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

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.