Multicanonical Estimation of Outage Probabilities in MIMO Channels

Communication over Multiple-Input Multiple-Output (MIMO) fading channels is of much interest in the current telecommunication context. Estimation of very small outage probabilities in such channels is an important, yet time consuming task, owing to the lengthy run-time requirements of traditional Monte Carlo (MC) simulations. Hence, fast and accurate methods for estimating outage capacities are of necessity. Importance sampling (IS) has been the most widely used efficient simulation tool for telecommunication networks in the past. However, IS requires an in-depth knowledge of the system to explore the optimal biasing distribution. The method described in this paper uses the concept of Multicanonical Monte Carlo (MMC) for the quick simulation of outage probabilities in MIMO channels. MMC can be considered an adaptive IS technique which employs a blind adaptation algorithm to converge to the optimal biasing distribution. Here, we elaborate the use of MMC and present an algorithm for efficient simulation of outage probabilities of Rayleigh fading MIMO channels. This method can easily be extended to other fading models of interest. Numerical results, which extend the known results in literature, of the MMC simulations in comparison with that of the MC simulations are presented.