Abstract: In a receiver for signals in a multilevel partial response class-IV communication system, the coefficients of a digital adaptive equalizer need to be updated to minimize the error due to noise and signal distortion. After initial convergence of the equalizer coefficients to near-optimum settings, an estimate of the mean-square error gradient for coefficient updating can be obtained in decision-directed mode from an estimate of the error signal. In the absence of a reference signal, initial convergence must be achieved in self-training mode. The decision-directed error signal is then replaced by a pseudo-error signal for the computation of an approximation of the mean-square error gradient. The invention provides a particular self-training procedure which outperforms known methods in terms of speed of convergence and achieved mean-square error values, and does not require timing recovery prior to equalizer convergence.