New insights for the filtered-X algorithm and robust adaptive equalization

The filtered-X LMS algorithm is the most popular method for adaptive filter design in the field of active acoustic and vibration control because of its simplicity and good robust performance. However, no investigation has been conducted on whether the filtered-X LMS algorithm has generic advantages over that of the conventional LMS algorithm in terms of their different structures. In this paper, a heuristic explanation is provided to show that, under certain conditions, the additional filter in the filtered-X LMS algorithm can increase the system's damping and move the closed-loop poles into deeper left halfplane, and hence increases the robust stability margin. In the illustrative example of a disturbed communication channel, Mont Carlo simulation results demonstrate that the filtered-X has a better robust performance than that of the conventional LMS.