An efficient regularized NLMF algorithm

A simplified forms of adaptive set-membership affine projection based on least mean fourth algorithm is proposed. Least mean fourth (LMF) algorithm is defined by taking the fourth power of error to against the non-Gaussian environment. A set-membership adaptive filtering is described firstly. Then, an affine projection algorithm is based on LMF algorithm. A simplified set-membership affine projection algorithm based on LMF is introduced. Adaptive threshold parameter and learning rate are presented for improvement of convergence rate. Numerical simulations show that the proposed algorithm can provide significantly to the conventional affine projection algorithm.

The problem of distributed estimation is considered for distributed network. A diffusion model on adaptive affine projection sign algorithm based on least mean fourth algorithm is introduced according to an Adapt-Then-Combine (ATC) design for the distributed framework. Least mean fourth (LMF) algorithm is defined by taking the fourth power of error to against the non-Gaussian environment. An adaptive affine projection sign algorithm based on LMF algorithm is proposed firstly. Then, an ATC diffusion model on adaptive affine projection sign algorithm based on LMF algorithm is presented in terms of the low complexity of sign approach with the order of adaptation and combination, named as ATC-DAPS-LMF. Numerical simulations verify that the proposed algorithm can perform significantly to the conventional affine projection sign algorithm.

Adaptive equalization is undoubtedly one of the cornerstones of digital communication as it allows for fast and reliable data transmission over practical channels that are non-ideal and that are plagued with serious problems such as signal dispersion and non-Gaussian interferences. In such cases, the performance of the well-known least-mean square (LMS) algorithm or that of any of its variants remains sub-optimal at best. As a remedy to this, the least-mean fourth (LMF) algorithm was later proposed but its high computational load was found to be a constraining factor in its practical implementation, particularly for real-time applications. Inspired from a previous work done on the LMS [1], we recently proposed a new algorithm [2], termed LMF-PTQ, combining the power of the LMF with the implementational advantages of the power-of-two quantization scheme. In this work, we demonstrate, through an extensive simulation study, the effectiveness of our proposed LMF-PTQ algorithm in the equalization of a time-varying channel in a CDMA system which suffers from both signal dispersion and non-Gaussian disturbances. The results obtained so far are very encouraging and provide us with ample enthusiasm to investigate the proposed algorithm further.

A modified least mean fourth (LMF) adaptive algorithm applicable to non-stationary signals is presented. The performance of the proposed algorithm is studied by simulation for non-stationarities in bandwidth, centre frequency and gain of a stochastic signal. These non-stationarities are in the form of linear, sinusoidal and jump variations of the parameters. The proposed LMF adaptation is found to have better parameter tracking capability than the LMS adaptation for the same speed of convergence.

In this work, the convergence analysis of the variable weight mixed-norm least-mean squares (LMS)-least mean-fourth (LMF) adaptive algorithm is derived. The proposed algorithm minimizes an objective function defined as a weighted sum of the LMS and LMF cost functions, where the weighting factor is time varying and adapts itself to allow the algorithm to keep track of the variations in the environment. As a by-product of this novel approach, new necessary and sufficient conditions for the LMF algorithm have been derived. Furthermore, a more general expression for the excess steady-state error for the LMF algorithm has been derived.

Recently, it has been shown that the stability of the least mean fourth (LMF) algorithm depends on the nonstationarity of the plant. The present paper investigates the possibility of overcoming this problem by normalization of the weight vector update term. A rigorous mean-square stability analysis is provided for a recent normalized LMF algorithm, which is normalized by a term that is second order in the estimation error and fourth order in the regressor. The analysis is done for a Markov plant with a stationary white input with even probability density function and a stationary zero-mean white noise. It is proved that the mean-square deviation (MSD) of the algorithm is bounded for all finite values of the input variance, noise variance, initial MSD, and mean-square plant parameter increment. Analytical results are supported by simulations.

One of the most important applications of adaptive filter is Interference or noise cancellation. The objective of adaptive interference cancellation is to obtain an estimate of the interfering signal and to subtract it from the corrupted signal and hence obtain a noise free signal. The tracking performances of the LMS and NLMS algorithms are compared when the input of the adaptive filter is no stationary For this purpose, the filter uses an adaptive algorithm to change the value of the filter coefficients, so that it acquires a better approximation of the signal after each iteration. The LMS (Least Mean Square), and its variant the NLMS (Normalized LMS) are two of the adaptive algorithms widely in use. This paper presents a comparative analysis of the LMS and the NLMS in case of interference cancellation from speech signals. For each algorithm, the effects of two parameters-filter length and step size have been analyzed. Finally, the performances of the two algorithms in different cases have been compared.

Among all adaptive noise cancellers, Widrow and Hoff's least mean square (LMS) algorithm has probably become the most popular because of its robustness, good tacking properties and simplicity of implementation. An important limitation of LMS algorithm is that the selection of a certain value for the step size implies compromise between speed of convergence and steady-state misadjustment, The variable step size normalized least-mean-square (VSS- NLMS) algorithm is appropriate to solve the conflicting requirement of fast convergence and low misadjustment of the LMS algorithm. To reduce noise in the output signal of the ANC, a step size for coefficient update is controlled according to the signal-to-noise ratio (SNR). This paper investigates the performance of a noise canceller with DSP processor (TI TMS320C6713) using the LMS algorithm, normalized least-mean-square (NLMS) algorithm, and VSS-NLMS algorithm. Results show the proposed combination of hardware and VSS-NLMS algorithm has not only a faster convergence rate but also lower distortion when compared with the fixed step size LMS algorithm and NLMS algorithm in real-time environments.

Recently, in the world wide the use of power electronics devices increases sharply. As a result, harmonic pollution becomes a vital problem than before. Harmonics rotate in the power system network and interfere with the system equipments, disturbing their normal operation which can deteriorate the quality of the delivered power. Therefore, efficient method with low computational time is a critical tool to estimate and quantify the harmonic that can be used in online control and mitigation of harmonics. Least Mean Square (LMS) is simple and popular algorithm that has been applied in many applications, but, noise can affect its performance. This paper presents and compare the performance of Least Mean Square (LMS), Least Mean Fourth (LMF) and a combined (LMS/LMF) in estimation harmonic component for the signal corrupted with noise contain low signal to noise ratio (SNR). The results show that LMF and LMS/LMF have better steady state performance as compared to LMS.

Mean-square stability of the Normalized Least-Mean Fourth algorithm for white Gaussian inputs

A novel adaptive filter algorithm has been proposed that provides faster convergence than the least mean square (LMS) and normalized LMS (NLMS) algorithms. The NLMS algorithm is studied and modified so that the error sequence is used for designing the step size parameter at each iteration. A strategy to reduce the computational complexity the NLMS adaptation requires is used in the proposed algorithm. Computer simulations demonstrate that in the scenario of channel equalization, the proposed algorithm based on the structure of a transversal filter accomplishes faster start-up than the combined LMS/F algorithm recently addressed.

It is shown that two algorithms obtained by simplifying a Kalman filter considered for a second-order Markov model are H∞ suboptimal. Similar to least mean squares (LMS) and normalised LMS (NLMS) algorithms, these second order algorithms can be thought of as approximate solutions to stochastic or deterministic least squares minimisation. It is proved that second-order LMS and NLMS are exact solutions causing the maximum energy gain from the disturbances to the predicted and filtered errors to be less than one, respectively. These algorithms are implemented in two steps. Operation of the first step is like conventional LMS/NLMS algorithms and the second step consists of the estimation of the weight increment vector and prediction of weights for the next iteration. This step applies simple smoothing on the increment of the estimated weights to estimate the speed of the weights. Also they are cost-effective, robust and attractive for improving the tracking performance of smoothly time-varying models.

In this paper, we propose an iterative mixed norm image restoration algorithm. A functional which combines the least mean squares (LMS) and the least mean fourth (LMF) functionals is proposed. A function of the kurtosis is used to determine the relative importance between the LMS and the LMF functionals. An iterative algorithm is utilized for obtaining a solution and its convergence is analyzed. Experimental results demonstrate the capability of the proposed approach.

In this paper, we propose an iterative mixed norm image restoration algorithm. A functional which combines the least mean squares (LMS) and the least mean fourth (LMF) functionals is proposed. A function of the kurtosis is used to determine the relative importance between the LMS and the LMF functionals. An iterative algorithm is utilized for obtaining a solution and its convergence is analyzed. Experimental results demonstrate the capability of the proposed approach.

In this paper, we present a regularized mixed norm multichannel image restoration algorithm. The problem of multichannel restoration using both within- and between-channel deterministic information is considered. 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 that defines the degree of smoothness of the solution, both 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 the parameters mentioned above are adjusted based on the partially restored image.