New results in the analysis of decision-feedback equalizers

This paper considers the decision feedback equalizers (DFE) with finite impulse response (FIR). Although they have been the subject of a number of studies, several longstanding problems in the analysis of these equalizers remained open. For the most part, the problems addressed in this paper are in the domain of high-SNR analysis, including the Diversity-Multiplexing Tradeoff (DMT) for DFE. We find that the DFE fixed-rate diversity follows the DMT analysis, unlike several examples from linear equalization in the recent literature where the fixed-rate diversity departed from the DMT expression. As part of the developments of this paper, the notion of the spectral representation of random processes is used to put the analysis of the decision feedback equalizers on a solid mathematical foundation.