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Blind 2-microphone acoustic noise reduction algorithms using efficient variable step-size adapted by minimizing the intercorrelation function

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ANALOG INTEGRATED CIRCUITS AND SIGNAL PROCESSING 2025年第2期123卷 1-18页

作者： Bendoumia, Redha Blida 1 Univ Dept Elect DIC Lab Blida Algeria

Recent advancements in adaptive noise signal reduction have utilized 2-microphones adaptive algorithms. Specifically, the normalized form of least-mean-square algorithm (NLMS) with fixed-step-size parameters (FS) has been combined with direct-and-recursive structures of source separation. Compared to conventional one-microphone methods, these combinations provide superior speech quality. However, the main limitation of these 2-microphones adapting algorithms (Direct combination: Forward NLMS and Recursive combination: Backward NLMS) lies in their poor steady state regime with large FS value, while small step-sizes values result a slow speed of convergence. To address these issues, we propose a new variable step-size (VS) approach in this study, based on minimizing the intercorrelation function in the time domain for the basic FNLMS and BNLMS algorithms. Our approach is proposed exactly to determine an optimal value of VS parameters by minimizing the intercorrelation between the enhanced signal and the noisy microphone signals. These methods improve steady state values and convergence speed at the same time. The proposed 2-microphones adapting algorithms were evaluated through simulations conducted in high-noise environments, using the system of mismatch criterion and estimation of output segmental signal-to-noise ratio ones. The comparative simulations results confirmed that our algorithms outperform FS algorithms in terms of steady state values and convergence speed.

关键词： variable step-size Intercorrelation function Output SegSNR Adaptive filtering algorithm Speech quality

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variable step-size IMPLICIT-EXPLICIT LINEAR MULTIstep METHODS FOR TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS

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Journal of Computational Mathematics 2008年第6期26卷 838-855页

作者： DongWang Steven J. Ruuth Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign B231 Newmark Civil Engineering Laboratory Urbana IL 61801 USA Department of Mathematics Simon Fraser University Burnaby BC Canada V5A 1S6

Implicit-explicit （IMEX） linear multistep methods are popular techniques for solving partial differential equations （PDEs） with terms of different types. While fixed timestep versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise in general situations where the temporal smoothness of the solution changes. In this paper we consider easily implementable variable step-size implicit-explicit （VSIMEX） linear multistep methods for time-dependent PDEs. Families of order-p, pstep VSIMEX schemes are constructed and analyzed, where p ranges from 1 to 4. The corresponding schemes are simple to implement and have the property that they reduce to the classical IMEX schemes whenever constant time step-sizes are imposed. The methods are validated on the Burgers＇ equation. These results demonstrate that by varying the time step-size, VSIMEX methods can outperform their fixed time step counterparts while still maintaining good numerical behavior.

关键词： Implicit-explicit (IMEX) linear multistep methods variable step-size Zero-stability Burgers' equation.

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variable step-size Constant Modulus Algorithm Employing Fuzzy Logic Controller

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WIRELESS PERSONAL COMMUNICATIONS 2010年第2期54卷 237-250页

作者： Ozen, A. Kaya, I. Soysal, B. Karadeniz Tech Univ Dept Elect & Elect Engn Trabzon Turkey Ataturk Univ Dept Elect & Elect Engn Erzurum Turkey

The Constant Modulus Algorithm (CMA), although it is the most commonly used blind equalization technique, converges very slowly. The convergence rate of the CMA is quite sensitive to the adjustment of the step size parameter used in the update equation as in the Least Mean Squares (LMS) algorithm. A novel approach in adjusting the step size of the CMA using the fuzzy logic based outer loop controller is presented in this paper. Inspired by successful works on the variable step size LMS algorithms, this work considers designing a training trajectory that it overcomes hurdles of an adaptive blind training via controlling the level of error power (LOEP) and trend of error power (TOEP) and then obtains a more robust training process for the simple CMA algorithm. The controller design involves with optimization of training speed and convergence rate using experience based linguistic rules that are generated as a part of FLC. The obtained results are compared with well-known versions of CMA;Conventional CMA, Normalized-CMA [Jones, IEEE conference record of the twenty-ninth asilomar conference on signals, systems and computers (Vol. 1, pp. 694-697), 1996], Modified-CMA [Chahed, et al., Canadian conference on electrical and computer engineering (Vol. 4, pp. 2111-2114), 2004], Soft Decision Directed-CMA (Chen, IEE Proceedings of Visual Image Signal Processing, 150, 312-320, 2003) for performance measure and validation.

关键词： Blind training CMA variable step-size Fuzzy logic control Linguistic rule Manual optimization

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variable step-size normalized LMS algorithm by approximating correlation matrix of estimation error

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SIGNAL PROCESSING 2010年第9期90卷 2792-2799页

作者： Cho, Hyeonwoo Kim, Sang Woo Pohang Univ Sci & Technol Div Elect & Comp Engn Pohang 790784 Gyungbuk South Korea

In this letter, we propose a variable step-size normalized least mean square (NLMS) algorithm. We study the relationship among the NLMS, recursive least square and Kalman filter algorithms. Based on the relationship, we derive an equation to determine the step-size of NLMS algorithm at each time instant. In steady state, the convergence of the proposed algorithm is verified by using the equation, which describes the relationship among the mean-square error, excess mean-square error, and measurement noise variance. Through computer simulation results, we verify the performance of the proposed algorithm and the change in the variable step-size over iterations. (C) 2010 Elsevier B.V. All rights reserved.

关键词： variable step-size Normalized least mean square algorithm Kalman filter Recursive least square State-space equation

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variable step-size MLMS Algorithm for Digital Predistortion in Wideband OFDM Systems

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IEEE TRANSACTIONS ON CONSUMER ELECTRONICS 2015年第1期61卷 10-15页

作者： Zhang, F. Wang, Y. Ai, B. Xidian Univ State Key Lab ISN Xian 710071 Peoples R China Beijing Jiaotong Univ State Key Lab RTCS Beijing 100044 Peoples R China

As one of the most promising linearization techniques, adaptive Digital Predistortion (PD) has been widely utilized in modern wireless communication systems for improving the efficiency of Power Amplifier (PA). In view of the non-stationary signal environment for the wideband PAs, an efficient indirect learning adaptive PD is proposed in the paper based on the Memory Polynomial Model (MPM). The coefficients of the proposed PD can be effectively identified by the Modified Least Mean Square (MLMS) learning algorithm. In addition, more stable convergence and lower steady-state error can be achieved simultaneously for the PAs with deep memory effects by adopting the variable step-size parameter. Theoretical analysis results regarding the learning stability, convergence behavior, and selection criteria of initial settings are derived. Simulations demonstrate that MLMS outperforms traditional LMS, Normalized LMS (NLMS), and Generalized Normalized Gradient Descent (GNGD) algorithms in terms of the Normalized Mean Square Error (NMSE) and out-of-band Power Spectral Density (PSD) under the noisy feedback condition for the wideband PAs1.

关键词： Digital predistortion Power amplifier variable step-size Modified least mean square

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variable step-size Sparsity-Induced Augmented Complex-Valued NLMS Algorithm

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2021年第9期40卷 4686-4695页

作者： Zong, Yulian Ni, Jingen Suzhou Univ Sch Elect & Informat Engn Suzhou 215006 Peoples R China

The widely linear model has attracted much attention due to its good features for non-circular adaptive signal processing in recent years. In this paper, a sparsity-induced augmented complex-valued NLMS algorithm is proposed to promote the performance of the adaptive filter for estimating sparse systems, which is established by incorporating the l(0)-norm regularization into the squared error normalized by the input vector. To address the problem of trade-off between fast convergence rate and low steady-state misalignment, we minimize the variance of the a posteriori error to derive an optimal step-size and then some practical problems are considered. Simulation results are provided to verify the superior performance of the proposed algorithm.

关键词： Widely linear model Sparse system variable step-size Complex-valued adaptive filter NLMS

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variable step-size NLMS and affine projection algorithms

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IEEE SIGNAL PROCESSING LETTERS 2004年第2期11卷 132-135页

作者： Shin, HC Sayed, AH Song, WJ Pohang Univ Sci & Technol Div Elect & Comp Engn Pohang South Korea Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90095 USA

This letter proposes two new variable step-size algorithms for normalized least mean square and affine projection. The proposed schemes lead to faster convergence rate and lower mis-adjustment error.

关键词： adaptive filters affine projection algorithm normalized least mean square (NLMS) variable step-size

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variable step-size LMS Algorithm With a Gradient-Based Weighted Average

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IEEE SIGNAL PROCESSING LETTERS 2009年第12期16卷 1043-1046页

作者： Hwang, Jeng-Kuang Li, Yuan-Ping Yuan Ze Univ Dept Commun Engn Chungli 32026 Taiwan Yuan Ze Univ Dept Elect Engn Chungli 32026 Taiwan

This paper proposes a new variable step-size least-mean-square (VSLMS) algorithm with an approach in which a gradient-based weighted average is used to improve the weakness of previous VSLMS for application to unknown channel estimation or system identification in low-SNR or colored input environments. The proposed scheme leads to a faster convergence rate and a lower misadjustment error.

关键词： Adaptive filters channel estimation least-mean-square (LMS) variable step-size

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variable step-size Widely Linear Complex-Valued Affine Projection Algorithm and Performance Analysis

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2020年 68卷 5940-5953页

作者： Shi, Long Zhao, Haiquan Zakharov, Yuriy Chen, Badong Yang, Yaoru Southwest Jiaotong Univ Minist Educ Key Lab Magnet Suspens Technol & Maglev Vehicle Chengdu 610031 Peoples R China Southwest Jiaotong Univ Sch Elect Engn Chengdu 610031 Peoples R China Univ York Dept Elect Engn York N Yorkshire England Xi An Jiao Tong Univ Inst Artificial Intelligence & Robot Xian 710049 Peoples R China

In this paper, a variable step-size widely linear complex-valued affine projection algorithm (VSS-WLCAPA) is proposed for processing noncircular signals. The variable step-size (VSS) is derived by minimizing the power of the augmented noise-free a posteriori error vector, which speeds up the convergence and reduces the steady-state misalignment. By exploiting the evolution of the covariance matrix of the weight error vector, we provide insight into the theoretical behavior of the VSS-WLCAPA algorithm. In the analysis, we take into account the dependency between the weight error vector and the noise vector, which is useful for accuracy of the theoretical prediction. To evaluate the mean step-size, the probability density function of the magnitude of the error is derived by employing polar coordinate transformation. Moreover, a special case when the projection order reduces to one is analysed in detail. The presented theoretical analysis is different from existing methodologies for analyzing affine projection algorithms due to the use of the Kronecker product. Simulation results for system identification scenarios demonstrate the merits of the proposed algorithm and verify the accuracy of the theoretical analysis. Wind prediction experiments support the superiority of the proposed VSS-WLCAPA as well.

关键词： Adaptive filter a posteriori error affine projection covariance matrix polar coordinate transformation probability density function variable step-size widely linear

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variable step-size convex regularized PRLS algorithms

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SIGNAL PROCESSING 2024年 214卷

作者： Wang, Yu Qin, Zhen Tao, Jun Xia, Yili Southeast Univ Sch Informat Sci & Engn Key Lab Underwater Acoust Signal Proc Minist Educ Nanjing 210096 Peoples R China Ohio State Univ Dept Comp Sci & Engn Columbus OH 43210 USA Southeast Univ Sch Informat Sci & Engn Nanjing 210096 Peoples R China Pengcheng Lab Shenzhen 518000 Peoples R China

The proportionate updating (PU) and zero-attracting (ZA) mechanisms have been applied independently in the development of sparsity-aware recursive least squares (RLS) algorithms. Recently, we propose an enhanced l1- proportionate RLS (l1-PRLS) algorithm by combining the PU and ZA mechanisms. The l1-PRLS employs a fixed step size which trades off the transient (initial convergence) and steady-state performance. In this letter, the l1- PRLS is improved in two aspects: first, we replace the l1 norm penalty by a general convex regularization (CR) function to have the CR-PRLS algorithm;second, we further introduce the variable step-size (VSS) technique to the CR-PRLS, leading to the VSS-CR-PRLS algorithm. Theoretical and numerical results were provided to corroborate the superiority of the improved algorithm.

关键词： Sparse RLS algorithms Proportionate updating Zero-attracting variable step-size

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