Stochastic analysis of the LMS algorithm with a saturation nonlinearity following the adaptive filter output

Costa, Márcio Holsbach; Bermudez, J.C.M.; Bershad, N.J.

doi:10.1109/78.928691

Cited by 41 publications

(46 citation statements)

References 17 publications

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“…The results obtained in [5] agreed with the observations of several authors in ANC area [2][3][4]6]. The possibility of quantifying the nonlinear effects on the performance surface motivated the search for new algorithms that could be capable of overcoming the poor steady-state performance of the LMS algorithm in a nonlinear environment.…”

Section: I Introductionsupporting

confidence: 93%

“…A recent work [5] studied the behavior of the LMS algorithm subjected to a nonlinear influence at the adaptive filter output. It was demonstrated that the mean converged weights corres pond to a biased solution with respect to the minimum of the MSE surface.…”

Section: I Introductionmentioning

confidence: 99%

“…Such nonlinearities can severely impair the adaptive algorithm performance in minimizing a cost function, usually the mean square output error (MSE) [5][6][7].…”

Section: I Introductionmentioning

confidence: 99%

“…Several adaptive modeling and control systems present saturation-type nonlinearities in the adaptive filter path [1][2][3][4][5][6]. Such nonlinearities can severely impair the adaptive algorithm performance in minimizing a cost function, usually the mean square output error (MSE) [5][6][7].…”

Section: I Introductionmentioning

confidence: 99%

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Optimum leakage factor for the MOV-LMS algorithm in nonlinear modeling and control systems

Bermudez

Costa

2002

IEEE International Conference on Acoustics Speech and Signal Processing

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This work studies the Minimum Output Variance Least Mean Square Estimator (MOV -LMS) when the output of the adaptive filter is constrained by a saturation-type nonlinearity. This situation is typical in several adaptive modeling and control systems where the associated hardware and transducers have a finite power handling capability. Analytical expressions are obtained for the behaviors of the mean weight vector and for mean square error for Gaussian inputs and slow learning. The optimum leakage factor is detenn ined, which provides an unbiased solution to the associated nonlinear mean square estimation. problem. Monte Carlo simulations show excellent agreemen t between model and simulations for transient and steady-state conditions. The results in this paper demonstrate that the MOV-LMS algorithm with the optimized leakage factor has a superior steady-state performance than the LMS algorithm in the studied nonlinear environment I, INTRODUCTIONSeveral adaptive modeling and control systems present saturation-type nonlinearities in the adaptive filter path [1-6]. Such nonlinearities can severely impair the adaptive algorithm performance in minimizing a cost function, usually the mean square output error (MSE) [5][6][7].Among the various existing adaptive solutions, the family of stochastic gradient-based algorithms (the LMS family) is a common choice due to its simplicity and robustness. Several works have studied the behavior of the LMS and its family in modeling and control applications, such as active noise control (ANC) [I]. A common assumption, for simplicity of analysis, is that the system is purely linear. However, it is well known that the associated hardware (power amplifiers, piezoelectric transducers and loudspeakers) is an important source of nonlinearities [2][3][4]. In order to avoid nonlinear distortions, the system is frequently overdesigned to keep signal power sufficiently low compared to the saturation levels.A recent work [5] studied the behavior of the LMS algorithm subjected to a nonlinear influence at the adaptive filter output. It was demonstrated that the mean converged weights corres pond to a biased solution with respect to the minimum of the MSE surface. This bias is a multiplicative scalar, which is a function of the system's degree of nonlinearity.The results obtained in [5] agreed with the observations of several authors in ANC area [2-4,6]. The possibility of quantifying the nonlinear effects on the performance surface motivated the search for new algorithms that could be capable of overcoming the poor steady-state performance of the LMS algorithm in a nonlinear environment. Such a solution would allow the use of cheaper amplifiers and transducers without a significant performance loss, therefore reducing implementation costs.Reference [7] proposed a new stochastic gradient-based algorithm, referred to here as the Nonlinear True-LMS algorithm. This algorithm is capable of reaching the minimum of the MSE surface, since the system's nonlinearity is incorporated in the weight update equ...

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Section: I Introductionsupporting

confidence: 93%

Section: I Introductionmentioning

confidence: 99%

“…Such nonlinearities can severely impair the adaptive algorithm performance in minimizing a cost function, usually the mean square output error (MSE) [5][6][7].…”

Section: I Introductionmentioning

confidence: 99%

Section: I Introductionmentioning

confidence: 99%

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Optimum leakage factor for the MOV-LMS algorithm in nonlinear modeling and control systems

Bermudez

Costa

2002

IEEE International Conference on Acoustics Speech and Signal Processing

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“…nn This approximation has been successfully applied in References [4,5]. In this section, we show that the MOV-FXLMS algorithm leads to a biased steady-state mean weight solution.…”

Section: The Mean Weight Behaviour In a Non-linear Environment}analysismentioning

confidence: 99%

A new adaptive algorithm for reducing non‐linear effects from saturation in active noise control systems

Costa

Bermudez

2004

Adaptive Control & Signal

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Adaptive algorithms applied to active noise and vibration control are frequently designed for maximum performance in linear environments. In many cases, non-linear effects can severely impair the adaptive algorithm performance. One of the most common non-linear effects is saturation, which can occur at the electronic circuits that drive the acoustic or mechanical transducers. An effective solution to mitigate such non-linear distortions is to embed an automatic control of the non-linear effects within the adaptive algorithm. Algorithms that use this approach are called minimum effort adaptive filters. This work presents a new minimum effort algorithm (MOV-FXLMS), based on the minimum output variance least mean square estimator, for situations in which the influence of the secondary path cannot be neglected and its output is constrained by a saturation non-linearity. Analytical expressions are obtained for the behaviour of the mean weight vector and for the mean square error for Gaussian inputs and slow learning. Monte Carlo simulations show excellent agreement with the predictions of the theoretical model. The optimum penalty factor (a design parameter of the MOV-FXLMS algorithm) is determined as a function of the system's degree of non-linearity. The new algorithm provides an unbiased solution to the associated nonlinear mean square estimation problem for small estimation errors of the secondary path and degree of non-linearity. Robustness of the algorithm's performance to such errors is addressed. The new algorithm is compared with the conventional FXLMS algorithm for performance.

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NLFXLMS and THF‐NLFXLMS Algorithms for Wiener‐Hammerstein Nonlinear Active Noise Control

Srazhidinov

Kamil

Noor

2017

Asian Journal of Control

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Nonlinear Filtered‐X LMS (NLFXLMS) is an indirect adaptive control algorithm for nonlinear active noise control (NANC) system. The algorithm has been developed for both Hammerstein and Wiener secondary paths where the nonlinearity is represented by scaled error function (SEF) and tangential hyperbolic function (THF). NLFXLMS algorithm is limited in practical application because the degree of nonlinearity has to be known in advance. This limitation leads to the development of the THF‐NLFXLMS algorithm where the degree of nonlinearity is estimated by modelling the secondary path. In this work, the NLFXLMS and THF‐NLFXLMS are extended to Wiener‐Hammerstein system. The performance of the proposed Wiener‐Hammerstein THF‐NLFXLMS is compared with NLFXLMS algorithm which is considered as the benchmark and second order Volterra algorithm of comparable computational complexity. Simulation results show that the THF‐NLFXLMS has a similar performance to NLFXLMS and outperforms the second order Volterra algorithm as the system becomes more nonlinear.

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Stochastic analysis of the LMS algorithm with a saturation nonlinearity following the adaptive filter output

Cited by 41 publications

References 17 publications

Optimum leakage factor for the MOV-LMS algorithm in nonlinear modeling and control systems

Optimum leakage factor for the MOV-LMS algorithm in nonlinear modeling and control systems

A new adaptive algorithm for reducing non‐linear effects from saturation in active noise control systems

NLFXLMS and THF‐NLFXLMS Algorithms for Wiener‐Hammerstein Nonlinear Active Noise Control

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