A unifying approach to the derivation of the class of PNLMS algorithms

Beth Jelfs; Danilo P. Mandic; Andrzej Cichocki

doi:10.1109/ICDSP.2007.4288512

A unifying approach to the derivation of the class of PNLMS algorithms

Beth Jelfs^*, Danilo P. Mandic, Andrzej Cichocki

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Citations (Scopus)

Abstract

A unifying approach to the derivation of the class of proportionate normalised least mean square (PNLMS) algorithms is provided. This is an important class of algorithms where the two most used algorithms are introduced empirically. It is shown that it is possible to derive PNLMS algorithms as a result of an optimisation procedure. This is achieved in a rigorous way, starting from the standard LMS through to the PNLMS with the "sparsification" factor in both the numerator and denominator of the weight update. The proposed approach is generic and also applies to other LMS types of adaptive algorithms. Simulations on benchmark sparse impulse responses support the approach.

Original language	English
Title of host publication	2007 15th International Conference on Digital Signal Processing, DSP 2007
Pages	35-38
Number of pages	4
DOIs	https://doi.org/10.1109/ICDSP.2007.4288512
Publication status	Published - 2007
Externally published	Yes

Keywords

LMS
Normalised LMS (NLMS)
Proportionate NLMS (PNLMS)

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering

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10.1109/ICDSP.2007.4288512

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title = "A unifying approach to the derivation of the class of PNLMS algorithms",

abstract = "A unifying approach to the derivation of the class of proportionate normalised least mean square (PNLMS) algorithms is provided. This is an important class of algorithms where the two most used algorithms are introduced empirically. It is shown that it is possible to derive PNLMS algorithms as a result of an optimisation procedure. This is achieved in a rigorous way, starting from the standard LMS through to the PNLMS with the {"}sparsification{"} factor in both the numerator and denominator of the weight update. The proposed approach is generic and also applies to other LMS types of adaptive algorithms. Simulations on benchmark sparse impulse responses support the approach.",

keywords = "LMS, Normalised LMS (NLMS), Proportionate NLMS (PNLMS)",

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year = "2007",

doi = "10.1109/ICDSP.2007.4288512",

language = "English",

isbn = "1424408822",

pages = "35--38",

booktitle = "2007 15th International Conference on Digital Signal Processing, DSP 2007",

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T1 - A unifying approach to the derivation of the class of PNLMS algorithms

AU - Jelfs, Beth

AU - Mandic, Danilo P.

AU - Cichocki, Andrzej

PY - 2007

Y1 - 2007

N2 - A unifying approach to the derivation of the class of proportionate normalised least mean square (PNLMS) algorithms is provided. This is an important class of algorithms where the two most used algorithms are introduced empirically. It is shown that it is possible to derive PNLMS algorithms as a result of an optimisation procedure. This is achieved in a rigorous way, starting from the standard LMS through to the PNLMS with the "sparsification" factor in both the numerator and denominator of the weight update. The proposed approach is generic and also applies to other LMS types of adaptive algorithms. Simulations on benchmark sparse impulse responses support the approach.

AB - A unifying approach to the derivation of the class of proportionate normalised least mean square (PNLMS) algorithms is provided. This is an important class of algorithms where the two most used algorithms are introduced empirically. It is shown that it is possible to derive PNLMS algorithms as a result of an optimisation procedure. This is achieved in a rigorous way, starting from the standard LMS through to the PNLMS with the "sparsification" factor in both the numerator and denominator of the weight update. The proposed approach is generic and also applies to other LMS types of adaptive algorithms. Simulations on benchmark sparse impulse responses support the approach.

KW - LMS

KW - Normalised LMS (NLMS)

KW - Proportionate NLMS (PNLMS)

UR - http://www.scopus.com/inward/record.url?scp=47649093162&partnerID=8YFLogxK

U2 - 10.1109/ICDSP.2007.4288512

DO - 10.1109/ICDSP.2007.4288512

M3 - Conference contribution

AN - SCOPUS:47649093162

SN - 1424408822

SN - 9781424408825

SP - 35

EP - 38

BT - 2007 15th International Conference on Digital Signal Processing, DSP 2007

ER -

A unifying approach to the derivation of the class of PNLMS algorithms

Abstract

Keywords

ASJC Scopus subject areas

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