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.
Bibliographical noteKAUST 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.