A New Formula to Compute the NLMS Algorithm at a Computational Complexity of O(2N)

Nobuhiko HIRUMA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A    No.11    pp.1545-1549
Publication Date: 2019/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.1545
Type of Manuscript: LETTER
Category: Digital Signal Processing
NLMS algorithm,  LMS algorithm,  adaptive filter,  H filter,  fast H filter,  system identification,  

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The least mean squares (LMS) algorithm has been widely used for adaptive filtering because of easily implementing at a computational complexity of O(2N) where N is the number of taps. The drawback of the LMS algorithm is that its performance is sensitive to the scaling of the input. The normalized LMS (NLMS) algorithm solves this problem on the LMS algorithm by normalizing with the sliding-window power of the input; however, this normalization increases the computational cost to O(3N) per iteration. In this work, we derive a new formula to strictly perform the NLMS algorithm at a computational complexity of O(2N), that is referred to as the C-NLMS algorithm. The derivation of the C-NLMS algorithm uses the H framework presented previously by one of the authors for creating a unified view of adaptive filtering algorithms. The validity of the C-NLMS algorithm is verified using simulations.