LMS algorithmic variants in active noise and vibration control

In this article we provide analyses of two low complexity LMS algorithmic variants as they typically appear in the context of FXLMS for active noise or vibration control in which the reference signal is not obtained by sensors but internally generated by the known engine speed. In particular we show that the algorithm with real valued error is robust and exhibits the same steady state quality as the original complex-valued LMS algorithm but at the expense of only achieving half the learning speed while its counterpart with real-valued regression vector behaves only equivalently in the statistical sense.