Efficient Estimation of the Left Tail of Bimodal Distributions with Applications to Underwater Optical Communication Systems

In this paper, we propose efficient importance sampling estimators to evaluate the outage probability of maximum ratio combining receivers over turbulence-induced fadings in underwater wireless optical channels. We consider two fading models: exponential-lognormal, and exponential-generalized Gamma. The cross-entropy optimization method is used to determine the optimal biased distribution. We show by simulations that the number of samples required by importance sampling estimator is much less compared to naive Monte Carlo for the same accuracy requirement.