The Tap-Leakage Algorithm: An Algorithm for the Stable Operation of a Digitally Implemented, Fractionally Spaced Adaptive Equalizer

Abstract

A fractionally spaced equalizer is a nonrecursive adaptive filter whose tap weights are spaced a fraction of a symbol interval apart. Such an equalizer can significantly enhance modem performance in the presence of severe linear distortion, when compared with a conventional synchronous equalizer whose taps are spaced a symbol interval apart. However, a digitally implemented, fractionally spaced equalizer generally will exhibit long‐term instability when the conventional tap‐adjustment algorithm is used. This occurs because, in contrast to the synchronous equalizer, a fractionally spaced equalizer generally will have many sets of tap values, which result in nearly equal values of mean‐squared error (mse). Some of these tap settings—which invariably will be attained because of biases in the digital tap‐updating circuitry—are large enough to cause register overflows and consequent performance deterioration. In this paper we report how a simple modification in the tap‐adjustment algorithm provides a solution to the above problem. The modified tap‐adjustment algorithm prevents the buildup of large coefficient values by systematically “leaking” or decreasing the magnitudes of all the equalizer tap weights. For an experimental modem operating at 9.6 kb/s, it has been demonstrated that the tap‐leakage adjustment algorithm prevents the accumulation of large equalizer tap values, while permitting the full performance gain of a fractionally spaced equalizer to be realized.

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