative distribution function (CDF) and the moments are derived. Two special correlation cases of the distribution are studied: the exponential and the constant. These series representations are readily applicable to the performance analysis of a 3-branch selection combining (SC) receiver operating in a Weibull correlation fading environment and the outage probability is derived. The proposed mathematical analysis is complemented by various numerical results, showing the effects of fading severity, correlation and the power decay factor