ESTIMATION VARIANCE BOUNDS OF IMPORTANCE SAMPLING SIMULATIONS IN DIGITAL-COMMUNICATION SYSTEMS

In practical applications of importance sampling (IS) simulation, we encounter two basic problems, that of determining the estimation variance and evaluating the proper IS parameters needed in the simulations. We derive new upper and lower bounds on the estimation variance which are applicable to IS techniques. Furthermore, the upper bound is simple to evaluate and may be minimized by the proper selection of the IS parameter. Thus, lower and upper on the improvement ratio of various IS technique relative to the direct Monte-Carlo simulation are also available. These bounds are shown to be useful and computationally simple to obtain. Based on the above proposed technique, we can readily find practical suboptimum IS parameters. Specific numerical results indicate that these bounding techniques are useful for IS simulations of linear and nonlinear communication systems with ISI in which BER and IS estimation variances cannot be obtained readily by prior techniques.