Approximation of Optimal Step Size Control for Acoustic Echo Cancellation

One of the most widely used gradient-based adaptation algorithms is the so called normalized least mean square (NLMS) algorithm. The rate of convergence, misadjustment and noise insensitivity of the NLMS-type algorithm depend on the proper choice of the step size parameter, which controls the weighting applied to each coefficient update. Different step size methods have been proposed to improve the convergence of NLMS-type filters, while preserving the steady-state performance. The step size methods considered here use either a step size parameter which varies with time or a separate, tap-individual step size for each filter tap. The derivation of the respective step size methods is based on different optimization criteria. In this paper a step size parameter is proposed satisfying a combined optimization criterion leading to a time variant and individual step size parameter. The realization aspects of the new concept are discussed for an acoustic echo control application as an example.