Excitation Conditions for Signed Regressor Least Mean Squares Adaptation

The stability of the signed regressor variant of least mean square (LMS) adaptation is found to be heavily dependent on the characteristics of the input sequence. Averaging theory is used to derive a persistence of excitation condition which guarantees exponential stability of the signed regressor algorithm. Failure to meet this condition (which is not equivalent to persistent excitation for LMS) can result in exponential instability, even with the use of leakage. This new persistence of excitation condition is then interpreted in both deterministic and stochastic settings.