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.
['Sheng Zhang', 'Jiashu Zhang', 'Hing Cheung So']
Mean square deviation analysis of LMS and NLMS algorithms with white reference inputs