The NLMS is Steady-State Schur-Convex

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

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 languageEnglish (US)
Pages (from-to)1-1
Number of pages1
JournalIEEE Signal Processing Letters
StatePublished - 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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