The NLMS is Steady-State Schur-Convex

Anum Ali; Muhammad Moinuddin; Tareq Y. Al-Naffouri

doi:10.1109/LSP.2021.3055460

The NLMS is Steady-State Schur-Convex

Anum Ali, Muhammad Moinuddin, Tareq Y. Al-Naffouri

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this work, we study the impact of input-spread on the steady-state excess mean squared error (EMSE) of the normalized least mean squares (NLMS) algorithm. First, we use the concept of majorization to order the input-regressors according to their spread. Second, we use Schur-convexity to show that the majorization order of the input-regressors is preserved in the EMSE. Effectively, we provide an analytical justification of the increase in steady-state EMSE as the input-spread increases.

Original language	English (US)
Pages (from-to)	1-1
Number of pages	1
Journal	IEEE Signal Processing Letters
DOIs	https://doi.org/10.1109/LSP.2021.3055460
State	Published - 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-02-01
Acknowledgements: This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant no. (DF-211-135-1441). The authors, therefore, acknowledge with thanks DSR technical and financial supports.

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title = "The NLMS is Steady-State Schur-Convex",

abstract = "In this work, we study the impact of input-spread on the steady-state excess mean squared error (EMSE) of the normalized least mean squares (NLMS) algorithm. First, we use the concept of majorization to order the input-regressors according to their spread. Second, we use Schur-convexity to show that the majorization order of the input-regressors is preserved in the EMSE. Effectively, we provide an analytical justification of the increase in steady-state EMSE as the input-spread increases.",

author = "Anum Ali and Muhammad Moinuddin and Al-Naffouri, {Tareq Y.}",

note = "KAUST Repository Item: Exported on 2021-02-01 Acknowledgements: This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant no. (DF-211-135-1441). The authors, therefore, acknowledge with thanks DSR technical and financial supports.",

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AU - Moinuddin, Muhammad

AU - Al-Naffouri, Tareq Y.

N1 - KAUST Repository Item: Exported on 2021-02-01 Acknowledgements: This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant no. (DF-211-135-1441). The authors, therefore, acknowledge with thanks DSR technical and financial supports.

PY - 2021

Y1 - 2021

N2 - In this work, we study the impact of input-spread on the steady-state excess mean squared error (EMSE) of the normalized least mean squares (NLMS) algorithm. First, we use the concept of majorization to order the input-regressors according to their spread. Second, we use Schur-convexity to show that the majorization order of the input-regressors is preserved in the EMSE. Effectively, we provide an analytical justification of the increase in steady-state EMSE as the input-spread increases.

AB - In this work, we study the impact of input-spread on the steady-state excess mean squared error (EMSE) of the normalized least mean squares (NLMS) algorithm. First, we use the concept of majorization to order the input-regressors according to their spread. Second, we use Schur-convexity to show that the majorization order of the input-regressors is preserved in the EMSE. Effectively, we provide an analytical justification of the increase in steady-state EMSE as the input-spread increases.

UR - http://hdl.handle.net/10754/667111

UR - https://ieeexplore.ieee.org/document/9340273/

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DO - 10.1109/LSP.2021.3055460

M3 - Article

SN - 1558-2361

SP - 1

EP - 1

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

ER -

The NLMS is Steady-State Schur-Convex

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