Analysis of the statistical characteristics of an adaptive delay line

An analysis is presented of the statistical characteristics of an adaptive delay line, whose delay time and gain are automatically controlled by an adaptive gradient algorithm of minimum rms error. The line is a special type of adaptive filter, designed for the identification of communication systems or channels with an unknown time of delay and fading, and also for the adaptive suppression of echo noise. The noise-suppression coefficient, power spectra, and variances of fluctuations of delay time and output signal are determined, and the optimal (in the sense of minimum total error of identification) parameters of the delay line are found.