Convergence behaviour of a jointly adaptive transversal and memory-based echo canceller

Abstract

A convergence analysis of a jointly adaptive transversal and memory-based or nonlinear echo canceller is presented. The coefficients of the transversal echo canceller (TEC) and the memory echo canceller (MEC) are updated simultaneously using the well-known least mean square (LMS) algorithm with separate adaptation constants and a common cancellation error. The amount of linear echo cancellation load-sharing between the TEC and MEC is shown to be governed by a fixed relationship that exists between the MEC coefficients and those TEC coefficients updated using the shared portion of the input symbol span. The average mean square error is derived for the case of binary input symbols and compared to that of an identical canceller adopting a sequential adaptation method where the TEC coefficients are adapted first and permitted to converge before MEC coefficient adaptation is initiated for jointly adaptive operation. Bounds for both adaptation constants are found for MSE convergence for the jointly adaptive case. The adaptation constants that yield the fastest jointly adaptive convergence are also derived. The sequential method is shown to have an overall convergence rate advantage that decreases as the ratio of the number of TEC coefficients to MEC coefficients becomes large. The theoretical results are supported by computer simulations.