Importance sampling simulation for evaluating lower-bound symbol error rate of the Bayesian DFE with multilevel signaling schemes

For the class of equalizers that employs a symbol-decision finite-memory structure with decision feedback, the optimal solution is known to be the Bayesian decision feedback equalizer (DFE). The complexity of the Bayesian DFE, however, increases exponentially with the length of the channel impulse response (CIR) and the size of the symbol constellation. Conventional Monte Carlo simulation for evaluating the symbol error rate (SER) of the Bayesian DFE becomes impossible for high channel signal-to-noise ratio (SNR) conditions. It has been noted that the optimal Bayesian decision boundary separating any two neighboring signal classes is asymptotically piecewise linear and consists of several hyperplanes when the SNR tends to infinity. This asymptotic property can be exploited for efficient simulation of the Bayesian DFE. An importance sampling (IS) simulation technique is presented based on this asymptotic property for evaluating the lower bound SER of the Bayesian DFE with a multilevel pulse amplitude modulation ( -PAM) scheme under the assumption of correct decisions being fed back. A design procedure is developed, which chooses appropriate bias vectors for the simulation density to ensure asymptotic efficiency (AE) of the IS simulation.