A note on the convergence analysis of LMS adaptive filters with Gaussian data

Foley, J.B.; Boland, Frank

doi:10.1109/29.1632

Cited by 28 publications

(12 citation statements)

References 7 publications

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“…Similar results are obtained in [7] by solving the difference equation in Φ(n) and in [8] by a matrix analysis technique.…”

Section: Mean Square Behaviorsupporting

confidence: 66%

“…The main reason is that both [14] and [16] assume that the denominator in (2) is uncorrelated with the numerator and an "average" but constant normalization for all the eigen-modes results. When the input is very colored, the scaling constants according to (8), I i (Λ), are considerably different for different modes. Hence, the averaging principle is less accurate in describing the convergence behavior.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…The convergence behavior of the LMS algorithm for Gaussian input was thoroughly studied in the classical work of Widrow et al [1], in which the concept of independence assumption was introduced. Other related studies of the LMS algorithm with independent Gaussian inputs include [6][7][8]. On the other hand, the NLMS algorithm generally possesses an improved convergence speed over the LMS algorithm, but its analysis is more complicated due to the step size normalization.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Convergence Behavior of NLMS Algorithm for Gaussian Inputs: Solutions Using Generalized Abelian Integral Functions and Step Size Selection

Chan

Zhou

2009

J Sign Process Syst Sign Image Video Technol

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This paper studies the mean and mean square convergence behaviors of the normalized least mean square (NLMS) algorithm with Gaussian inputs and additive white Gaussian noise. Using the Price's theorem and the framework proposed by Bershad in IEEE Transactions on Acoustics, Speech, and Signal Processing (1986, 1987), new expressions for the excess mean square error, stability bound and decoupled difference equations describing the mean and mean square convergence behaviors of the NLMS algorithm using the generalized Abelian integral functions are derived. These new expressions which closely resemble those of the LMS algorithm allow us to interpret the convergence performance of the NLMS algorithm in Gaussian environment. The theoretical analysis is in good agreement with the computer simulation results and it also gives new insight into step size selection.

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“…Similar results are obtained in [7] by solving the difference equation in Φ(n) and in [8] by a matrix analysis technique.…”

Section: Mean Square Behaviorsupporting

confidence: 66%

Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Convergence Behavior of NLMS Algorithm for Gaussian Inputs: Solutions Using Generalized Abelian Integral Functions and Step Size Selection

Chan

Zhou

2009

J Sign Process Syst Sign Image Video Technol

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show abstract

“…Since the independence assumptions are satisfied in this case, it is possible to compute the learning curve exactly, as follows [3], [4]. Let the input covariance matrix be .…”

Section: Consider a Lengthmentioning

confidence: 99%

“…4 To address the above general case, it is necessary to know all the fourth-order moments and cross correlations between the entries of . Assuming that these fourth-order moments are known, we can simplify (20) using Kronecker products, as we now show.…”

Section: ) Evaluating the Mean Ofmentioning

confidence: 99%

On the learning mechanism of adaptive filters

Nascimento¹,

Sayed

2000

IEEE Trans. Signal Process.

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Abstract-This paper highlights, both analytically and by simulations, some interesting phenomena regarding the behavior of ensemble-average learning curves of adaptive filters that may have gone unnoticed. Among other results, the paper shows that even ensemble-average learning curves of single-tap LMS filters actually exhibit two distinct rates of convergence: one for the initial time instants and another, faster one, for later time instants. In addition, such curves tend to converge faster than predicted by mean-square theory and can converge even when a mean-square stability analysis predicts divergence. These effects tend to be magnified by increasing the step size. Two of the conclusions that follow from this work are 1) mean-square stability alone may not be the most appropriate performance measure, especially for larger step sizes. A combination of mean-square stability and almost sure (a.s.) stability seems to be more appropriate. 2) Care is needed while interpreting ensemble-average curves for larger step sizes. The curves can lead to erroneous conclusions unless a large number of experiments are averaged (at times of the order of tens of thousands or higher).Index Terms-Adaptive filter, almost-sure convergence, Chebyshev's inequality, law of large numbers, learning curve, mean square convergence, rate of convergence.

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Adaptive Antennas for Wireless Networks

Blaunstein¹,

Christodoulou²

2006

Radio Propagation and Adaptive Antennas for Wireless Communication Links

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A note on the convergence analysis of LMS adaptive filters with Gaussian data

Cited by 28 publications

References 7 publications

Convergence Behavior of NLMS Algorithm for Gaussian Inputs: Solutions Using Generalized Abelian Integral Functions and Step Size Selection

Convergence Behavior of NLMS Algorithm for Gaussian Inputs: Solutions Using Generalized Abelian Integral Functions and Step Size Selection

On the learning mechanism of adaptive filters

Adaptive Antennas for Wireless Networks

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