Nonlinear importance sampling techniques for efficient simulation of communication systems

The use of nonlinear biasing techniques in importance sampling (IS) simulations is discussed. For tail probability estimation, two new nonlinear IS (NLIS) approaches are presented: shift of absolute values (SAV) and sample elimination (SE). In the case of linear systems with Gaussian input, the SAV method is shown to be uniformly more efficient than the linear techniques and very robust with respect to suboptimal parameterization. With respect to suboptimal choice of its parameter, the efficiency of the SE method is more sensitive than that of all other IS techniques discussed. Both NLIS methods are found to be easily implementable alternatives to the standard linear IS(LIS) techniques. The estimation of very-low-interval probabilities is considered as a new field for the application of IS techniques. The author presents both an LIS and an NLIS approach for this problem and provides performance analyses. A uniform bound on the required sample size is obtained for both techniques, thus emphasizing their high efficiency. Both methods are shown to be very robust with respect to suboptimal parameterization