Mean square deviation analysis of LMS and NLMS algorithms with white reference inputs

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)20-26
Journal / PublicationSignal Processing
Publication statusPublished - 1 Feb 2017


This paper investigates the mean square performance of the least mean square (LMS) and normalized LMS (NLMS) algorithms with white reference inputs. Their closed-form mean square deviation (MSD) expressions for the transient and steady-state regimes are derived. Additionally, bounds on the step-size which guarantee mean square stability are given. It is found that the step-size bound and transient behavior of the LMS and the steady-state MSD of the NLMS depend on the kurtosis of the input signal. Convergence rates and steady-state MSDs of the two algorithms are then compared, which shows that the normalized variant with a large step-size would offer faster convergence rate than the LMS scheme. However, when small step-sizes are employed, the LMS achieves lower steady-state MSD than the NLMS at the same convergence rate.

Research Area(s)

  • Kurtosis, LMS, NLMS, Steady-state, Step-size bound