Ambiguity resistant precoders in ISI/multipath cancellation: distance and optimality

Abstract

Ambiguity resistant (AR) precoding has been proposed in intersymbol interference (ISI) and multipath cancellation, where the ISI/multipath channel may have frequency-selective fading characteristics and its knowledge is not necessarily known. With the AR precoding, no diversity is necessary at the receiver. In the precoding, the AR property of the precoder plays an important role. We introduce the concepts of precoder distance and optimal precoders, and characterize and construct all optimal systematic AR precoders, when additive channel random noise is considered. A necessary and sufficient condition for an AR precoder to be optimal is given, which is easy to check. With the optimal precoders, numerical simulations are presented to show the improved performance over the known AR precoders in ISI cancellation applications.