Optimum open eye equalizer design for nonminimum phase channels

This paper contains results on the design of optimum equalizers to eliminate intersymbol interference (ISI) in linear nonminimum phase channels conveying binary signals. The optimization is with respect to an open eye condition with a delay d. For causal stable channels with nc nonminimum phase zeros, we argue that this problem requires only the consideration of the 7ic-tap FIR modified channel that has all the nc nonminimum phase zeros of the original channel. We show that if this modified channel can be equalized to yield an equalized system that is open eye with delay d, then the optimizing equalizer is, in fact, (d -?ic)-tap FIR with all zeros outside the unit circle. We also give a simple necessary and sufficient condition to determine if for a particular d, a given channel can be equalized to achieve an equalized response that is open eye with delay d.