A useful and general technique for improving the efficiency of Monte Carlo simulation of digital communication systems

Importance sampling is a potentially powerful method for reducing simulation runtimes when estimating the bit error rate (BER) of communications systems using Monte Carlo simulation. Analytically minimizing the variance of the importance sampling estimator with respect to the biasing parameters has only yielded solutions for systems for which the bit error rate (BER) could be found analytically (i.e., a linear system with additive Gaussian noise). A technique for finding a near-optional set of biasing parameters for the translation biasing scheme is presented. A key feature of this technique is that repetitive, very short simulation runs are used to determine near-optimal translation values. The method is also shown to exploit a theoretically justifiable relationship, for small sample sizes, between the BER estimate and the amount of translation. Only mild assumptions about the noise distribution and system are required. Experimentally, improvement factors ranging from three to eight orders of magnitude are obtained for different avalanche photodiode noise distributions