BER analysis of Bayesian equalization using orthogonal hyperplanes

Abstract

Bayesian symbol-by-symbol detection using a finite sequence observation space has been the subject of renewed research interest. The Bayesian transverse equalizer (BTE) and Bayesian decision feedback equalizer (BDFE) are two common Bayesian detectors. It is often difficult to evaluate the bit-error rate (BER) performance of these Bayesian detectors since the BER cannot be analytically evaluated and the high complexity of these detectors makes simulation techniques computationally prohibitive, especially at low BERs. We propose a framework to evaluate the BER for the BTE and a lower bound on the BER for the BDFE. This framework is based on finding an approximation of the conditional error probability for each of the noiseless channel states in the observation space. The optimal Bayesian decision boundary is approximated by a set of hyperplanes, and each hyperplane is rotated some minimal angle to make them mutually orthogonal/parallel. The conditional probability of error can be readily evaluated on the topology of orthogonal/parallel rotated hyperplanes. Our BER evaluation is accurate and does not require simulations. A reduced complexity approach to evaluate the BER is also developed.