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 stati onary channel may be-influenced by the filter,parameter dimension as w ell 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 o f a novel measure of the expected convergence rate of the LMS/FIR filt er followed by analysis of this convergence rate measure. The analysis indicates that unless the: input signal is white, the expected conver gence rate decreases with increasing dimension down to a limiting valu e, which is determined by the input signal's autocorrelation level.