On the use of improved importance sampling (IIS) in the simulation of digital communication systems

Importance sampling (IS) has been of increasing interest due to its potential for significantly improving the efficiency of the simulation of high performance digital communication systems. This work makes some theoretical contributions to the use of IS when the sampling density is a translated version of the original noise density. An asymptotic analysis is used to determine the optimum translation vector for a large class of non-linear and/or non-Gaussian systems as the probability of the event of interest goes to zero. The reduction in sample size with respect to standard Monte Carlo methods is calculated and a simple bound is derived. In addition the asymptotic optimality and equivalence of two adaptive IS algorithms at convergence is established. Numerical results are shown to be in close agreement with the developed theory