An upper bound on the error probability in decision-feedback equalization

Abstract

An upper bound on the error probability of a decision-feedback equalizer which takes into account the effect of error propagation is derived. The bound, which assumes independent data symbols and noise samples, is readily evaluated numerically for arbitrary tap gains and is valid for multilevel and nonequally likely data. One specific result for equally likely binary symbols is that if the worst case intersymbol interference when the first <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</tex> feedback taps are Set to zero is less than the original signal voltage, then the error probability is multiplied by at most a factor of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2^J</tex> relative to the error probability in the absence of decision errors at high <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S/N</tex> ratios. Numerical results are given for the special case of exponentially decreasing tap gains. These results demonstrate that the decision-feedback equalizer has a lower error probability than the linear zero-forcing equalizer when there is both a high <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S/N</tex> ratio and a fast roll-off of the feedback tap gains.