A Normalized Least-Mean-Square Algorithm Based on Variable-Step-Size Recursion With Innovative Input Data

This letter presents a variable-step-size normalized least-mean-square algorithm, where the step size is updated only when the current input vector is innovative from the last updated input vector. The instant innovativeness of the two input vectors is investigated through the relation between the angle of the two input vectors and the condition number of the input covariance matrix. Once the condition number is obtained, the resulting algorithm performs an excellent transient and steady-state behavior with different correlations in inputs. To reduce the computational burden of obtaining the condition number, this letter also presents a simple method to determine the condition number based on the power method.