SAMPLE REJECTION AND IMPORTANCE SAMPLING IN THE SIMULATION OF MULTIDIMENSIONAL SIGNALING SYSTEMS

Sample rejection has been proposed as a means for improving the effici ency of computer simulation used for error rate estimation. Previous w ork has not examined quantitatively the feasibility of sample rejectio n for improving the efficiency of simulation of multidimensional signa lling schemes. The present work aims to determine the usefulness of sa mple rejection for the simulation of such systems. Two methods based o n sample rejection are described for the Monte Carlo simulation of sma ll error probabilities, P(e), in digital communication systems. The fi rst is based on the observation that when P(e) is small most of the no ise vectors are known in advance not to cause errors, and consequently need not be simulated. Discarding such noise vectors will result in s avings in computer simulation time. The second method is based on gene rating noise vectors whose probability density function has a hole car ved around the origin. This method replaces the original noise input d ensity function by a biased noise input density and is a form of impor tance sampling. The expected savings in computer time achieved by use of these methods is investigated. Quantitative results are obtained fo r multidimensional signalling schemes without memory. The expected sav ings are compared to those achieved by the use of conventional importa nce sampling. The suitability of the two methods for simulation of mul tidimensional systems with memory is considered. Our work shows that a lthough sample rejection is a strong biasing technique in unidimension al situations, it looses its advantage rapidly as the dimensionality o f the problem increases. It offers some advantage for the simulation o f systems with small dimensionality (less than nine) or by application in combination with other importance sampling schemes.