The curse of dimension on the learning rate of the LMS adaptive FIR filter

We quantify the relationship between the learning rate of the LMS adaptive FIR filter and its dimension when the input signal is correlated. It is argued that: Trace(R_n^-1)/n, where n is the filter dimension and R_n is the n×n input signal covariance matrix, provides the link between convergence rate, filter dimension and input signal correlation. Analyses of this function show quantitatively that the convergence rate will deteriorate with increasing filter dimension, n, and, for sufficiently large n, with input signal correlation. For AR modelled voiced speech input signals, in particular, the convergence rate is shown to be considerably poorer than that for white signals