Quick simulation of detector error probabilities in the presence of memory and nonlinearity

One would like to compare and analyze digital communication systems based upon their overall probability of error. Unfortunately, easily evaluated closed form expressions for these probabilities are almost impossible to derive due to the complexity of the stochastic systems usually encountered. Hence, one must often resort to simulation to obtain the desired quantities. The most obvious technique is Monte Carlo simulation, which directly counts the number of errors in repeated trials. The problem is that error probabilities are usually quite small, requiring numerous simulation runs to sufficiently “hit” the rare event to gain adequate knowledge of its statistics. This places severe demands on the computer´s random number generator. Importance sampling strategies simulate under altered input signal distributions (e.g., translation or stretching) so as to “speedup” convergence of the error estimators. The authors discuss a speedup technique termed quick simulation based upon results in large deviation theory. The quick simulation method is shown to compare favorably with three other importance sampling techniques for simulating a simple nonlinear system with memory