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Asymptotic properties of sign algorithms for adaptive filtering

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2003年第9期48卷 1545-1556页

作者： Chen, HF Yin, G Chinese Acad Sci Inst Syst Sci Lab Syst & Control Beijing 100080 Peoples R China Wayne State Univ Dept Math Detroit MI 48202 USA

This paper develops asymptotic properties of a class of sign-error algorithms with expanding truncation bounds for adaptive filtering. Under merely stationary ergodicity and finite second moments of the reference and output signals, and using trajectory-subsequence (TS) method, it is proved that the algorithm convergers almost surely. Then, a mean squares estimate is derived for the estimation error and a suitably scaled sequence of the estimation error is shown to converge to a diffusion process. The scaling factor together with the stationary covariance gives the rate of convergence result. Moreover, an algorithm under mean squares criterion with expanding truncation bounds is also examined. Compared with the existing results in the literature, sufficient conditions for almost sure convergence are much relaxed. A simple example is provided for demonstration purpose.

关键词： almost sure convergence diffusion limit ergodicity expanding truncation rate of convergence sign algorithm

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Proportionate Affine Projection sign algorithms for Network Echo Cancellation

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IEEE TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING 2011年第8期19卷 2273-2284页

作者： Yang, Zengli Zheng, Yahong Rosa Grant, Steven L. Missouri Univ Sci & Technol Dept Elect & Comp Engn Rolla MO 64509 USA

Two proportionate affine projection sign algorithms (APSAs) are proposed for network echo cancellation (NEC) applications where the impulse response is often real-valued with sparse coefficients and long filter length. The proposed proportionate-type algorithms can achieve fast convergence and low steady-state misalignment by adopting a proportionate regularization matrix to the APSA. Benefiting from the characteristics of l(1)-norm optimization, affine projection, and proportionate matrix, the new algorithms are more robust to impulsive interferences and colored input than the proportionate least mean squares (PNLMS) algorithm and the robust proportionate affine projection algorithm (Robust PAPA). The new algorithms also achieve much faster convergence rate in sparse impulse responses than the original APSA and the normalized sign algorithm (NSA). The new algorithms are robust to all types of NEC impulse response with different sparseness without the need to change parameters or estimate the sparseness of the impulse response. The computational complexity of the new algorithms is lower than the affine projection algorithm (APA) family due to the elimination of the matrix inversion.

关键词： Adaptive filter affine projection network echo canceller (NEC) proportionate adaptive algorithm sign algorithm sparse response

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Iterate-averaging sign algorithms for adaptive filtering with applications to blind multiuser detection

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IEEE TRANSACTIONS ON INFORMATION THEORY 2003年第3期49卷 657-671页

作者： Yin, GG Krishnamurthy, V Ion, C Wayne State Univ Dept Math Detroit MI 48202 USA Univ British Columbia Dept Elect & Comp Engn Vancouver BC V6T 1Z4 Canada Univ Melbourne Melbourne Vic Australia

Motivated by the recent developments on iterate averaging of recursive stochastic approximation algorithms and asymptotic analysis of sign-error algorithms for adaptive filtering,. this work develops two-stage sign algorithms for adaptive filtering. The proposed algorithms are based on constructions of a sequence of estimates using large step sizes followed by iterate averaging. Our main effort is devoted to improving the performance of the algorithms by establishing Asymptotic normality of a suitably scaled sequence of the estimation errors. The asymptotic covariance is calculated and shown to be the smallest possible. Hence, the asymptotic efficiency or asymptotic optimality is obtained. Then variants of the algorithm including sign-regressor procedures and constant-step algorithms are studied. The minimal window width of averaging is also dealt with. Finally, iterate-averaging algorithms for blind multiuser detection in direct sequence/code-division multiple-access (DS/CDMA,) systems are proposed and developed, and numerical examples are examined.

关键词： adaptive filtering asymptotic efficiency iterate average rate of convergence sign algorithm

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PROPORTIONATE AFFINE PROJECTION sign algorithmS FOR SPARSE SYSTEM IDENTIFICATION IN IMPULSIVE INTERFERENCE

PROPORTIONATE AFFINE PROJECTION SIGN ALGORITHMS FOR SPARSE S...

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IEEE International Conference on Acoustics, Speech, and signal Processing (ICASSP)

作者： Yang, Zengli Zheng, Yahong Rosa Grant, Steven L. Missouri Univ Sci & Technol Dept Elect & Comp Engn Rolla MO 65409 USA

ISBN: (纸本)9781457705397

Two proportionate affine projection sign algorithms (APSAs) are proposed for system identification applications, such as network echo cancellation (NEC), where the impulse response is often real-valued with sparse coefficients and long filter length. The proposed proportionate-type algorithms can achieve fast convergence and low steady-state misalignment by adopting a proportionate regularization matrix to the APSA. Benefiting from the characteristic of l(1)-norm algorithms, affine projection, and proportionate matrix, the new algorithms are robust to impulsive interferences and colored input, and achieve much faster convergence rate in sparse impulse responses than the original APSA, the normalized sign algorithm (NSA), and the proportionate least mean square (PNLMS) algorithm. The computational complexity of the new algorithms is lower than the affine projection algorithm (APA) family due to elimination of matrix inversion.

关键词： Adaptive filter network echo cancellation (NEC) proportionate adaptive algorithm affine projection algorithm sign algorithm

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A family of normalized dual sign algorithms

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DIGITAL signAL PROCESSING 2021年 110卷 102954-102954页

作者： Zong, Yulian Ni, Jingen Chen, Jie Soochow Univ Sch Elect & Informat Engn Suzhou 215006 Peoples R China Northwestern Polytech Univ Sch Marine Sci & Technol Ctr Intelligent Acoust & Immers Commun Xian 710072 Peoples R China

The classical sign algorithm (SA) has attracted much attention in many applications because of its low computational complexity and robustness against impulsive noise. However, its steady-state mean-square derivation (MSD) is large when a large step-size is used to guarantee a relatively fast convergence rate. To address this problem, the dual sign algorithm (DSA) was developed by using a piecewise cost function in the literature. In this paper a family of normalized DSAs (NDSAs) is proposed to further improve the performance of the DSA in terms of MSD. Specifically, two sparse NDSAs are firstly developed, by using the l(1)-norm and l(0)-norm constraints, respectively;on this basis, some variable step-size algorithms are then proposed based on mean-square a posteriorierror minimization. Finally, simulation results are provided to show the superior performance of our proposed algorithms. (C) 2020 Elsevier Inc. All rights reserved.

关键词： sign algorithm Sparsity Variable step-size Impulsive noise

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sign normalised spline adaptive filtering algorithms against impulsive noise

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signAL PROCESSING 2018年 148卷 234-240页

作者： Liu, Chang Zhang, Zhi Tang, Xiao Dongguan Univ Technol Sch Elect Engn 1 DaXue Rd Dongguan 523808 Peoples R China

In this paper, a sign normalised least mean square algorithm (SNLMS) based on Wiener spline adaptive filter, called SAF-SNLMS, is proposed. The proposed algorithm is derived by minimising the absolute value of the a posteriori error. Moreover, to further improve the convergence performance of the SAF-SNLMS, the variable step-size scheme is introduced. Simulation results demonstrate the SAF-SNLMS and its variable step-size variant obtain more robust performance when compared with the existing spline adaptive filter algorithms in impulsive noise. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Spline adaptive filter Nonlinear adaptive filter sign algorithm Variable step-size

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Two Improved Wavelet Transform Domain LMS sign Adaptive Filter algorithms Against Impulsive Interferences

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CIRCUITS SYSTEMS AND signAL PROCESSING 2021年第2期40卷 958-979页

作者： Abadi, Mohammad Shams Esfand Mesgarani, Hamid Khademiyan, Seyed Mahmoud Shahid Rajaee Teacher Training Univ Fac Elect Engn POB 16785-163 Tehran Iran Shahid Rajaee Teacher Training Univ Dept Appl Math POB 16785-163 Tehran Iran

In this paper, the improved wavelet transform domain least mean squares (IWTDLMS) adaptive algorithm is established. The IWTDLMS algorithm has a faster convergence speed than the conventional WTDLMS for colored input signals. Since the performances of WTDLMS and IWTDLMS are degraded in impulsive noise interference, the IWTDLMS sign algorithm (IWTDLMS-SA) is proposed. In comparison with IWTDLMS, the IWTDLMS-SA has lower computational complexity. In order to improve the performance of IWTDLMS-SA, the variable step-size IWTDLMS-SA (VSS-IWTDLMS-SA) is introduced. TheVSS-IWTDLMS-SA is derived by minimizing the l(1)-norm of the a posteriori error vector. To increase the tracking ability of the VSS-IWTDLMS-SA, the modified VSS-IWTDLMS-SA (MVSS-IWTDLMS-SA)is presented. The simulation results demonstrate that the proposed algorithms have a faster convergence rate and lower misadjustment than the conventional WTDLMS. The robustness feature of the IWTDLMS-SA, VSS-IWTDLMS-SA, and MVSS-IWTDLMS-SA against impulsive noises is also verified through several experiments in a system identification setup.

关键词： Adaptive filters sign algorithm Variable step size Wavelet transform Impulsive noise interference

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Two variants of the sign subband adaptive filter with improved convergence rate

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signAL PROCESSING 2014年第PART B期96卷 325-331页

作者： Ni, Jingen Chen, Xiaoping Yang, Jian Soochow Univ Sch Elect & Informat Engn Suzhou 215006 Peoples R China

sign algorithms (SAs) have attracted much attention because of their robustness against impulsive interference. To reduce the computational cost of SAs, a sign subband adaptive filter (SSAF) has recently been proposed. However, the SSAF converges slowly and the convergence rate of the SSAF does not increase with the number of subbands. In this paper, two variants of the SSAF, called the affine projection SSAF (AP-SSAF) and the proportionate SSAF (P-SSAF), are proposed to solve this problem. The AP-SSAF updates the tap-weight vector based on several previous input vectors, which can not only maintain robustness against impulsive interference, but also increase the convergence rate for both white and colored input signals;the P-SSAF incorporates a gain distribution matrix into the SSAF to proportionately adapt the tap-weight vector of the adaptive filter, which can both maintain robustness against impulsive interference and increase the convergence rate of the SSAF for sparse system identification. Simulation results are presented to demonstrate the improved performance of the AP-SSAF and the P-SSAF. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Affine projection Proportionate adaptive filtering sign algorithm Subband adaptive filter

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Affine Projection sign Subband Adaptive Filter

Affine Projection Sign Subband Adaptive Filter

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4th International Conference on Image Analysis and signal Processing (IASP)

作者： Ni, Jingen Chen, Xiaoping Yang, Jian Soochow Univ Sch Elect & Informat Engn Suzhou Peoples R China

ISBN: (纸本)9781467325455

sign algorithms (SAs) have attracted much attention because of their robustness against impulsive interference. To reduce the computational cost of SAs, a sign subband adaptive filter (SSAF) has recently been proposed. In this paper, an affine projection sign subband adaptive filter (APSSAF) is proposed, which updates the tap-weight vector based on several previous input vectors. The APSSAF not only maintains the robustness against impulsive interference, but also increases the convergence rate. Simulation results are presented to demonstrate the improved performance of the proposed algorithm.

关键词： adaptive filtering sign algorithm affine projection subband adaptive filter

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sign Subband Adaptive Filter with Selection of Number of Subbands 12

Sign Subband Adaptive Filter with Selection of Number of Sub...

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12th International Conference on Informatics in Control Automation and Robotics (ICINCO)

作者： Jeong, Jae Jin Kim, Seung Hun Koo, Gyogwon Kim, Sang Woo Pohang Univ Sci & Technol POSTECH Dept Elect Engn Pohang 790784 Kyungbuk South Korea Pohang Univ Sci & Technol POSTECH Dept Creat IT Excellence Engn Pohang 790784 Kyungbuk South Korea Pohang Univ Sci & Technol POSTECH Future IT Innovat Lab Pohang 790784 Kyungbuk South Korea

ISBN: (纸本)9789897581496

The sign subband adaptive filter (SSAF) algorithm is introduced to reduce performance degradation of least-mean-square-type algorithms due to a correlated input signal or an impulsive noise environments. However, this algorithmh has huge computational complexity when the length of the unknown system is large. In this paper, we focus on reduce computational complexity of the conventional SSAF algorithm and propose an SSAF algorithm which selects number of subbands according to convergence state. The specific bands which contributes to decrease the mean-square deviation are used to update the adaptive filter. Thus, the proposed algorithm reduces the computational complexity compared to the conventional SSAF algorithm. The selection mehtod is derived by analysing the mean-square deviation. Through the computer simulation, simulation results are presented that demonstrate the fast convergence rate of the proposed algorithm and save the computational cost.

关键词： Adaptive Filter Impulsive Noise sign algorithm Mean-Square Deviation

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