Convergence and steady-state analysis of a variable step-size normalized LMS algorithm

Active noise control (ANC) is used to reduce undesirable noise, particularly at low frequencies. There are many algorithms based on the least mean square (LMS) algorithm, such as the filtered-x LMS (FxLMS) algorithm, which have been widely used for ANC systems. However, the LMS algorithm cannot balance convergence speed and steady-state error due to the fixed step size and tap length. Accordingly, in this article, two improved LMS algorithms, namely, the iterative variable step-size LMS (IVS-LMS) and the variable tap-length LMS (VT-LMS), are proposed for active vehicle interior noise control. The interior noises of a sample vehicle are measured and thereby their frequency characteristics. Results show that the sound energy of noise is concentrated within a low-frequency range below 1000 Hz. The classical LMS, IVS-LMS and VT-LMS algorithms are applied to the measured noise signals. Results further suggest that the IVS-LMS and VT-LMS algorithms can better improve algorithmic performance for convergence speed and steady-state error compared with the classical LMS. The proposed algorithms could potentially be incorporated into other LMS-based algorithms (like the FxLMS) used in ANC systems for improving the ride comfort of a vehicle.

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A Variable Step Size LMS Based on Sparsity for System Identification

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.475-476.1060 ◽

2013 ◽

Vol 475-476 ◽

pp. 1060-1066

Author(s):

X.Q. Chen ◽

Hua Ju ◽

Wei Fan ◽

W.G. Huang ◽

Z.K. Zhu

Keyword(s):

Steady State ◽

System Identification ◽

Lms Algorithm ◽

Variable Step Size ◽

Least Mean Square ◽

Step Size ◽

Practical Applications ◽

Variable Step ◽

Size Adjustment ◽

State Error

In many practical applications, the impulse responses of the unknown system are sparse. However, the standard Least Mean Square (LMS) algorithm does not make full use of the sparsity, and the general sparse LMS algorithms increase steady-state error because of giving much large attraction to the small factor. In order to improve the performance of sparse system identification, we propose a new algorithm which introduces a variable step size method into the Reweighted Zero-Attracting LMS (RZALMS) algorithm. The improved algorithm, whose step size adjustment is controlled by the instantaneous error, is called Variable step size RZALMS (V-RZALMS). The variable step size leads to yielding smaller steady-state error on the premise of higher convergent speed. Moreover, the sparser the system is, the better the V-RZALMS performs. Three different experiments are implemented to validate the effectiveness of our new algorithm.

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A New Variable Step-Size NLMS Algorithm and its Performance Evaluation in Echo Cancelling Applications

Journal of Applied Research and Technology ◽

10.22201/icat.16656423.2011.9.03.425 ◽

2011 ◽

Vol 9 (03) ◽

Cited By ~ 3

Author(s):

F. M. Casco-Sánchez ◽

R. C. Medina-Ramírez ◽

M. López-Guerrero

Keyword(s):

Cross Correlation ◽

Echo Cancellation ◽

Lms Algorithm ◽

Variable Step Size ◽

Step Size ◽

Filter Output ◽

Nlms Algorithm ◽

Variable Step ◽

Size Adjustment ◽

Normalized Lms

In this work we introduce a variable step-size normalized LMS algorithm for adaptive echo cancellation in a FIRstructure. In the proposed scheme, the step-size adjustment is controlled by using the square of the cross-correlationbetween the squared output error and the adaptive filter output. The proposed algorithm (that we call VSSSC aftervariable step size based on the squared cross-correlation) was evaluated using white noise and speech signals.Simulation results show that our proposal achieves better performance than similar algorithms in single and doubletalk. The proposed algorithm can be used in a number of applications such as in echo reduction for long-haul voicecommunications.

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Steady state performance analysis of an approximately optimal variable step size LMS algorithm

2008 3rd IEEE Conference on Industrial Electronics and Applications ◽

10.1109/iciea.2008.4582744 ◽

2008 ◽

Cited By ~ 3

Author(s):

Li Ning ◽

Zhang Yonggang ◽

Hao Yanling

Keyword(s):

Steady State ◽

Performance Analysis ◽

Lms Algorithm ◽

Variable Step Size ◽

Step Size ◽

Variable Step ◽

Steady State Performance

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A Novel Variable Step Size LMS Algorithm Based on Modified Hyperbolic Tangent and Its Simulation

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.490-495.1426 ◽

2012 ◽

Vol 490-495 ◽

pp. 1426-1430 ◽

Cited By ~ 1

Author(s):

Fu Qing Tian ◽

Rong Luo

Keyword(s):

Steady State ◽

Noise Suppression ◽

Lms Algorithm ◽

Variable Step Size ◽

Hyperbolic Tangent ◽

Step Size ◽

Low Snr ◽

Variable Step ◽

Overall Performance ◽

Simulation Results

In the paper, a new variable step size LMS algorithm based on modified hyperbolic tangent is presented. In the algorithm, the step size is adjusted by the estimation of the autocorrelation between and .The algorithm introduces the compensation monomial to improve the convergence and the parameters to improve the shape and bottom characteristic of hyperbolic tangent. Therefore, the algorithm has faster convergence, better performance of noise suppression，lower steady state error and misadjustment. The theoretical analysis and simulation results all show that the overall performance of the new algorithm exceeds greatly some existent others under low SNR condition.

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Simulation Realization of Adaptive Filtering Based on a Normalized LMS Algorithm

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.373-375.1159 ◽

2013 ◽

Vol 373-375 ◽

pp. 1159-1163

Author(s):

Ya Feng Li ◽

Zi Wei Zheng

Keyword(s):

Adaptive Filtering ◽

Notch Filter ◽

Lms Algorithm ◽

Variable Step Size ◽

Step Size ◽

Filtering Algorithm ◽

Adaptive Notch Filter ◽

Variable Step ◽

Simulation Results ◽

Normalized Lms

This paper presents the new algorithm which is an improved normalized variable step size LMS adaptive filtering algorithm. A normalized LMS algorithm with variable step size iterative formula is deduced and at the same time the simulation results prove that the new algorithm has good performance. The LMS adaptive filtering algorithm has been widely used in many applications such as system identification, noise cancellation and the adaptive notch filter ,the paper analyses the application and implement the simulation by matlab. the result shows the proposed algorithm has been applied well.

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