Diffusion leaky LMS algorithm: analysis and implementation

The diffusion least-mean square (dLMS) algorithms have attracted much attention owing to its robustness for distributed estimation problems. However, the performance of such filters may change when they are implemented for suppressing noises from speech signals. To overcome this problem, a diffusion leaky dLMS algorithm is proposed in this work, which is characterized by its numerical stability and small misadjustment for noisy speech signals when the unknown system is a lowpass filter. Finally, two implementations of the leaky dLMS are introduced. It is demonstrated that the leaky dLMS can be effectively introduced into a noise reduction network for speech signals.Comment: Start from Feb. 7th, 2016. In simulation studies, the unknown vector of interest is a lowpass filter of order M=

KLMAT: A Kernel Least Mean Absolute Third Algorithm

In this paper, a kernel least mean absolute third (KLMAT) algorithm is developed for adaptive prediction. Combining the benefits of the kernel method and the least mean absolute third (LMAT) algorithm, the proposed KLMAT algorithm performs robustly against noise with different probability densities. To further enhance the convergence rate of the KLMAT algorithm, a variable step-size version (VSS-KLMAT algorithm) is proposed based on a Lorentzian function. Moreover, the stability and convergence property of the proposed algorithms are analyzed. Simulation results in the context of time series prediction demonstrate that the effectiveness of proposed algorithms.Comment: submitted to the journal in March, 17th, 201

Two improved normalized subband adaptive filter algorithms with good robustness against impulsive interferences

To improve the robustness of subband adaptive filter (SAF) against impulsive interferences, we propose two modified SAF algorithms with an individual scale function for each subband, which are derived by maximizing correntropy-based cost function and minimizing logarithm-based cost function, respectively, called MCC-SAF and LC-SAF. Whenever the impulsive interference happens, the subband scale functions can sharply drop the step size, which eliminate the influence of outliers on the tap-weight vector update. Therefore, the proposed algorithms are robust against impulsive interferences, and exhibit the faster convergence rate and better tracking capability than the sign SAF (SSAF) algorithm. Besides, in impulse-free interference environments, the proposed algorithms achieve similar convergence performance as the normalized SAF (NSAF) algorithm. Simulation results have demonstrated the performance of our proposed algorithms.Comment: 14 pages,8 figures,accepted by Circuits, Systems, and Signal Processing on Feb 23, 201

A novel normalized sign algorithm for system identification under impulsive noise interference

To overcome the performance degradation of adaptive filtering algorithms in the presence of impulsive noise, a novel normalized sign algorithm (NSA) based on a convex combination strategy, called NSA-NSA, is proposed in this paper. The proposed algorithm is capable of solving the conflicting requirement of fast convergence rate and low steady-state error for an individual NSA filter. To further improve the robustness to impulsive noises, a mixing parameter updating formula based on a sign cost function is derived. Moreover, a tracking weight transfer scheme of coefficients from a fast NSA filter to a slow NSA filter is proposed to speed up the convergence rate. The convergence behavior and performance of the new algorithm are verified by theoretical analysis and simulation studies.Comment: This paper has been accepted by Circuits, Systems, and Signal Processing. pp 1-22, First online: 17 November 201

Diffusion Maximum Correntropy Criterion Algorithms for Robust Distributed Estimation

Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adaptation to combination MCC and combination to adaptation MCC, are developed to deal with the distributed estimation over network in impulsive (long-tailed) noise environments. The cost functions used in distributed estimation are in general based on the mean square error (MSE) criterion, which is desirable when the measurement noise is Gaussian. In non-Gaussian situations, such as the impulsive-noise case, MCC based methods may achieve much better performance than the MSE methods as they take into account higher order statistics of error distribution. The proposed methods can also outperform the robust diffusion least mean p-power(DLMP) and diffusion minimum error entropy (DMEE) algorithms. The mean and mean square convergence analysis of the new algorithms are also carried out.Comment: 17 pages,10 figure

A Band-independent Variable Step Size Proportionate Normalized Subband Adaptive Filter Algorithm

Proportionate-type normalized suband adaptive filter (PNSAF-type) algorithms are very attractive choices for echo cancellation. To further obtain both fast convergence rate and low steady-state error, in this paper, a variable step size (VSS) version of the presented improved PNSAF (IPNSAF) algorithm is proposed by minimizing the square of the noise-free a posterior subband error signals. A noniterative shrinkage method is used to recover the noise-free a priori subband error signals from the noisy subband error signals. Significantly, the proposed VSS strategy can be applied to any other PNSAF-type algorithm, since it is independent of the proportionate principles. Simulation results in the context of acoustic echo cancellation have demonstrated the effectiveness of the proposed method.Comment: 21 pages,8 figures, 2 tables, accepted by AEU-International Journal of Electronics and Communications on May 31, 201

Diffusion Leaky Zero Attracting Least Mean Square Algorithm and Its Performance Analysis

Recently, the leaky diffusion least-mean-square (DLMS) algorithm has obtained much attention because of its good performance for high input eigenvalue spread and low signal-to-noise ratio (SNR). However, the leaky DLMS algorithm may suffer from performance deterioration in the sparse system. To overcome this drawback, the leaky zero attracting DLMS (LZA-DLMS) algorithm is developed in this paper, which adds an l1-norm penalty to the cost function to exploit the property of sparse system. The leaky reweighted zero attracting DLMS (LRZA-DLMS) algorithm is also put forward, which can improve the estimation performance in the presence of time-varying sparsity. Instead of using the l1-norm penalty, in the reweighted version, a log-sum function is employed as the substitution. Based on the weight error variance relation and several common assumptions, we analyze the transient behavior of our findings and determine the stability bound of the step-size. Moreover, we implement the steady state theoretical analysis for the proposed algorithms. Simulations in the context of distributed network system identification illustrate that the proposed schemes outperform various existing algorithms and validate the accuracy of the theoretical results

Robustness of Maximum Correntropy Estimation Against Large Outliers

The maximum correntropy criterion (MCC) has recently been successfully applied in robust regression, classification and adaptive filtering, where the correntropy is maximized instead of minimizing the well-known mean square error (MSE) to improve the robustness with respect to outliers (or impulsive noises). Considerable efforts have been devoted to develop various robust adaptive algorithms under MCC, but so far little insight has been gained as to how the optimal solution will be affected by outliers. In this work, we study this problem in the context of parameter estimation for a simple linear errors-in-variables (EIV) model where all variables are scalar. Under certain conditions, we derive an upper bound on the absolute value of the estimation error and show that the optimal solution under MCC can be very close to the true value of the unknown parameter even with outliers (whose values can be arbitrarily large) in both input and output variables. Illustrative examples are presented to verify and clarify the theory.Comment: 8 pages, 7 figure

Set-membership improved normalized subband adaptive filter algorithms for acoustic echo cancellation

In order to improve the performances of recently-presented improved normalized subband adaptive filter (INSAF) and proportionate INSAF algorithms for highly noisy system, this paper proposes their set-membership versions by exploiting the theory of set-membership filtering. Apart from obtaining smaller steady-state error, the proposed algorithms significantly reduce the overall computational complexity. In addition, to further improve the steady-state performance for the algorithms, their smooth variants are developed by using the smoothed absolute subband output errors to update the step sizes. Simulation results in the context of acoustic echo cancellation have demonstrated the superiority of the proposed algorithms.Comment: 22 pages,8 figures, 3 tables,accepted by IET signal processing on 27-Jul-201

Set-membership NLMS algorithm based on bias-compensated and regression noise variance estimation for noisy inputs

The bias-compensated set-membership normalised LMS (BCSMNLMS) algorithm is proposed based on the concept of set-membership filtering, which incorporates the bias-compensation technique to mitigate the negative effect of noisy inputs. Moreover, an efficient regression noise variance estimation method is developed by taking the iterative-shrinkage method. Simulations in the context of system identification demonstrate that the misalignment of the proposed BCSM-NLMS algorithm is low for noisy inputs