On Optimal ambiguity resistant precoders in ISI/multipath cancellation

Ambiguity resistant precoding has been recently proposed in intersymbol interference (ISI) and multipath cancellations, where the ISI/multipath channel may have frequencyselective 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 for a précéder plays an important role. In this paper, more families and properties of AR precoders are presented and characterized. In particular, all systematic AR precoders are characterized. More importantly, we introduce the concepts of precoder distance and optimal precoders and characterize and construct all optimal systematic AR precoders where additive channel random noise is concerned. A necessary and sufficient condition for an AR précéder to be optimal is given, and it is 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.