The steady-state of the (Normalized) LMS is schur convex

Khaled A. Al-Hujaili; Tareq Y. Al-Naffouri; Muhammad Moinuddin

doi:10.1109/ICASSP.2016.7472609

The steady-state of the (Normalized) LMS is schur convex

Khaled A. Al-Hujaili, Tareq Y. Al-Naffouri, Muhammad Moinuddin

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

3 Scopus citations

Abstract

In this work, we demonstrate how the theory of majorization and schur-convexity can be used to assess the impact of input-spread on the Mean Squares Error (MSE) performance of adaptive filters. First, we show that the concept of majorization can be utilized to measure the spread in input-regressors and subsequently order the input-regressors according to their spread. Second, we prove that the MSE of the Least Mean Squares Error (LMS) and Normalized LMS (NLMS) algorithms are schur-convex, that is, the MSE of the LMS and the NLMS algorithms preserve the majorization order of the inputs which provide an analytical justification to why and how much the MSE performance of the LMS and the NLMS algorithms deteriorate as the spread in input increases. © 2016 IEEE.

Original language	English (US)
Title of host publication	2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	4900-4904
Number of pages	5
ISBN (Print)	9781479999880
DOIs	https://doi.org/10.1109/ICASSP.2016.7472609
State	Published - Jun 24 2016

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01

Access to Document

10.1109/ICASSP.2016.7472609

Cite this

@inproceedings{11b7bddc5717416690545073039dd34f,

title = "The steady-state of the (Normalized) LMS is schur convex",

abstract = "In this work, we demonstrate how the theory of majorization and schur-convexity can be used to assess the impact of input-spread on the Mean Squares Error (MSE) performance of adaptive filters. First, we show that the concept of majorization can be utilized to measure the spread in input-regressors and subsequently order the input-regressors according to their spread. Second, we prove that the MSE of the Least Mean Squares Error (LMS) and Normalized LMS (NLMS) algorithms are schur-convex, that is, the MSE of the LMS and the NLMS algorithms preserve the majorization order of the inputs which provide an analytical justification to why and how much the MSE performance of the LMS and the NLMS algorithms deteriorate as the spread in input increases. {\textcopyright} 2016 IEEE.",

author = "Al-Hujaili, {Khaled A.} and Al-Naffouri, {Tareq Y.} and Muhammad Moinuddin",

note = "KAUST Repository Item: Exported on 2020-10-01",

year = "2016",

month = jun,

day = "24",

doi = "10.1109/ICASSP.2016.7472609",

language = "English (US)",

isbn = "9781479999880",

pages = "4900--4904",

booktitle = "2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)",

publisher = "Institute of Electrical and Electronics Engineers (IEEE)",

}

The steady-state of the (Normalized) LMS is schur convex. / Al-Hujaili, Khaled A.; Al-Naffouri, Tareq Y.; Moinuddin, Muhammad.
2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Institute of Electrical and Electronics Engineers (IEEE), 2016. p. 4900-4904.

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

TY - GEN

T1 - The steady-state of the (Normalized) LMS is schur convex

AU - Al-Hujaili, Khaled A.

AU - Al-Naffouri, Tareq Y.

AU - Moinuddin, Muhammad

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2016/6/24

Y1 - 2016/6/24

N2 - In this work, we demonstrate how the theory of majorization and schur-convexity can be used to assess the impact of input-spread on the Mean Squares Error (MSE) performance of adaptive filters. First, we show that the concept of majorization can be utilized to measure the spread in input-regressors and subsequently order the input-regressors according to their spread. Second, we prove that the MSE of the Least Mean Squares Error (LMS) and Normalized LMS (NLMS) algorithms are schur-convex, that is, the MSE of the LMS and the NLMS algorithms preserve the majorization order of the inputs which provide an analytical justification to why and how much the MSE performance of the LMS and the NLMS algorithms deteriorate as the spread in input increases. © 2016 IEEE.

AB - In this work, we demonstrate how the theory of majorization and schur-convexity can be used to assess the impact of input-spread on the Mean Squares Error (MSE) performance of adaptive filters. First, we show that the concept of majorization can be utilized to measure the spread in input-regressors and subsequently order the input-regressors according to their spread. Second, we prove that the MSE of the Least Mean Squares Error (LMS) and Normalized LMS (NLMS) algorithms are schur-convex, that is, the MSE of the LMS and the NLMS algorithms preserve the majorization order of the inputs which provide an analytical justification to why and how much the MSE performance of the LMS and the NLMS algorithms deteriorate as the spread in input increases. © 2016 IEEE.

UR - http://hdl.handle.net/10754/621365

UR - http://ieeexplore.ieee.org/document/7472609/

UR - http://www.scopus.com/inward/record.url?scp=84973309348&partnerID=8YFLogxK

U2 - 10.1109/ICASSP.2016.7472609

DO - 10.1109/ICASSP.2016.7472609

M3 - Conference contribution

SN - 9781479999880

SP - 4900

EP - 4904

BT - 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -

The steady-state of the (Normalized) LMS is schur convex

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this