On optimal ambiguity resistant precoders in ISI/multipath cancellation

Ambiguity resistant (AR) preceding has recently been proposed in intersymbo l interference (ISI) and multipath cancellations, where the ISI/multipath c hannel may have frequency-selective fading characteristics and its knowledg e is not necessarily known. With the AR preceding, no diversity is necessar y at the receiver, In the preceding, the AR property for a precoder plays a n important rule. In this paper, more families and properties of AR precode rs are presented and characterized. In particular all systematic AR precode rs are characterized. More importantly, we introduce the concepts of precod er distance and optimal precoders, and characterize and construct all optim al systematic AR precoders, when additive channel random noise is concerned , A necessary and sufficient condition for an AR precoder to be optimal is given, which is easy to check. With the optimal precoders, numerical simula tions are presented to show the improved performance over the known AR prec oders in ISI cancellation applications.