Decision-Feedback Equalisation Using Multiple-Hyperplane Partitioning for Detecting ISI-Corrupted $M$-ary PAM Signals

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Description/Abstract

A novel decision feedback equaliser (DFE) scheme is derived based on multiple-hyperplane partitioning of signal space for detecting $M$-ary PAM symbols transmitted through an intersymbol interference (ISI) and noisy channel. The proposed scheme is based on the observation that the optimal Bayesian decision boundary separating any two neighbouring signal classes is asymptotically piecewise linear and consists of several hyperplanes, when the signal to noise ratio (SNR) tends to infinity. An algorithm is developed to determine these hyperplanes, which are then used to partition the observation signal space. The resulting detector can closely approximate the optimal Bayesian detector and, in the asymptotic case of large SNR, achieves the full Bayesian DFE performance, at an advantage of considerably reduced detector complexity. Index Terms—Asymptotic decision boundary, Bayesian decision-feedback equalizer, multiple-hyperplane detector, signal space partitioning.