Importance Sampling Methodologies for Simulation of Communication Systems with Time-Varying Channels and Adaptive Equalizers

Formula-based analysis of communication links with time-varying channels and adaptive equalizers is not always tractable Monte Carlo simulation must be used to obtain bit error rate (BER) estimates of the system. Conventional Monte Carlo simulation will not provide estimates for low BER's due to excessive run time. Although importance sampling (IS) techniques offer the potential for large speed-up factors for BER estimation using MC simulation, IS techniques have not been used for simulating communication links with adaptive equalizers. In this paper we present, for the first time, two IS methodologies for MC simulation of communication links characterized by time-varying channels and adaptive equalizers. One methodology is denoted here as the "twin system" (TS) method. A key feature of the TS method is that biased noise samples are input to the adaptive equalizer, but the equalizer is only allowed to adapt to these samples for a time interval equal to the memory of the system. In addition to the TS technique, we also present a statistically biased, but simpler technique for using IS with adaptive equalizers which is based on the independence assumption between the equalizer input and the equalizer taps (the "IA" method). Experimental results are presented that show run time speed-up factors of two to seven orders of magnitude for a static linear channel with memory, and of two to almost five orders of magnitude for a slowly varying, random linear channel with memory, for both the IA and TS methods. 1. This research was sponsored in part by an IBM Fellowship. 2. Portions of this paper have been presented at the IEEE GLOBECOM'92, Orlando, Florida, December 1992. Importance Sampling Methodologies ... , Al-Qaq, Devetsikiotis, & Townsend