Multidimensional signal space partitioning using a minimal set of hyperplanes for detecting ISI-corrupted symbols

A signal space partitioning technique is presented for detecting symbols transmitted through intersymbol interference channels. The decision boundary is piecewise linear and is made up of several hyperplanes. The goal here is to minimize the number of hyperplanes for a given performance measure, namely, the minimum distance between any signal and the decision boundary, Unlike in Voronoi partitioning, individual hyperplanes are chosen to separate signal clusters rather than signal pairs. The convex regions associated with individual signals, which together form the overall decision region, generally overlap or coincide among in-class signals. The technique leads to an asymptotically optimum detector when the target distance is set at half the minimum distance associated with the maximum-likelihood sequence detector. Complexity and performance can be easily traded as the target distance is a flexible design parameter.