Krylov-proportionate adaptive filtering techniques not limited to sparse systems

Research output: Contribution to journalArticle

30 Citations (Scopus)

Abstract

This paper proposes a novel adaptive filtering scheme named the Krylov-proportionate normalized least-mean-square (KPNLMS) algorithm. KPNLMS exploits the benefits (i.e., fast convergence for sparse unknown systems) of the proportionate NLMS algorithm, but its applications are not limited to sparse unknown systems. A set of orthonormal basis vectors is generated from a certain Krylov sequence. It is proven that the unknown system is sparse with respect to the basis vectors in case of fairly uncorrelated input data. Different adaptation gain is allocated to a coefficient of each basis vector, and the gain is roughly proportional to the absolute value of the corresponding coefficient of the current estimate. KPNLMS enjoys i) fast convergence, ii) linear complexity per iteration, and iii) no use of any a priori information. Numerical examples demonstrate significant advantages of the proposed scheme over the reduced-rank method based on the multistage Wiener filter (MWF) and the transform-domain adaptive filter (TDAF) both in noisy and silent situations.

Original languageEnglish
Pages (from-to)927-943
Number of pages17
JournalIEEE Transactions on Signal Processing
Volume57
Issue number3
DOIs
Publication statusPublished - 2009
Externally publishedYes

Fingerprint

Adaptive filtering
Adaptive filters
Mathematical transformations

Keywords

  • Adaptive filtering
  • Krylov subspace
  • Proportionate normalized least-mean-square algorithm

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

Cite this

Krylov-proportionate adaptive filtering techniques not limited to sparse systems. / Yukawa, Masahiro.

In: IEEE Transactions on Signal Processing, Vol. 57, No. 3, 2009, p. 927-943.

Research output: Contribution to journalArticle

@article{2f76da3de08446cfbf93db26554e794a,
title = "Krylov-proportionate adaptive filtering techniques not limited to sparse systems",
abstract = "This paper proposes a novel adaptive filtering scheme named the Krylov-proportionate normalized least-mean-square (KPNLMS) algorithm. KPNLMS exploits the benefits (i.e., fast convergence for sparse unknown systems) of the proportionate NLMS algorithm, but its applications are not limited to sparse unknown systems. A set of orthonormal basis vectors is generated from a certain Krylov sequence. It is proven that the unknown system is sparse with respect to the basis vectors in case of fairly uncorrelated input data. Different adaptation gain is allocated to a coefficient of each basis vector, and the gain is roughly proportional to the absolute value of the corresponding coefficient of the current estimate. KPNLMS enjoys i) fast convergence, ii) linear complexity per iteration, and iii) no use of any a priori information. Numerical examples demonstrate significant advantages of the proposed scheme over the reduced-rank method based on the multistage Wiener filter (MWF) and the transform-domain adaptive filter (TDAF) both in noisy and silent situations.",
keywords = "Adaptive filtering, Krylov subspace, Proportionate normalized least-mean-square algorithm",
author = "Masahiro Yukawa",
year = "2009",
doi = "10.1109/TSP.2008.2009022",
language = "English",
volume = "57",
pages = "927--943",
journal = "IEEE Transactions on Signal Processing",
issn = "1053-587X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "3",

}

TY - JOUR

T1 - Krylov-proportionate adaptive filtering techniques not limited to sparse systems

AU - Yukawa, Masahiro

PY - 2009

Y1 - 2009

N2 - This paper proposes a novel adaptive filtering scheme named the Krylov-proportionate normalized least-mean-square (KPNLMS) algorithm. KPNLMS exploits the benefits (i.e., fast convergence for sparse unknown systems) of the proportionate NLMS algorithm, but its applications are not limited to sparse unknown systems. A set of orthonormal basis vectors is generated from a certain Krylov sequence. It is proven that the unknown system is sparse with respect to the basis vectors in case of fairly uncorrelated input data. Different adaptation gain is allocated to a coefficient of each basis vector, and the gain is roughly proportional to the absolute value of the corresponding coefficient of the current estimate. KPNLMS enjoys i) fast convergence, ii) linear complexity per iteration, and iii) no use of any a priori information. Numerical examples demonstrate significant advantages of the proposed scheme over the reduced-rank method based on the multistage Wiener filter (MWF) and the transform-domain adaptive filter (TDAF) both in noisy and silent situations.

AB - This paper proposes a novel adaptive filtering scheme named the Krylov-proportionate normalized least-mean-square (KPNLMS) algorithm. KPNLMS exploits the benefits (i.e., fast convergence for sparse unknown systems) of the proportionate NLMS algorithm, but its applications are not limited to sparse unknown systems. A set of orthonormal basis vectors is generated from a certain Krylov sequence. It is proven that the unknown system is sparse with respect to the basis vectors in case of fairly uncorrelated input data. Different adaptation gain is allocated to a coefficient of each basis vector, and the gain is roughly proportional to the absolute value of the corresponding coefficient of the current estimate. KPNLMS enjoys i) fast convergence, ii) linear complexity per iteration, and iii) no use of any a priori information. Numerical examples demonstrate significant advantages of the proposed scheme over the reduced-rank method based on the multistage Wiener filter (MWF) and the transform-domain adaptive filter (TDAF) both in noisy and silent situations.

KW - Adaptive filtering

KW - Krylov subspace

KW - Proportionate normalized least-mean-square algorithm

UR - http://www.scopus.com/inward/record.url?scp=61549107173&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=61549107173&partnerID=8YFLogxK

U2 - 10.1109/TSP.2008.2009022

DO - 10.1109/TSP.2008.2009022

M3 - Article

VL - 57

SP - 927

EP - 943

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 3

ER -