Multiple Importance Sampling for Symbol Error Rate Estimation of Maximum-Likelihood Detectors in MIMO Channels

In this paper we propose a multiple importance sampling (MIS) method for the efficient symbol error rate (SER) estimation of maximum likelihood (ML) multiple-input multipleoutput (MIMO) detectors. Given transmitted from input lattice, obtaining SER requires computation an integral outside its Voronoi region in high-dimensional space, which closed-form solution does not exist. Hence, must be approximated through crude or naive Monte Carlo (MC) simulations. This practice is widely used literature despite inefficiency, particularly severe at high signal-to-noise-ratio (SNR) systems with stringent requirements. It well-known that more sophisticated MC-based techniques such as MIS, when carefully designed, can reduce variance estimators several orders magnitude respect to rare-event estimation, equivalently, they need significantly less samples attaining desired performance. The proposed MIS provides unbiased estimates by mixture components are chosen and parametrized. number components, parameters their weights mixture, automatically method. As result, flexible, easy-to-use, theoretically sound, presents performance variety scenarios. We show our simulations SERs lower than 10 -8 accurately estimated just xmlns:xlink="http://www.w3.org/1999/xlink">4 random samples.