On feed-through terms in the lms algorithm

The well known least mean squares (LMS) algorithm is studied as a control system. When applied in a noise canceller a block diagram approach is used to show that the step size has two upper limits. One is the conventional limit beyond which instability results. The second limit shows that if the step size is chosen to be too large then feed-through terms consisting of signal times noise will result in an additive term at the noise canceller output. This second limit is smaller than the first and will cause distortion at the noise canceller output

Analysis of the Error Signal of the LMS Algorithm.

An analysis of the error signal of the Least-Mean- Square (LMS) algorithm is conducted from the robust control theory viewpoint. The difference equation that relates the input of the LMS algorithm and the error signal is presented. This equation is used to build the matrix that maps the input vector to the error vector. It is shown that has at least one singular value greater than 1. Therefore, the system may amplify noise at high frequencies. Nevertheless, the tap-weight vector may be chosen to prevent that noise amplification and improve the disturbance rejection performance of the LMS algorithm