On the stability and performance of the adaptive line enhancer

In this presentation the stable and optimal operation of the adaptive line enhancer (ALE) is considered. By improving the estimate of the steady-state mean square error (MSE), a tighter stability constraint is obtained, as well as more accurate expressions for the SNR gain attained by the ALE when filtering sinusoidal signals in white noise. Since the LMS algorithm used for adapting the ALE weights aims at minimizing the MSE, and not at maximizing the output SNR, the proper choice of the algorithm´s parameters for maximizing the SNR gain is considered. In particular, it is shown that for a given step-size parameter µ (which satisfies the stability constraint) there exists an optimal number of weights which maximizes the SNR gain. Computer simulations verify the analytical results.