A Geometric Theory of Intersymbol Interference

In a companion paper,
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a geometric approach to the study of intersymbol interference was introduced. In the present paper this approach is applied to the performance analysis of the Viterbi algorithm maximum likelihood detector (MLD) of Forney.
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It is shown that a canonical relationship exists between the minimum distance, which Forney has shown determines the performance of the MLD, and the performance and tap-gains of the decision-feedback equalizer (DFE). Upper and lower bounds on the minimum distance are derived, as is an iterative technique for computing it exactly. The performances of the MLD, DFE, and zero-forcing equalizer (ZFE) are compared on the √f channel representative of coaxial cables and some wire pairs. One important conclusion is that, previous statements notwithstanding,
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even the MLD experiences a substantial penalty in S/N ratio relative to the isolated pulse bound on this channel of practical interest.