Quantifying the convergence speed of LMS adaptive FIR filter with autoregressive inputs

In general the least mean squares adaptive finite impulse response (FIR) filter converges more slowly with an increase in filter length and input signal correlation level. An explicit expression is presented relating the convergence speed of this adaptive filter to the FIR filter length and the correlation characteristics of autoregressive (AR) modelled input signals. The expression provides a simple means for justifying (or not) the cost of input signal whitening techniques within for example acoustic echo cancellation, in which very large FIR filter lengths and highly correlated AR modelled speech input signals occur