Developments in the Theory and Application of Importance Sampling

The assessment of bit error rate (BER) performance of a digital communication system via computer simulation has traditionally been done using the Monte Carlo method. For very low BER, this method requires excessive computer time. This time can be substantially reduced by using extrapolation based on importance sampling (IS). In applying IS to a complex system, many considerations must be addressed, chief among which is the reliability (variance) of the estimator as a function of the system particulars. We discuss a number of these considerations and, specifically, derive a number of expressions for the variance. We find that the variance improvement may be severely limited by the dimensionality (or memory) of the system. We describe a means for circumventing this limitation through the definition of a statistically equivalent impulse response. For a linear system, this amounts to the ordinary impulse response. The simulation can be structured to estimate the equivalent impulse response using statistical regression. This new approach has been implemented and found to yield significant runtime improvement over conventional importance sampling for linear systems of large dimensionality. We believe this technique will work also for mildly nonlinear systems, as might be encountered in typical satellite Communications.