An efficient normalized LMS algorithm

The task of adaptive estimation in the presence of random and highly nonlinear environment such as wireless channel estimation and identification of non-stationary system etc. has been always challenging. The least mean square (LMS) algorithm is the most popular algorithm for adaptive estimation and...

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Published inNonlinear dynamics Vol. 110; no. 4; pp. 3561 - 3579
Main Authors Zerguine, Azzedine, Ahmad, Jawwad, Moinuddin, Muhammad, Al-Saggaf, Ubaid M., Zoubir, Abdelhak M.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2022
Springer Nature B.V
Subjects
Online AccessGet full text
ISSN0924-090X
1573-269X
DOI10.1007/s11071-022-07773-0

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Abstract The task of adaptive estimation in the presence of random and highly nonlinear environment such as wireless channel estimation and identification of non-stationary system etc. has been always challenging. The least mean square (LMS) algorithm is the most popular algorithm for adaptive estimation and it belongs to the gradient family, thus inheriting their low computational complexity and their slow convergence. To deal with this issue, an efficient normalization of the LMS algorithm is proposed in this work which is achieved by normalizing the input signal with an intelligent mixture of weighted signal and error powers which results in a variable step-size type algorithm. The proposed normalization scheme can provide both significant faster convergence in initial adaptation phase while maintaining a lower steady-state mean-square-error compared to the conventional normalized LMS (NLMS) algorithm. The proposed algorithm is tested on adaptive denoising of signals, estimation of unknown channel, and tracking of random walk channel and its performance is compared with that of the standard LMS and NLMS algorithms. Mean and mean-square performance of the proposed algorithm is investigated in both stationary and non-stationary environments. We derive the closed-form expressions of various performance measures by evaluating multi-dimensional moments. This is done by statistical characterization of required random variables by employing the approach of Indefinite Quadratic Forms. Simulation and experimental results are presented to corroborate our theoretical claims.
AbstractList The task of adaptive estimation in the presence of random and highly nonlinear environment such as wireless channel estimation and identification of non-stationary system etc. has been always challenging. The least mean square (LMS) algorithm is the most popular algorithm for adaptive estimation and it belongs to the gradient family, thus inheriting their low computational complexity and their slow convergence. To deal with this issue, an efficient normalization of the LMS algorithm is proposed in this work which is achieved by normalizing the input signal with an intelligent mixture of weighted signal and error powers which results in a variable step-size type algorithm. The proposed normalization scheme can provide both significant faster convergence in initial adaptation phase while maintaining a lower steady-state mean-square-error compared to the conventional normalized LMS (NLMS) algorithm. The proposed algorithm is tested on adaptive denoising of signals, estimation of unknown channel, and tracking of random walk channel and its performance is compared with that of the standard LMS and NLMS algorithms. Mean and mean-square performance of the proposed algorithm is investigated in both stationary and non-stationary environments. We derive the closed-form expressions of various performance measures by evaluating multi-dimensional moments. This is done by statistical characterization of required random variables by employing the approach of Indefinite Quadratic Forms. Simulation and experimental results are presented to corroborate our theoretical claims.
Author Ahmad, Jawwad
Al-Saggaf, Ubaid M.
Zerguine, Azzedine
Zoubir, Abdelhak M.
Moinuddin, Muhammad
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CitedBy_id crossref_primary_10_1007_s00034_024_02755_6
crossref_primary_10_1109_JSEN_2024_3356657
crossref_primary_10_1088_1361_6501_ad4dc5
crossref_primary_10_1109_ACCESS_2023_3319394
Cites_doi 10.1109/TAC.1967.1098599
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10.1109/TSP.2011.2181505
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10.1016/j.ijleo.2016.11.152
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7773_CR23
References_xml – reference: CostaMBermudezJA noise resilient variable step-size LMS algorithmSignal Process.200888373374810.1016/j.sigpro.2007.09.0151186.94097
– reference: WidrowBMcCoolJMLarimoreMGJohnsonCRStationary and Nonstationary Learning Characteristics of the LMS Adaptive FilterIEEE Proceedings1976641151116242181410.1109/PROC.1976.10286
– reference: SulymanAIZerguineAConvergence and steady-state analysis of a variable step-size NLMS algorithmSignal Process.2003831255127310.1016/S0165-1684(03)00044-61144.93377
– reference: Al-NaffouriTYMoinuddinMExact performance analysis of the $\epsilon $-NLMS algorithm for colored circular Gaussian inputsIEEE Trans. Signal Process.2010581050805090275987710.1109/TSP.2010.20523591392.94065
– reference: RickerWEStock and recruitmentJ. Fish. Res. Board Can.19541155962310.1139/f54-039
– reference: WalachEWidrowBThe least mean fourth (LMF) adaptive algorithm and its familyIEEE Trans. Inf. Theory1984IT–3027528310.1109/TIT.1984.1056886
– reference: GradshteynISRyzhikIMTable of Integral, Series, and Products, Corrected and Enlarged Edition1980New YorkAcademic Press, INC0521.33001
– reference: KwongRHJohnstonEWA variable step size LMS algorithmIEEE Trans. Signal Process.1992401633164210.1109/78.1434350850.93839
– reference: BelaziAAbd El-LatifAAA simple yet efficient S-box method based on chaotic sine mapOPTIK20171301438144410.1016/j.ijleo.2016.11.152
– reference: MethewsVJXieZA stochastic gradient adaptive filter with gradient adaptive step sizeIEEE Trans. Signal Process.1993412075208710.1109/78.218137
– reference: HuangH-CLeeJA new variable step-size NLMS algorithm and its performance analysisIEEE Trans. Signal Process.201260420552060293421910.1109/TSP.2011.21815051393.94268
– reference: HaykinSAdaptive Filter Theory19963Upper-Saddle RiverPrentice-Hall0723.93070
– reference: Al-NaffouriTYSayedAHTransient analysis of adaptive filters with error nonlinearitiesIEEE Trans. Signal Process.200351365366310.1109/TSP.2002.808108
– reference: BershadNJBehavior of the $\epsilon $-normalized LMS algorithm with Gaussian inputsIEEE Trans. Acoust. Speech Signal Process.1987ASSP–35563664410.1109/TASSP.1987.1165197
– reference: RogersTDWhitleyDCChaos in the cubic mappingMath. Model.1983492571172210.1016/0270-0255(83)90030-10531.58033
– reference: ZerguineAChanMKAl-NaffouriTYMoinuddinMCowanCFNConvergence and tracking analysis of a variable normalized LMF (XE-NLMF) algorithmSignal Process.200889577879010.1016/j.sigpro.2008.10.0221161.94373
– reference: Chan, M.K., Cowan, C.F.N.: Using a normalised LMF algorithm for channel equalisation with co-channel interference. In: EUSIPCO 2002, pp. 48–51 (2002)
– reference: NagumoJINodaAA learning method for system identificationIEEE Trans. Autom. Control19671228228710.1109/TAC.1967.1098599
– reference: Al-NaffouriTYMoinuddinMAjeebNHassibiBMoustakasALOn the distribution of indefinite quadratic forms in Gaussian random variablesIEEE Trans. Commun.201664115316510.1109/TCOMM.2015.2496592
– reference: SayedAHAdaptive Filters2008New YorkJohn Wiley & Sons10.1002/9780470374122
– reference: Costa, M., Bermudez, J.: A robust variable step size algorithm for LMS adaptive filters. In: IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP, vol. 3 (2006)
– reference: AboulnasrTMayyasKA robust variable step-size LMS type algorithm: analysis and simulationIEEE Trans. Signal Process.19974563163910.1109/78.558478
– reference: Hosseini, K., Montazeri, A., Alikhanian, H., Kahaei, M.H.: New classes of LMS and LMF adaptive algorithms. In: 2008 3rd International Conference on Information and Communication Technologies: From Theory to Applications, pp. 1–5 (2008)
– reference: ShanTJKailathTAdaptive algorithms with an automatic gain control featureIEEE Trans. Acoust. Speech Signal Process.198835122127
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SubjectTerms Adaptive algorithms
Algorithms
Automotive Engineering
Classical Mechanics
Control
Convergence
Dynamical Systems
Engineering
Mechanical Engineering
Nonstationary environments
Original Paper
Performance evaluation
Quadratic forms
Random variables
Random walk
Vibration
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