Importance Sampling Simulation and Multiple-Hyperplane Realization of the Bayesian Decision Feedback Equaliser

Abstract

For the class of equalisers that employs a symbol-decision finite-memory structure with decision feedback, the optimal solution is known to be the Bayesian decision feedback equaliser (DFE). The complexity of the optimal Bayesian DFE however increases exponentially with the length of the channel impulse response (CIR). It has been noted that, when the signal to noise ratio (SNR) tends to infinity, the decision boundary of the Bayesian DFE is asymptotically piecewise linear and consists of several hyperplanes. This asymptotic property can be exploited for efficient simulation and implementation of the Bayesian DFE. An importance sampling (IS) simulation technique is presented based on this asymptotic property for evaluating the lower-bound bit error rate (BER) of the Bayesian DFE 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 of the IS simulation. As the set of hyperplanes that form the asymptotic Bayesian decision boundary can easily be found, they can be used to partition the observation space. The resulting multiple-hyperplane detector can closely approximate the optimal Bayesian detector, at an advantage of considerably reduced decision complexity.

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ORCID for L. Hanzo: orcid.org/0000-0002-2636-5214

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