Accurate Outage Probability Evaluation of Equal Gain Combining Receivers

We consider the evaluation of the outage probability (OP) for L-branch equal gain combining diversity receivers operating over fading channels, i.e. equivalently the cumulative distribution function (CDF) of the sum of the L channel envelopes. Generally, closed-form expressions of the OP values are out of reach. Moreover, the use of naive Monte Carlo (MC) simulations is not a good alternative since it is expensive in terms of number of samples when small values of OP are considered. In this paper, we use the concept of importance sampling (IS), being known to yield accurate estimates using few number of simulations runs. The proposed IS scheme is essentially based on sample rejection where the IS probability density function (PDF) is the truncation of the underlying PDF over the L dimensional sphere. It assumes the knowledge of the CDF of the sum of the L channel gains in a closed-form expression. Such an assumption is not restrictive since it holds for various challenging fading models. As an illustration, we apply the proposed estimator to the cases of independent Rayleigh, correlated Rayleigh, and independent and identically distributed Rice fading channels and prove that it achieves the well-desired bounded relative error property. Finally, we validate these theoretical results through some selected experiments.