Importance sampling simulation methods for recursive and non-recursive symbol-by-symbol detectors

An importance sampling (IS) simulation method is developed for evaluating the bit-error rate of one-shot and recursive Bayesian equalizers (symbol-by-symbol detectors.) It is shown that the one-shot Bayesian equalizer structure closely resembles that of a multi-user detector for CDMA. Hence, noise biasing IS methods developed previously for CDMA detectors should also be appropriate for Bayesian equalizers. At low SNRs, the decision boundary far the one-shot Bayesian equalizer approaches a hyperplane. This hyperplane is viewed as an approximation to the true decision boundary at high SNRs, and can thus be used to construct an appropriate noise bias vector. With a slight modification, it is shown that the IS technique for the one-shot Bayesian equalizer can also be applied to the Abend and Fritchman (1970) recursive algorithm, and finally, to an adaptive Bayesian blind equalizer. IS simulations are carried out for both the nonadaptive Bayesian equalizers and for the blind recursive equalizer