Adaptive data echo cancellation using cost function adaptation. (Q1583565)

For a digital echo canceller it is desirable to reduce the adaptation time, during which the transmission of useful data is not possible. LMS is a non-optimal algorithm in this case as the signals involved are statistically non-Gaussian. \textit{E. Walach} and \textit{B. Widrow} [The least mean fourth (LMF) adaptive algorithm and its family, IEEE Trans. Inf. Theory 30, 275--283 (1994)] investigated the use of a power of 4, while other research established algorithms with an arbitrary integer [\textit{Pei} and \textit{Tseng}, IEEE J. Selected Areas Commun. 12, 1540--1547 (1994)] or non-quadratic power [\textit{Shah} and \textit{Cowan}, IEE. Proc.-Vis. Image Signal Process. 142, 187--191 (1995)]. This paper suggests that continuous and automatic, adaptation of the error exponent gives a more satisfactory result. The family of cost function adaptation (CFA) stochastic gradient algorithm proposed allows an increase in convergence rate and an improvement of residual error. As a special case, the staircase CFA algorithm is first presented, then the smooth CFA is developed. Details of implementations are also discussed. Results of simulation are provided to show the properties of the proposed family of algorithms.