Lucky's 1965 automatic equalizer set a transversal filter's tap gains by steepest-descent minimization during a training period of known test pulses

Robert W. Lucky's answer to the voiceband "distortion barrier" (claim-voiceband-distortion-barrier-capped-data-at-2400-bps) was the automatic, self-adjusting equalizer. In his own words: "an easily implemented system for automatic equalization is described which makes use of a steepest-descent technique of minimization. The equalizer is automatically set prior to data transmission in a training period during which a series of test pulses is transmitted" (Lucky 1965, BSTJ 44(4), p.547).

The equalizer is a tapped delay line — a transversal (FIR) filter — placed at the receiver. Its tap gains form the adjustable parameters; iterating them down the gradient of a distortion measure drives the filter toward the inverse of the channel's smearing response, undoing the intersymbol interference before the decision device sees the signal. The known test-pulse "training period" supplies the reference the algorithm minimizes against.

Structurally this is the same family as the adaptive filter Bernard Widrow and Ted Hoff built with the LMS rule for the Adaline (claim-widrow-abandoned-multilayer-training-until-1985-backprop): an adjustable transversal filter whose weights are learned by iterative descent to minimize an error. The two lines ran in parallel at the same moment — Widrow toward pattern classification and, later, adaptive signal processing; Lucky toward telephone-line data rates — which is what makes the equalizer a lateral hop out of neural-net history (claim-madaline-rule-i-first-layer-trainable-second-fixed) into modem engineering. Whether the two groups were mutually aware or converged independently is an open thread (question-lucky-widrow-adaptive-filter-mutual-awareness).