BERG Publications

MS Thesis, Cornell University, 1996

Blind Adaptive Decision Feedback Equalization: A Class of Bad Channels

Raúl Casas

Abstract

In digital communications, an equalizer that can fully cancel intersymbol interference from a linear dispersive channel with finite time span while not amplifying noise, and that can be implemented with relative ease is bound to be popular. That is the case with the decision feedback equalizer (DFE), a receiver component that has gained the attention of researchers and practitioners for over thirty years. The difficulty in analyzing the DFE, arising from its feedback structure and nonlinearity, has made it hard to asses DFE performance in comparison to other schemes, such as the linear feedforward baud and fractionally-spaced equalizers, and has hindered the development of a comprehensive DFE theory.

One of the major areas lacking understanding of the behavior of a DFE is in the blind adaptation of its equalizer parameters. Due to the inherent complexities of this nonlinear stochastic system, little is known about the convergence properties of adaptive algorithms, like the decision-directed algorithm, when used to blindly update a DFE. This thesis works on expanding the theory on decision-directed DFE (DD-DFE).

Since the literature rarely mentions the initialization of DD-DFE, and the decision-directed algorithm, used in both DFEs and linear feedforward filters, is known to have convergence problems when there are sufficient symbol estimate errors, this work studies the convergence of DD-DFE from the most natural initialization (when no estimate of the channel dynamics is available): the origin. It is shown that certain channels guarantee that DD-DFE will converge as desired, and as the main result of the thesis, it is shown that certain channels from a dense set, classified as bad channels, guarantee that DD-DFE will converge to a bad minimum.