Normalized Least Mean Fourth Research Articles

Sparse echo cancellation using variants of least mean fourth and least mean square algorithms

Echo cancellation is the most essential and indispensable component of telephone networks. The impulse responses of most of the networks are sparse in nature; that is, the impulse response has a small percentage of its components with a significant magnitude (large energy), while the rest are zero or small. In these sparse environments, conventional adaptive algorithms like least mean square (LMS) and normalized LMS (NLMS) show substandard and inferior performances. In this paper, the performances of the normalized least mean square (NLMS) algorithm, the normalized least mean fourth (NLMF) and the proportionate normalized least mean fourth (PNLMF) are compared for sparse echo cancellation. The sparseness of both the echo response and the input signal is exploited in this algorithm to achieve improved results at a low computational cost. The PNLMF algorithm showed better results and faster convergence in sparse and non sparse systems, but its results in sparse environments are more impressive. The NLMF algorithm shows good results in sparse environments but not in non-sparse environments. The PNLMS algorithm can be considered superior to the NLMF and NLMS algorithms with respect to the error profile. A modified algorithm, the sparse controlled modified proportionate normalized LMF (SCMPNLMF) algorithm, is proposed, and its performances are compared with the other algorithms.

Three-phase grid-tied photovoltaic system with an adaptive current control scheme in active power filter

ABSTRACT In this article, an adaptive normalized least mean fourth (NLMF) control scheme is employed to generate the anti-harmonic currents of photovoltaic (PV) integrated with grid system for harmonic elimination and power factor (PF) correction (PFC). In addition, a fuzzy tuned PID-based adaptive dc voltage regulator is integrated in the proposed scheme to regulate the reference voltage of the dc bus. The proposed FPID-based NLMF control scheme attains the features of power quality (PQ) related issues elimination such as PFC and harmonics elimination with an extraction of photovoltaic (PV) generated maximum power through the grid interfacing converter (VSC) at a unity PF. Moreover, the PV system’s feed-forward (FF) component is included in the control strategy to enrich the aggressive behavior of the system. The NLMF current controller is employed to measure the three-phase calculated currents by extracting the fundamental weight constituents of the load currents for harmonic mitigation in the presence of point of common coupling (PCC). The proposed control topology is developed on MATLAB/SIMULINK software platform under different load and grid transient conditions. A dSPACE based real-time laboratory platform is developed to justify the proposed scheme under different conditions such as steady-state, load dynamic, removed and unbalanced, grid voltage distorted, unbalanced, swell and sag conditions. The presented control scenario’s results are obtained satisfactory and the grid current’s THD are in the IEEE-519 regular limits.

A Normalized Adaptive Filtering Algorithm Based on Geometric Algebra

In this paper, we extend the original Normalized Least Mean Fourth (NLMF) and Normalized Least Mean Square (NLMS) adaptive filtering algorithms into Geometric Algebra (GA) space to enable them to process multidimensional signals. We redefine the cost functions and propose the GA based NLMF and NLMS algorithms (GA-NLMF & GA-NLMS). We take full advantage of the ability of GA to represent multidimensional signals in GA space. GA-NLMS minimizes the cost function of the normalized mean square of the error signal, and remain stable as the input signal of the filter increases. GA-NLMS has fast convergence rate but higher steady-state error. The GA-NLMF algorithm minimizes the cost function of the normalized mean fourth of the error signal. Simulation results show that our proposed GA-NLMS adaptive filtering algorithm outperforms original NLMS algorithm in terms of convergence rate and steady-state error, and GA-NLMF outperforms both NLMF and GA-NLMS algorithms. GA-NLMF has faster convergence rate and lower steady state error, which is proved in the experiments.

Bias-Compensated Normalized Least-Mean Fourth Algorithm for Noisy Input

This paper proposes a bias-compensated normalized least-mean fourth (NLMF) algorithm to compensate for the bias caused by noisy input. In the proposed algorithm, we add a bias-compensation vector to the conventional NLMF algorithm, and the bias-compensation vector is then derived based on the unbiasedness criterion. Simulation results in system identification context show that the proposed algorithm provides lower steady-state misalignment as compared to the conventional NLMF algorithm.

A Stable Normalized Least Mean Fourth Algorithm With Improved Transient and Tracking Behaviors

The stability problems of the least mean fourth (LMF) algorithm put a limitation on its tracking capability. The paper investigates the possibility of solving this problem via stabilization of the algorithm. The analysis is done for a Markov plant. It is found that the available stable normalized LMF (NLMF) algorithm has a tracking limitation for high signal-to-noise ratio. The paper presents a new stable NLMF algorithm that is free of this limitation. Mean-square stability of the algorithm is proved. Expressions are derived for the minimum steady-state mean square deviation (MSD) and the corresponding convergence time. The new algorithm outperforms the available stable NLMF algorithm in both the transient and steady states. The new algorithm is also compared with the NLMS algorithm when the adaptation parameter of each algorithm is set to the value that minimizes its steady-state MSD. For large initial MSD, the algorithm outperforms the NLMS algorithm, even for Gaussian noise. For small initial MSD, the algorithm outperforms the NLMS algorithm for sub-Gaussian noise, while the situation is opposite for Gaussian noise. Analytical results are supported by simulations.

Stochastic Analysis of a Stable Normalized Least Mean Fourth Algorithm for Adaptive Noise Canceling With a White Gaussian Reference

The least mean fourth (LMF) algorithm has several stability problems. Its stability depends on the variance and distribution type of the adaptive filter input, the noise variance, and the initialization of the filter weights. A global solution to these stability problems was presented recently for a normalized LMF (NLMF) algorithm. Here, a stochastic analysis of the mean-square deviation (MSD) of the globally stable NLMF algorithm is provided. The analysis is done in the context of adaptive noise canceling with a white Gaussian reference input and Gaussian, binary, and uniform desired signals. The analytical model is shown to accurately predict the results of Monte Carlo simulations. Comparisons of the NLMF and NLMS algorithms are then made for various parameter selections. It is then shown under what conditions the NLMF algorithm is superior to NLMS algorithm for adaptive noise canceling.

Modified NLMF adaptation of Volterra filters used for nonlinear acoustic echo cancellation

When dealing with adaptive nonlinear filters used in acoustic echo cancellation, the tradeoff between convergence rate and steady-state error is an important issue. This tradeoff is favorably addressed here using a modified version of the normalized least-mean-fourth (NLMF) algorithm applied to an adaptive second-order Volterra structure. A convergence rate improvement is obtained at the same steady-state error by amending the step size of the conventional NLMF algorithm using a new step-size function that depends on the norm of an error vector of a certain length. The efficiency of the proposed method is compared with that of the conventional adapted second-order Volterra filter for nonlinear acoustic echo cancellation in terms of echo return loss enhancement (ERLE). From simulations conducted for input signals with different probability density functions, the new approach is shown to outperform the normalized least-mean-square (NLMS) second-order Volterra filter in terms of the convergence rate of the same steady-state error. The proposed technique was also tested in acoustic scenarios with impulse noise and separately with distinct local signal powers. The performance of the method was also compared to that of the traditional NLMF algorithm and of the variable NLMF (XE-NLMF) algorithm.

Convergence and steady-state analysis of the normalized least mean fourth algorithm

The normalized least mean-fourth (NLMF) algorithm is presented in this work and shown to have potentially faster convergence. Unlike the LMF algorithm, the convergence behavior of the NLMF algorithm is independent of the input data correlation statistics. Sufficient conditions for the NLMF algorithm convergence in the mean are obtained and an analysis of the steady-state performance is carried out with a new approach. The latter uses the concept of feedback and bypasses the need for working directly with the weight error covariance matrix. Simulation results obtained in a system identification scenario confirms the theoretical predictions on performance of the NLMF algorithm.