KAUST DepartmentElectrical Engineering Program
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AbstractIn this work, we demonstrate how the theory of majorization and schur-convexity can be used to assess the impact of input-spread on the Mean Squares Error (MSE) performance of adaptive filters. First, we show that the concept of majorization can be utilized to measure the spread in input-regressors and subsequently order the input-regressors according to their spread. Second, we prove that the MSE of the Least Mean Squares Error (LMS) and Normalized LMS (NLMS) algorithms are schur-convex, that is, the MSE of the LMS and the NLMS algorithms preserve the majorization order of the inputs which provide an analytical justification to why and how much the MSE performance of the LMS and the NLMS algorithms deteriorate as the spread in input increases. © 2016 IEEE.
CitationAl-Hujaili KA, Al-Naffouri TY, Moinuddin M (2016) The steady-state of the (Normalized) LMS is schur convex. 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Available: http://dx.doi.org/10.1109/ICASSP.2016.7472609.
Conference/Event name41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016