“…2, and the most popular adaptive algorithm for controlling the filter weights is the leastmean-squares (LMS) stochastic gradient search approach first reported, in the context of adaptive filters, by Widrow [1]. Such adaptive filter designs are extensively reported in the literature and are widely applied in practical communications equipment, ranging from speech-band data modems [6] to wideband microwave digital radio systems [7]. In many of these applications the need for a separate Paper 3054F (E7, E10), first received llth July 1983 and in revised form 11th January 1984 The authors are with the Department of Electrical Engineering, University of Edinburgh, King's Buildings, Edinburgh EH9 3JL, Scotland training signal is overcome by differencing the filtered output with the detector output, after the decision process, in order to derive the error signal [6,7].…”