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

Fractionally spaced equalizers (FSES), which are nonrecursive, tapped, delay-line adaptive filters, are currently receiving much attention1"7 because of the significant performance advantage they provide when compared with a conventional synchronous equalizer. Since an FSE has the capability to adaptively realize the optimum linear receiver, it can greatly improve the performance of a modem in the presence of severe linear distortion. More specifically, significant performance improvements have been observed owing to the ability of an FSE to compensate effectively for delay distortion at the limits of private-line, voice-grade channel conditioning. 8 However, in laboratory experiments with a digitally implemented FSE it was noticed that after an extended period of operation some of the equalizer tap weights would invariably become large, while the mean-squared error (mse) remained at a satisfactory level. The taps generally would become so large that one or more registers, which compute partial sums of the equalizer output, would overflow, and the modem performance was then substantially degraded. This phenomenon is a consequence of the fact that an FSE, in contrast to a conventional synchronous equalizer, generally has many sets of tap values that correspond to roughly the same mse. Included in the set of tap values that correspond to the minimum mse are some tap coefficients of relatively large magnitude. These large tap values can be attained because of the cumulative effect of noise or any bias in the digital circuitry that performs the equalizer updating.