TY - JOUR
T1 - The NLMS is Steady-State Schur-Convex
AU - Ali, Anum
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/
U2 - 10.1109/LSP.2021.3055460
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 -