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The NLMS Is Steady-State Schur-Convex
Journal article   Peer reviewed

The NLMS Is Steady-State Schur-Convex

Anum Ali, Muhammad Moinuddin and Tareq Y. Al-Naffouri
IEEE signal processing letters, Vol.28, pp.389-393
2021
DOI: https://doi.org/10.1109/LSP.2021.3055460

Abstract

Adaptive filters Convergence Correlation Eigenvalues and eigenfunctions input-spread majorization mean squared error Schur-convexity Signal processing algorithms Signal to noise ratio Standards Steady-state
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.

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