Rare-Event Simulation of Outage Probability in GSC/MRC Systems under Rician Fading

This paper studies the estimation of outage probability in GSC/MRC SIMO systems under Rician fading in the rare-event regime. The difficulty arises from the evaluation of the CDF of a partial sum of ordered non-central chi-square random variables, motivating the use of enhanced Monte-Carlo methods. For independent fading, we propose partition importance sampling (PIS), a theory-driven estimator tailored to this structure, and prove that it achieves bounded relative error (BRE). We further adapt exponential twisting, proving its BRE property, and cross-entropy to this setting. We then extend ET and CE to correlated Rician fading, where the joint distribution of the power gains is no longer tractable, yielding the ETC and CEC estimators; ETC enjoys the bounded-relative-error guarantee under arbitrary mean and arbitrary covariance. Numerical experiments compare these methods with universal importance sampling and multilevel splitting for independent fading, and an asymptotic approximation in the correlated case. Empirically, CE shows the most robust performance in the independent case; PIS and ET are competitive but degrade for larger means, with ET further degrading when the selected subset is much smaller than the antenna array. ETC yields a better estimate than the asymptotic approximation for moderately rare events.