On the equivalence of a reduced-complexity recursive power normalization algorithm and the exponential window power estimation

The transform-domain least-mean-square (TD-LMS) algorithm provides significantly faster convergence than the LMS algorithm for coloured input signals. However, a major disadvantage of the TD-LMS algorithm is the large computational complexity arising from the unitary transform and power normalization operations. In this paper we establish the equivalence of a recently proposed recursive power normalization algorithm and the traditional exponential window power estimation algorithm. The proposed algorithm is based on the matrix inversion lemma and is optimized for implementation on a digital signal processor (DSP). It reduces the number of divisions from N to one for a TD-LMS adaptive filter with N coefficients. This provides a significant reduction in computational complexity for DSP implementations. The equivalence of the reduced-complexity algorithm and the exponential window power estimation algorithm is demonstrated in simulation examples.