Variable step-size NLMS algorithm with oblique projection

For the case when the input signals are highly correlated, this paper introduces a innovative update form of the normalized least-mean-squares (NLMS) algorithm, where the concept of normalization is taken from the oblique projection. By supplying a lemma that the trace norm of any square matrix is preserved under the congruence transformation via the unitary matrices, this paper designs optimal variable step sizes minimizing the trace norm of the estimation-error covarinace matrices. Simuations confirms that the proposed algorithm outperforms exiting algorithms.