Zero-attracting Least Mean Square Research Articles

An Optimized Zero-Attracting LMS Algorithm for the Identification of Sparse System

This paper introduces an optimized zero-attractor to improve the performance of least mean square (LMS)-based algorithms for the identification of sparse system. Compared with previous LMS-based algorithms for sparse system identification, the performance of the proposed optimized zero-attracting LMS (OZ-LMS) is much less sensitive to the tuning parameters and measurement noise power, and performs much better for sparse system. Comprehensive performance analysis of the mean-square deviation (MSD) of OZ-LMS is derived in detail. Moreover, the parameter selection rules for optimal steady-state MSD are discussed. Simulation results, using white Gaussian noise and speech input signals, show improved performance over existing methods. Furthermore, we show that the numerical results of OZ-LMS agree with the theoretical predictions.

Advanced wavelet transform based shunt hybrid active filter in PV integrated power distribution system for power quality enhancement

Power quality (PQ) issues are significant in inverter-fed distributed generation system with non-linear loads which degrades the performance of the consumer equipments and the power system itself. Therefore, this work presents an improved photovoltaic (PV) coupled hybrid filter for the improvement in PQ in an active distribution system. A shunt hybrid active filter (SHAF) integrated with PV is designed with the help of an advanced signal processing approach called dual tree-complex wavelet transform (DT-CWT) for extracting the frequency information in the voltage and current due to the PQ disturbances. For calculating the reference current and switching signals, zero attracting least mean square (ZA-LMS) is considered in the hybrid filter and adaptive perturb and observe-fuzzy algorithm is proposed for maximum power point tracking in PV system to improve the performance under different operating conditions. The system model using the proposed technique is developed in MATLAB/Simulink and real-time experimental set up using two different controllers, i.e. the conventional proportional-integral (PI) and fuzzy-PI controllers. The results on comparison illustrates better performance of the proposed ZA-LMS and DT-CWT with fuzzy-PI based SHAF technique for PQ improvements with respect to that of LMS/normalised LMS with PI/fuzzy-PI based SHAF under different operating scenarios.

Polynomial variable scaling factor improved least sum of exponentials algorithm with maximum correntropy criterion

In this paper, a polynomial variable scaling factor improved least sum of exponentials algorithm with maximum correntropy criterion is proposed for sparse system identification. Sparse system estimation problem is increasing important topics in broadband wireless communications systems. Sparse learning algorithms for system identification achieved a better performance under Gaussian assumption, such as the zero-attracting least mean square (ZA-LMS). However, in non-Gaussian environments the existing algorithms suffer from performance degradation due to random impulsive noises. To further improve the robustness of the zero-attracting algorithms, an attempt has been made to design an improved sum of error exponentials that utilize the maximum correntropy criterion. In addition, a polynomial zero attractor is introduced to enhance the capability of sparse system identification. The test on sparse system identifications under an impulsive noise environment demonstrates that the proposed algorithm has a low steady-state misalignment compared with the others.

Model-driven online parameter adjustment for zero-attracting LMS

Abstract Zero-attracting least-mean-square (ZA-LMS) algorithm has been widely used for online sparse system identification. Similarly to most adaptive filtering algorithms and sparsity-inducing regularization techniques, ZA-LMS appears to face a trade-off between convergence speed and steady-state performance, and between sparsity level and estimation bias. It is therefore important, but not trivial, to optimally set the algorithm parameters. To address this issue, a variable-parameter ZA-LMS algorithm is proposed in this paper, based on a model of the stochastic transient behavior of the ZA-LMS. By minimizing the excess mean-square error (EMSE) at each iteration on the basis of a white input assumption, we obtain closed-form expression of the step-size and regularization parameter. To improve the performance, we introduce the same strategy for the reweighted ZA-LMS (RZA-LMS). Simulation results illustrate the effectiveness of the proposed algorithms and highlight their performance through comparisons with state-of-the-art algorithms, in the case of white and correlated inputs.

Cauchy Distribution Function-Penalized LMS for Sparse System Identification

It is well known that the zero-attracting least mean square (ZA-LMS) algorithm and reweighted zero-attracting LMS (RZA-LMS) algorithm outperform the standard LMS algorithm in sparse systems. However, because the ZA-LMS algorithm does not distinguish the size of the tap coefficients, its performance in low-sparse or non-sparse systems declines rapidly. Although RZA-LMS selectively attracts taps with small magnitudes, there is extra attraction to large tap coefficients, which can increase the steady-state mean square error (MSE). In this paper, a Cauchy distribution function-penalized LMS (C-LMS) algorithm is proposed. The proposed algorithm changed the penalty term of the cost function into Cauchy distribution function, which can decrease the attraction to large tap coefficients and enhances the force to the small tap coefficients. The simulation results indicate that the C-LMS can achieve lower steady-state MSE than other algorithms in sparse systems and demonstrates similar performance to the conventional LMS algorithm in non-sparse system.

Grid interfaced solar photovoltaic system using ZA-LMS based control algorithm

Renewable energy sources such as solar photovoltaic can meet increasing energy demand in countries where there is sufficient availability of sun light. Intermittent nature of this kind of renewable energy sources demands a control which can handle fast dynamics of the system. This paper presents a grid coupled solar photovoltaic (SPV) system which includes solar photovoltaic array, incremental conductance based MPPT and boost converter. Grid integration of SPV array is performed using three phase voltage source converter (VSC) controlled with a fast and robust control algorithm. A Zero Attracting Least Mean Square (ZA-LMS) based controller is proposed to generate reference grid currents. These currents are compared along with sensed grid currents to generate switching pulses for three phase VSC. The proposed system is used to feed real power demand of load along with power quality refinement features such as suppression of harmonics, maintaining grid current at unity power factor and balancing of loads. Performance of the ZA-LMS controller is compared with conventional controllers such as normalized least mean square (NLMS) and dq0 frame theory. These controllers are compared for various characteristics concerning weight convergence, mathematical complexity, computational burden on real time controller and harmonic compensation. Proposed controller is implemented using dSPACE 1104 and tested on developed laboratory prototype of grid connected VSC working as shunt active power filter. Performance of the controller is observed and verified for steady state and dynamic load conditions.

Adaption Penalized Complex LMS for Sparse Under-Ice Acoustic Channel Estimations

Accurate channel information is usually required in under-ice acoustic (UIA) communication, which exhibits a sparse characteristic. A type of norm-constrained least mean square (LMS) algorithm performs well in estimating the real-valued (passband) channels but cannot be directly applied to complex-valued (baseband) channels. This paper generalizes norm-constrained complex LMS. Complex-valued zero-attracting LMS and $l_{0}$ -norm LMS (C $l_{0} $ -LMS) are mentioned first. These two algorithms render a fixed penalty to each coefficient, which may deteriorate the performance. Then, we propose a complex-valued adaption penalized LMS (CAP-LMS) to further utilize the sparsity of the UIA channels. The adaption penalty is achieved by dividing $p$ -norm-like constraints into two separate groups according to the $l_{1} $ -norm of each coefficient. For the dominant coefficients in the large group, the norm constraint disappears to reduce the estimation bias. For the small coefficients, the adaption penalty aims to accelerate the convergence speed. Simulation results are presented to demonstrate the superior performance of the CAP-LMS algorithm. Data processing results from two under-ice experiments show the feasibility and validity of the proposed algorithms in practical UIA applications.

Transient Performance Analysis of Zero-Attracting LMS

Zero-attracting least-mean-square (ZA-LMS) algorithm has been widely used for online sparse system identification. It combines the LMS framework and $\ell_1$-norm regularization to promote sparsity, and relies on subgradient iterations. Despite the significant interest in ZA-LMS, few works analyzed its transient behavior. The main difficulty lies in the nonlinearity of the update rule. In this work, a detailed analysis in the mean and mean-square sense is carried out in order to examine the behavior of the algorithm. Simulation results illustrate the accuracy of the model and highlight its performance through comparisons with an existing model.

Robust Adaptive Algorithm by an Adaptive Zero Attractor Controller of ZA-LMS Algorithm

This paper proposes a new approach to identify time varying sparse systems. The proposed approach uses Zero-Attracting Least Mean Square (ZA-LMS) algorithm with an adaptive optimal zero attractor controller which can adapt dynamically to the sparseness level and provide appreciable performance in all environments ranging from sparse to nonsparse conditions. The optimal zero attractor controller is derived based on the criterion that confirms largest decrease in mean square deviation (MSD) error. A simple update rule is also proposed to change the zero attractor controller based on the level of sparsity. It is found that, for nonsparse system, the proposed approach converges to LMS (as ZA-LMS cannot outperform LMS when the system is nonsparse) and, for highly sparse system, as the proposed approach is based on optimal zero attractor controller, it converges either similar to ZA-LMS or even better than ZA-LMS (depending on the value of zero attractor controller chosen for ZA-LMS algorithm). The performance of the proposed algorithm is better than ZA-LMS and LMS when the system is semisparse. Simulations were performed to prove that the proposed algorithm is robust against variable sparsity level.

Improved adaptive sparse channel estimation using mixed square/fourth error criterion

Sparse channel estimation problem is one of challenge technical issues in broadband wireless communications. Square error criterion based adaptive sparse channel estimation (SEC-ASCE) algorithms, e.g., zero-attracting least mean square (ZA-LMS) and reweighted ZA LMS (RZA-LMS), have been proposed to mitigate noises as well as to exploit the channel sparsity. However, the conventional SEC-ASCE algorithms are vulnerable to performance deteriorate due to 1) random scaling of input training signal, and 2) unable to balance between convergence speed and transient-state mean square error (MSE) performance. In this paper, a mixed square/fourth error criterion (SFEC) based ASCE algorithms (SEFC-ASCE), i.e., zero-attracting least mean square/fourth error (ZA-LMS/F) and reweighted ZA-LMS/F (RZA-LMS/F), are proposed to enhance estimation performance while without exhausting a lot computational complexity. First, regularization parameters of the ZA-LMS/F and RZA-LMS/F algorithms are selected by means of Monte-Carlo simulations. Second, lower bounds of the proposed channel estimation algorithms are derived and analyzed. Finally, simulation results are given to show that the proposed sparse LMS/F-type algorithms achieve better estimation performance than the conventional algorithms.

Maximum correntropy criterion based sparse adaptive filtering algorithms for robust channel estimation under non-Gaussian environments

Sparse adaptive channel estimation problem is one of the most important topics in broadband wireless communications systems due to its simplicity and robustness. So far many sparsity-aware channel estimation algorithms have been developed based on the well-known minimum mean square error (MMSE) criterion, such as the zero-attracting least mean square (ZALMS),which are robust under Gaussian assumption. In non-Gaussian environments, however, these methods are often no longer robust especially when systems are disturbed by random impulsive noises. To address this problem, we propose in this work a robust sparse adaptive filtering algorithm using correntropy induced metric (CIM) penalized maximum correntropy criterion (MCC) rather than conventional MMSE criterion for robust channel estimation. Specifically, MCC is utilized to mitigate the impulsive noise while CIM is adopted to exploit the channel sparsity efficiently. Both theoretical analysis and computer simulations are provided to corroborate the proposed methods.

Zero‐attracting variable‐step‐size least mean square algorithms for adaptive sparse channel estimation

SummaryRecently, sparsity‐aware least mean square (LMS) algorithms have been proposed to improve the performance of the standard LMS algorithm for various sparse signals, such as the well‐known zero‐attracting LMS (ZA‐LMS) algorithm and its reweighted ZA‐LMS (RZA‐LMS) algorithm. To utilize the sparsity of the channels in wireless communication and one of the inherent advantages of the RZA‐LMS algorithm, we propose an adaptive reweighted zero‐attracting sigmoid functioned variable‐step‐size LMS (ARZA‐SVSS‐LMS) algorithm by the use of variable‐step‐size techniques and parameter adjustment method. As a result, the proposed ARZA‐SVSS‐LMS algorithm can achieve faster convergence speed and better steady‐state performance, which are verified in a sparse channel and compared with those of other popular LMS algorithms. The simulation results show that the proposed ARZA‐SVSS‐LMS algorithm outperforms the standard LMS algorithm and the previously proposed sparsity‐aware algorithms for dealing with sparse signals. Copyright © 2015 John Wiley & Sons, Ltd.

A Variable Step Size LMS Based on Sparsity for System Identification

In many practical applications, the impulse responses of the unknown system are sparse. However, the standard Least Mean Square (LMS) algorithm does not make full use of the sparsity, and the general sparse LMS algorithms increase steady-state error because of giving much large attraction to the small factor. In order to improve the performance of sparse system identification, we propose a new algorithm which introduces a variable step size method into the Reweighted Zero-Attracting LMS (RZALMS) algorithm. The improved algorithm, whose step size adjustment is controlled by the instantaneous error, is called Variable step size RZALMS (V-RZALMS). The variable step size leads to yielding smaller steady-state error on the premise of higher convergent speed. Moreover, the sparser the system is, the better the V-RZALMS performs. Three different experiments are implemented to validate the effectiveness of our new algorithm.

Improved least mean square algorithm with application to adaptive sparse channel estimation

Least mean square (LMS)-based adaptive algorithms have attracted much attention due to their low computational complexity and reliable recovery capability. To exploit the channel sparsity, LMS-based adaptive sparse channel estimation methods have been proposed based on different sparse penalties, such as ℓ1-norm LMS or zero-attracting LMS (ZA-LMS), reweighted ZA-LMS, and ℓp-norm LMS. However, the aforementioned methods cannot fully exploit channel sparse structure information. To fully take advantage of channel sparsity, in this paper, an improved sparse channel estimation method using ℓ0-norm LMS algorithm is proposed. The LMS-type sparse channel estimation methods have a common drawback of sensitivity to the scaling of random training signal. Thus, it is very hard to choose a proper learning rate to achieve a robust estimation performance. To solve this problem, we propose several improved adaptive sparse channel estimation methods using normalized LMS algorithm with different sparse penalties, which normalizes the power of input signal. Furthermore, Cramer-Rao lower bound of the proposed adaptive sparse channel estimator is derived based on prior information of channel taps' positions. Computer simulation results demonstrate the advantage of the proposed channel estimation methods in mean square error performance.