Quantifying the effects of dimension on the convergence rate of the LMS adaptive FIR estimator

The convergence rate of an LMS adaptive FIR filter to an unknown stationary channel may be influenced by the filter parameter dimension as well as by the input signal´s characteristics. This dimension influence may be of importance in applications, such as adaptive acoustic echo cancellation, in which the unknown channel is typically modeled as a “long” FIR filter. The paper includes the development and proposal of a novel measure of the expected convergence rate of the LMS/FIR filter followed by analysis of this convergence rate measure. The analysis indicates that unless the input signal is white, the expected convergence rate decreases with increasing dimension down to a limiting value, which is determined by the input signal´s autocorrelation level