The equivalence of two unified solutions for optimum space-time processing

Ariyavisitakul et al. (IEEE Trans. Commun., vol.47, p.1073-83, 1999 July) provided a unified analysis of optimum space-time processors based on the following two analytical diversity receiver models: 1) a general model-with a linear filter on each diversity branch, and 2) a "matched filter" model-with a bank of matched filters on each branch, followed by common filter. Closed-form results were given for each receiver model, in terms of the minimum mean-square-error or maximum signal-to-noise ratio solutions for different types of equalizers, including a linear equalizer (LE), a decision-feedback equalizer (DFE), and a maximum-likelihood sequence estimator (MLSE). Although we implied that the two receiver models lead to the same optimum solutions, this requires some proof that is not directly obtainable from the results we presented. We therefore provide such a proof in the present paper for the completeness of the overall unified analysis.