Multiple hyperplane detector for implementing the asymptotic Bayesian decision feedback equalizer

Abstract— A detector based on multiple-hyperplane partitioning of the signal space is derived for realizing the optimal Bayesian decision feedback equaliser (DFE). It is known 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. The proposed technique determines these hyperplanes and uses them to partition the observation space. The resulting detector can closely approximate the optimal Bayesian detector, at an advantage of considerably reduced decision complexity.