Some new properties of the LMS FIR-ALE

The properties of the LMS (least mean square) FIR (finite impulse response) ALE (adaptive line enhancer) when the input consists of p real sinusoids is examined. Unlike the general input case, it is shown that the convergence and sensitivity properties of this ALE are fairly good. The Wiener-Hopf solution is shown to depend only on the 2 p dominant eigenvalues of the covariance matrix. This in turn is used to show that the covergence of the LMS algorithm for the zero initial condition depends only on the dominant 2p eigenvalues. It is also shown that when a filter of length L, where L ≫2p, is used, the parameter sensitivity is fairly low. The low parameter sensitivity is traced to the minimum-norm characterization of the solution in the noise-free case. The minimum-norm criterion also turns out to be useful in selecting an appropriate value for the decorrelation delay δ