An efficient approach to the exponentially correlated Rayleigh distribution

A useful formulation for the multivariate Rayleigh probability density function (PDF) with an exponential form for its correlation matrix is presented. Furthermore, the corresponding multivariate Rayleigh cumulative distribution function (CDF) is derived in a nested infinite series representation, which converges rapidly and can be efficiently used in many wireless applications with diversity reception. Finally, bounds on the error resulting from truncation of the infinite series are also derived.