Convergence Behaviour of Lms - Typealgorithms for Adaptive Noise Con - Trol in Noisy Doppler

ALGORITHMS FOR ADAPTIVE NOISE CONTROL IN NOISY DOPPLER ENVIRONMENTS ROBERT W. STEWART, STEPHAN WEISS, DAVID H. CRAWFORD Signal Processing Division, Dept. of Electronic and Electrical Engineering, University of Strathclyde, Glasgow G1 1XW, Scotland, UK Abstract. This paper discusses the convergence and tracking behaviour of LMStype algorithms in a certain type of environment, which is characterised by a Doppler shift in frequency between the two signals available to the algorithm and rapid variations in signal power. We show the linear time-varying characteristics of the underlying system and derive optimum trajectories to which we can compare the adaptation and tracking ability of rst order LMS and NLMS adaptive lters. We also present simulations using higher lter orders and real world noise, for which particular emphasis is put on the presence of observation noise. An excursion into the theory of non-stationary convergence and tracking of adaptive algorithms provides justi cation for the observed behaviour of the algorithms.