Loop-shaping techniques applied to the least-mean-squares algorithm

The least-mean-squares (LMS) algorithm is analysed as a feedback control system. It is shown that despite the fact that LMS is a time-variant system that in fact it behaves much as a linear time-invariant (LTI) closed-loop control system. Therefore, it is possible to treat the LMS algorithm as a control system in the classical sense and define properties such as bandwidth to determine how fast a response (and hence convergence) is maximally possible. Similarly, the steady-state error response to a deterministic noise-free input can also be calculated. Moreover, it is then shown that classical control-based loop-shaping techniques can be used to improve the performance of the algorithm.