• The Journal of the Acoustical Society of Korea
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• v.35 no.1
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• pp.55-62
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• 2016

The least-mean fourth (LMF) algorithm is well known for its fast convergence and low steady-state error especially in non-Gaussian noise environments. Recently, there has been increasing interest in the least mean square (LMS) algorithms with variable step size. It is because the variable step-size LMS algorithms have shown to outperform the conventional fixed step-size LMS in the various situations. In this paper, a variable step-size LMF algorithm is proposed, which adopts an algebraic optimal step size as a variable step size. It is expected that the proposed algorithm also outperforms the conventional fixed step-size LMF. The superiority of the proposed algorithm is confirmed by the simulations in the time invariant and time variant channels.

• Journal of IKEEE
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• v.15 no.4
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• pp.293-298
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• 2011

In the paper, we propose a new CMF(Constant Modulus Fourth) algorithm for WCDMA(Wideband Code Multiple Access) RF(Radio Frequency) Repeater. CMF algorithm is proposed by modifying the CMA(Constant Modulus Algorithm) algorithm and improved performances are achieved by properly adjusting step size values. The steady state MSE(Mean Square Error) performance of the proposed CMF algorithm with step size of 0.35 is about 4dB better than that of the conventional CMA algorithm. And the proposed CMF algorithm requires 400~1100 less iterations than the LMS(Least Mean Square) and NLMS(Normalized Least Mean Square) algorithms at MSE of -25dB.

• The Journal of the Acoustical Society of Korea
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• v.37 no.3
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• pp.156-162
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• 2018

The LMF (Least Mean Fourth) algorithm is well known for its fast convergence and low steady-state error especially in non-Gaussian noise environments. Recently, there has been increasing interest in the LMS (Least Mean Square) algorithms with self-adjusted step size. It is because the self-adjusted step-size LMS algorithms have shown to outperform the conventional fixed step-size LMS in the various situations. In this paper, a self-adjusted step-size LMF algorithm is proposed, which adopts an averaged gradient based step size as a self-adjusted step size. It is expected that the proposed algorithm also outperforms the conventional fixed step-size LMF. The superiority of the proposed algorithm is confirmed by the simulations in the time invariant and time variant channels.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.8
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• pp.616-625
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• 2002

In this paper, we drove the filtered-x least mean fourth (FXLMF) algorithm where the error raised to the power of four is minimized and analyzed its convergence behavior for a multiple sinusoidal acoustic noise and Gaussian measurement noise. The application of the FXLMF adaptive filter to active noise control requires to estimate the transfer characteristics of the acoustic path between the output and the error signal of the adaptive controller. The results of the convergence analysis of the FXLMF algorithm indicate that the effects of the parameter estimation inaccuracy on the convergence behavior of the algorithm are characterized by two distinct components phase estimation error and estimated gain. In particular, the convergence is shown to be strongly affected by the accuracy of the phase response estimate. Also, we newly show that the convergence behavior can differ depending on the relative sizes of the Gaussian noise and the convergence constant.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.12A
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• pp.2043-2049
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• 2001

In this paper we study the convergence behavior of the least mean fourth(LMF) algorithm where the error raised to the power of four is minimized for a multiple sinusoidal input and Gaussian measurement noise. Here we newly obtain the convergence equation for the sum of the mean of the squared weight errors, which indicates that the transient behavior can differ depending on the relative sizes of the Gaussian noise and the convergence constant. It should be noted that no similar results can be expected from the previous analysis by Walach add Widrow.

• The Journal of the Acoustical Society of Korea
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• v.18 no.2E
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• pp.3-9
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• 1999

In this paper we study the convergence behavior of the least mean fourth(LMF) algorithm where the error raised to the power of four is minimized for a multiple sinusoidal input and Gaussian measurement noise. Here we newly obtain the convergence equation for the sum of the mean of the squared weight errors, which indicates that the transient behavior can differ depending on the relative sizes of the Gaussian noise and the convergence constant. It should be noted that no similar results can be expected from the previous analysis by Walach and Widrow/sup [1]/.

• The Journal of the Korea institute of electronic communication sciences
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• v.14 no.5
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• pp.805-810
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• 2019

Recently, a majority of 4G mobile telecommunication manufacturers prefer repeaters with good adaptability. In this paper, we propose a new LMF(: Least Means Fourth) algorithm for LTE(: Long Term Evolution) RF(: Radio Frequency) Repeater. The proposed algorithm is a modification of the LMF, which appropriately adjusts the step size and improves performance according to the Sign function. The steady state MSE(: Mean Square Error) performance of the proposed LMF algorithm with step size of 0.009 is low level at about -25dB, and the proposed LMF algorithm requires 500 less iterations than the conventional algorithms at MSE of -25dB.

• The Journal of the Acoustical Society of Korea
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• v.14 no.1
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• pp.22-30
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• 1995

In this Paper we study the convergence behavior of the least mean fourth (LMF) algorithm where the error raised to the power of four is minimized for a multiple sinusoidal input and Gaussian measurement noise. Here we newly obtain the convergence equation for the sum of the mean of the squared weight errors, which indicates that the transient behavior can differ depending on the relative sizes of the Gaussian noise and the convergence constant. It should be noted that no similar results can be expected from the previous analysis by Walach and Widrow.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.2C
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• pp.272-282
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• 2004

This paper introduces a regularized mixed norm multi-channel image restoration algorithm using both within-and between- channel deterministic information. For each channel a functional which combines the least mean squares (LMS), the least mean fourth (LMF), and a smoothing functional is proposed. We introduce a mixed norm parameter that controls the relative contribution between the LMS and the LMF, and a regularization parameter defining the degree of smoothness of the solution, where both parameters are updated at each iteration according to the noise characteristics of each channel. The novelty of the proposed algorithm is that no knowledge of the noise distribution for each channel is required and that the parameters mentioned above are adjusted based on the partially restored image.

• Proceedings of the IEEK Conference
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• 2001.09a
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• pp.915-918
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• 2001

In this paper we study a new convergence behavior of the least mean fourth (LMF) algorithm where the error raised to the power of four is minimized for a multiple sinusoidal input and Gaussian measurement noise. Here we newly obtain the convergence equation for the sum of the mean of the squared weight errors, which indicates that the transient behavior can differ depending on the relative sizes of the Gaussian noise and the convergence constant. It should be noted that no similar results can be expected from the previous analysis by Walach and Widrow.