Efficient Computation of Multivariate Rayleigh and Exponential Distributions

We propose an efficient approach for the computation of cumulative distribution functions of N correlated Rayleigh or exponential random variables (RVs) for arbitrary covariance matrices, which arise in the design and analysis of many wireless systems. Compared to the approaches in the literature, it employs a fast and accurate randomized quasi-Monte Carlo method that markedly reduces the computational complexity by several orders of magnitude as N or the correlation among the RVs increases. Numerical results show that an order of magnitude larger values of N can now be computed for. Its application to the performance analysis of selection combining is also shown.