Stochastic analysis of the LMS algorithm for cyclostationary colored Gaussian and non-Gaussian inputs

Bershad, N.J.; Eweda, Eweda; Bermudez, J.C.M.

doi:10.1016/j.dsp.2019.02.011

Cited by 12 publications

(7 citation statements)

References 21 publications

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“…We set the forgetting factor λ to 0.995 for RLS and DRLS algorithms. Initialization parameter δ used in (20) was set to different values depending on the scenario; see Fig. 2.…”

Section: Simulation Resultsmentioning

confidence: 99%

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Transient Theoretical Analysis of Diffusion RLS Algorithm for Cyclostationary Colored Inputs

Wei

Chen

Richard

2021

IEEE Signal Process. Lett.

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Convergence of the diffusion RLS (DRLS) algorithm to steady-state has been extensively studied in the literature, whereas no analysis of its transient convergence behavior has been reported yet. In this letter, we conduct a theoretical analysis of the transient behavior of the DRLS algorithm for cyclostationary colored inputs, in the mean and mean-square error sense. The resulting analytical models allows us to thoroughly investigate the convergence behavior of the algorithm over adaptive networks in such complex scenarios. Simulation results support the accuracy and correctness of the theoretical findings.

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“…We set the forgetting factor λ to 0.995 for RLS and DRLS algorithms. Initialization parameter δ used in (20) was set to different values depending on the scenario; see Fig. 2.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…where the recursive relation (20) is invoked for the update of matrix K n . As a consequence, (42) enables us to investigate the network transient convergence behavior of the DRLS with ATC diffusion strategy in the mean-square sense.…”

Section: B Mean-square Weight Error Analysismentioning

confidence: 99%

Transient Theoretical Analysis of Diffusion RLS Algorithm for Cyclostationary Colored Inputs

Wei

Chen

Richard

2021

IEEE Signal Process. Lett.

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“…The theory on the Least Mean Square (LMS) [1,2] algorithm dates back to the 1960s [3,4] but comprehensive analyses of the algorithm using the independence assumption seem to have been published in the 1980s [5,6]. The independence assumption [1,7] states that the input data vector is statistically independent or that the filter weights are independent of the input data vectors. It has been shown that using this assumption and for moderate step-sizes, the theoretical results agree very well with experiments.…”

Section: Introductionmentioning

confidence: 99%

“…More recently, several efforts have been made to analyze the LMS algorithm without the independence assumption with a less complex theory than the presented in [10], namely using Butterweck iterative procedure [12][13][14][15][16][17]. Moreover, there is ongoing work to generalize the previous analysis to non-stationary and non-gaussian inputs [7,[18][19][20]. This work proposes an analysis that allows obtaining some of the known results and new results easily.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the LMS and NLMS Algorithms Using the Misalignment Norm

Lopes

2023

Preprint

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This work describes the convergence of the misalignment square norm (MSN) of the NLMS and LMS algorithms. It is shown that the MSN decrease is almost proportional to the mean square error (MSE). This allows obtaining simple expressions for the steady-state MSE. Also, it allows limiting the amount of time that the MSE takes large values and a curve that limits the MSE of LMS at any given time, independent of the input and background noise signals' properties. Finally, it is also shown that many complications in the analysis of the LMS and NLMS algorithms can come from variations in the input vector square norm. The proposed analysis becomes very simple for long filters or constant power signals.

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“…The work in [24] applied the proposed variable step size LMS algorithm on active vibration control study case. Stochastic analysis of the LMS algorithm on colored input signals can be found in [26] and the references therein. To reduce the number of the calculations required to process the input data in LMS algorithm, a block by block manipulation of the noise data based on the fast Fourier-transform (FFT) and the overlap-save method is proposed in [27].…”

Section: Introductionmentioning

confidence: 99%

A Novel Adaptive LMS Algorithm with Genetic Search Capabilities for System Identification of Adaptive FIR and IIR Filters

2019

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In this paper we introduce a novel adaptation algorithm for adaptive filtering of FIR and IIR digital filters within the context of system identification. The standard LMS algorithm is hybridized with GA (Genetic Algorithm) to obtain a new integrated learning algorithm, namely, LMS-GA. The main aim of the proposed learning tool is to evade local minima, a common problem in standard LMS algorithm and its variants and approaching the global minimum by calculating the optimum parameters of the weights vector when just estimated data are accessible. In the proposed LMS-GA technique, first, it works as the standard LMS algorithm and calculates the optimum filter coefficients that minimize the mean square error, once the standard LMS algorithm gets stuck in local minimum, the LMS-GA switches to GA to update the filter coefficients and explore new region in the search space by applying the cross-over and mutation operators. The proposed LMS-GA is tested under different conditions of the input signal like input signals with colored characteristics, i.e., correlated input signals and investigated on FIR adaptive filter using the power spectral density of the input signal and the Fourier-transform of the input’s correlation matrix. Demonstrations via simulations on system identification of IIR and FIR adaptive digital filters revealed the effectiveness of the proposed LMS-GA under input signals with different characteristics.

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Stochastic analysis of the LMS algorithm for cyclostationary colored Gaussian and non-Gaussian inputs

Cited by 12 publications

References 21 publications

Transient Theoretical Analysis of Diffusion RLS Algorithm for Cyclostationary Colored Inputs

Transient Theoretical Analysis of Diffusion RLS Algorithm for Cyclostationary Colored Inputs

Analysis of the LMS and NLMS Algorithms Using the Misalignment Norm

A Novel Adaptive LMS Algorithm with Genetic Search Capabilities for System Identification of Adaptive FIR and IIR Filters

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