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

详细信息    查看全文

• 作者：Sheng Zhang^a ; ^{604266280@qq.com" class="auth_mail" title="E-mail the corresponding author} ; Jiashu Zhang^a ; ^{jszhang@home.swjtu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Hing Cheung So^b ; ¹ ; ^{hcso@ee.cityu.edu.hk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：LMS ; NLMS ; Step-size bound ; Steady-state ; Kurtosis
• 刊名：Signal Processing
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：131
• 期：Complete
• 页码：20-26
• 全文大小：1447 K

文摘

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.