Sample rejection and importance sampling in the simulation of multidimensional signalling systems

Abstract

Sample rejection has been proposed as a means for improving the efficiency of computer simulation used for error rate estimation. Previous work has not examined quantitatively the feasibility of sample rejection for improving the efficiency of simulation of multidimensional signalling schemes. The present work aims to determine the usefulness of sample rejection for the simulation of such systems. Two methods based on sample rejection are described for the Monte Carlo simulation of small error probabilities, Pe, in digital communication systems. The first is based on the observation that when Pe is small most of the noise vectors are known in advance not to cause errors, and consequently need not be simulated. Discarding such noise vectors will result in savings in computer simulation time. The second method is based on generating noise vectors whose probability density function has a hole carved around the origin. This method replaces the original noise input density function by a biased noise input density and is a form of importance sampling. The expected savings in computer time achieved by use of these methods is investigated. Quantitative results are obtained for multidimensional signalling schemes without memory. The expected savings are compared to those achieved by the use of conventional importance sampling. The suitability of the two methods for simulation of multidimensional systems with memory is considered. Our work shows that although sample rejection is a strong biasing technique in unidimensional situations, it looses its advantage rapidly as the dimensionality of the problem increases. It offers some advantage for the simulation of systems with small dimensionality (less than nine) or by application in combination with other importance sampling schemes.