
For FullText PDF, please login, if you are a member of IEICE,
or go to Pay Per View on menu list, if you are a nonmember of IEICE.

A New Formula to Compute the NLMS Algorithm at a Computational Complexity of O(2N)
Kiyoshi NISHIYAMA Masahiro SUNOHARA Nobuhiko HIRUMA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E102A
No.11
pp.15451549 Publication Date: 2019/11/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E102.A.1545
Type of Manuscript: LETTER Category: Digital Signal Processing Keyword: NLMS algorithm, LMS algorithm, adaptive filter, H_{∞} filter, fast H_{∞} filter, system identification,
Full Text: PDF(582KB)>>
Summary:
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 slidingwindow 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 CNLMS algorithm. The derivation of the CNLMS 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 CNLMS algorithm is verified using simulations.

