Robust performance of the adaptive periodic noise canceller in a closed-loop system

This paper addresses the issue of robustness of the LMS-driven Adaptive Periodic Noise Canceller (APNC) in a closed-loop system. The concept of robustness provides a framework within which it is possible to make a useful assessment of algorithm performance. By adopting an analysis based on H
^∞
-theory, conditions are shown under which the APNC, driven by the LMS algorithm, will exhibit robust performance properties. Results are presented for the case of a broadband signal input to a one-dimensional closed-loop system. They display the relationship between the algorithm stepsize, the magnitude of the feedback coefficient and their bounds for robust performance. This result can be directly related to the use of the APNC in an echo control application.