• 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.

• 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.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.

• 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.

• The Journal of the Acoustical Society of Korea
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• v.16 no.3
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• pp.38-44
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• 1997

In this study, wer derived LMF-Sato, LMSF-Sato complex blind equalization algorithms for complex data. And then, the convergence rates, the convergence characteristics at the steady state and the stability of the proposed LMF and LMSF blind equalization algorithms are compared with those of LMS-Sato blind equalization algorithm. In simulations with 16-QAM data, LMF-Sato and LMSF-Sato algorithms showed better performance comparing with LMS-Sato algorithm generally. When the initial estimation errors of the weights of the equalizer are large, LMF-Sato algorithm showed ill characteristic in stability. However, LMSF-Sato algorithm has good covergence characteristics and preserves robustness.

• 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.26 no.12A
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• pp.2050-2058
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• 2001

In this paper, we propose the filtered-x least mean fourth (LMF) algorithm where the error raised to the power of four is minimized and analyze its convergence behavior for a multiple sinusoidal acoustic noise and Gaussian measurement noise. Application of the filtered-x LMF adaptive filter to active noise cancellation (ANC) requires estimating of the transfer characteristic of the acoustic path between the output and error signal of the adaptive controller. The results of 7he convergence analysis of the filtered-x LMF algorithm indicates 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 convergence behavior can differ depending on the relative sizes of the Gaussian measurement noise and convergence constant.

• The Journal of the Acoustical Society of Korea
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• v.15 no.3E
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• pp.66-73
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• 1996

In this paper, we propose the filtered-x least mean fourth (LMF) algorithm where the error raised to the power of four is minimized and analyze its convergence behavior for a multiple sinusoidal acoustic noise and Gaussian measurement noise. Application of the filtered-x LMF adaptive filter to active noise control(ANC) requires estimating of the transfer characteristic of the acoustic path between the output and error signal of the adaptive controller. The results of the convergence analysis of the filtered-x LMF algorithm indicates 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 convergence behavior can differ depending on the relative sizes of the Gaussian measurement noise and convergence constant.

• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.1715-1718
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• 2003

본 논문에서 우리는 정규화 된 혼합 노름(norm)을 이용한 다중 채널 영상 복원 알고리즘을 제안한다. 채널 내부와 채널 사이의 결정론적 정보를 이용하는 다중채널 복원 문제를 고려한다. 각 채널에서, LMS(Least Mean Square), LMF(Least Mean Fourth), 평탄 함수가 결합된 함수가 제안되었다. LMS와 LMF 사이의 적절한 분배를 제어하는 혼합 노를 매개변수와 해의 평탄 정도를 정의하는 정규화 매개 변수를 소개하며, 두 매개 변수는 각 채널의 잡음 특성에 따라 매번 반복적으로 갱신된다. 제안된 알고리즘은 각 채널의 잡음분포에 대한 지식이 필요하지 앉고 앞에서 언급된 매개 변수는 부분적으로 복원된 영상에 기반을 두고 조절하게 된다.

• The Journal of the Acoustical Society of Korea
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• v.14 no.1E
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• pp.56-64
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• 1995

The least mean fourth (LMF) adaptive algorithm is a stochastic gradient method that minimizes the error in the mean fourth sense. Despite its potential advantages, the algorithm is much less popular than the conventional least mean square (LMS) algorithm in practice. This seems partly because the analysis of the LMF algorithm is much more difficult than that of the LMS algorithm, and thus not much still has been known about the algorithm. In this paper, we explore the statistical convergence behavior of the LMF algorithm when the input to the adaptive filter is zero-mean, wide-sense stationary, and Gaussian. Under a system idenrification mode, a set of nonlinear evolution equations that characterizes the mean and mean-squared behavior of the algorithm is derived. A condition for the conbergence is then found, and it turns out that the conbergence of the LMF algorithm strongly depends on the choice of initial conditions. Performances of the LMF algorithm are compared with those of the LMS algorithm. It is observed that the mean convergence of the LMF algorithm is much faster than that of the LMS algorithm when the two algorithms are designed to achieve the same steady-state mean-squared estimation error.