Optimum open eye equalizer design for non-minimum phase channels

This paper contains results on the design of optimum equalizers to eliminate intersymbol interference in linear non-minimum phase channels conveying binary signals. The optimization is with respect to an open eye condition with a given delay. For causal stable channels with non-minimum phase zeros, we argue that this problem requires only the consideration of the FIR modified channel that has all the non-minimum 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 a specified delay, then the optimizing equalizer is, in fact FIR with all zeros outside the unit circle, and the impulse response of the equalised channel does not extend beyond the delay. We also give a simple necessary and sufficient condition to determine if for a particular delay, a given channel can be equalized to achieve an equalized response that is open eye.