Joint distribution functions of three or four correlated Rayleigh signals and their application in diversity system analysis

Few theoretical results are known about the joint distribution of three or more correlated Rayleigh random variables (RVs). Consequently, theoretical results for the performance of 3-branch and 4-branch equal gain combining (EGC), selection combining (SC) and generalized SC (GSC) over arbitrarily correlated Rayleigh fading channels are not known. This paper derives new infinite series representations of the joint probability density function (pdf) and the joint cumulative distribution function (edf) of the tri-variate and a certain class of quadri-variate correlated Rayleigh distribution. The new pdf and cdf expressions are used to derive the outage probability of 3-branch SC and the moments of the 3-branch EGC output signal-to-noise ratio (SNR) over arbitrarily correlated Rayleigh fading. New bounds for the complementary cdf (ccdf) of the L-branch SC output SNR are also derived. These long-standing diversity theory problems, which have resisted a solution, can now be completely solved.