Importance sampling simulation for evaluating lower-bound symbol error rate of the Bayesian DFE with multi-level signalling schemes

Abstract

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 evaluation 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 neighbouring 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 multi-level pulse amplitude modulation ($M$-PAM) schemes, 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.

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