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To improve the robust characteristic and filtering accuracy of the traditional adaptive filtering algorithms (AFAs) under censored regression (CR) model in impulsive interference environments, some robust CR-type AFAs (R-CR-AFAs) have been developed. However, these exiting R-CR-AFAs may suffer from high steady-state misalignment in parameter estimation scenario. Therefore, in this paper, we first construct a unified framework to develop a class of R-CR-AFAs by adopting various robust strategies with error nonlinearities as cost functions. Then the mean and mean-square stability ranges and steady-state convergence behavior of the R-CR-AFAs are analyzed via resorting to some frequently-utilized assumptions and lemmas. In particular, a novel censored regression generalized modified Blake-Zisserman adaptive filtering (CR-GMBZ-AF) algorithm is presented to achieve higher steady-state estimation accuracy contrasted to related R-CR-AFAs benefiting from the advantages of the newly proposed GMBZ criterion based on the unified framework. Numerical simulation experiments manifest that the developed CR-GMBZ-AF algorithm arrives at better learning performance in comparison with state-of-the-art algorithms and the theoretical steady-state model demonstrates good agreement with simulation results under parameter estimation and acoustic echo cancellation scenarios. [ABSTRACT FROM AUTHOR]

Abstract We propose two sparsity-aware normalized subband adaptive filter (NSAF) algorithms by using the gradient descent method to minimize a combination of the original NSAF cost function and the l 1 -norm penalty function on the filter coefficients. This l 1 -norm penalty exploits the sparsity of a system in the coefficients update formulation, thus improving the performance when identifying sparse systems. Compared with prior work, the proposed algorithms have lower computational complexity with comparable performance. We study and devise statistical models for these sparsity-aware NSAF algorithms in the mean square sense involving their transient and steady-state behaviors. This study relies on the vectorization argument and the paraunitary assumption imposed on the analysis filter banks, and thus does not restrict the input signal to being Gaussian or having another distribution. In addition, we propose to adjust adaptively the intensity parameter of the sparsity attraction term. Finally, simulation results in sparse system identification demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

Abstract A bias-compensated constrained least mean square (BC-CLMS) adaptive filter algorithm for noisy input is proposed. To derive the proposed algorithm, we present a novel cost function whose gradient vector is unbiased. Thereby, the proposed algorithm can mitigate the effect of input noise and obtain an unbiased estimation. Then, the detail performance analysis of the proposed algorithm is also provided. Finally, simulations are carried out to illustrate the advantage of the proposed algorithm. In addition, the correctness of performance analysis is also verified by simulations. [ABSTRACT FROM AUTHOR]

This paper analyzes the statistical behavior of the bias-compensated sign subband adaptive filtering algorithm with individual-weighting-factors (BC-IWF-SSAF) under errors-in-variables (EIV) model. The theoretical expressions for transient and steady-state behaviors of BC-IWF-SSAF in the mean and mean-square senses are derived through utilizing some reasonable assumptions and Price's theorem. Furthermore, the stability ranges of algorithm are provided. To accomplish performance enhancement, the variable step-size version (VSS) of BC-IWF-SSAF, called VSS-BC-IWF-SSAF algorithm, is developed based on the transient model via minimizing the mean-square deviation (MSD) at every iteration to tackle the contradictory requirements of quick convergence rate and high filtering accuracy caused by fixed step-size (FSS). Finally, Monte-Carlo simulations under system identification and acoustic echo cancellation applications certificate the effectiveness of statistical analysis and variable step-size strategy. [ABSTRACT FROM AUTHOR]

In all presented analyses of the normalized subband adaptive filter (NSAF) algorithm, there is a common assumption that the length of the adaptive filter is equal to that of the unknown system. In many practices, however, the adaptive filter usually works in an under-modeling situation. Namely, the length of the adaptive filter is less than that of the unknown system. Therefore, for this case, the existing analysis results for the NSAF algorithm are not applicable. In this paper, we analyze the performance of the deficient length NSAF algorithm based on some reasonable assumptions and approximations. More precisely, the expressions that characterize the transient-state and steady-state mean-square behavior of the algorithm are presented. Simulation results in various scenarios support our theoretical expressions. In addition, based on our analyses, a variable step size NSAF algorithm suitable for the under-modeling case is developed, which improves the performance. [ABSTRACT FROM AUTHOR]

Although the least mean p th power (LMP) and normalized LMP (NLMP) algorithms of adaptive Volterra filters outperform the conventional least mean square (LMS) algorithm in the presence of α -stable noise, they still exhibit slow convergence and high steady-state kernel error in nonlinear system identification. To overcome these limitations, an enhanced recursive least mean p th power algorithm with logarithmic transformation (RLogLMP) is proposed in this paper. The proposed algorithm is adjusted to minimize the new cost function with the p -norm logarithmic transformation of the error signal. The logarithmic transformation, which can diminish the significance of outliers under α -stable noise environment, increases the robustness of the proposed algorithm and reduces the steady-state kernel error. Moreover, the proposed method improves the convergence rate by the enhanced recursive scheme. Finally, simulation results demonstrate that the proposed algorithm is superior to the LMP, NLMP, normalized least mean absolute deviation (NLMAD), recursive least squares (RLS) and nonlinear iteratively reweighted least squares (NIRLS) algorithms in terms of convergence rate and steady-state kernel error. [ABSTRACT FROM AUTHOR]

Abstract: To compensate the linear and nonlinear distortions and to track the characteristic of the time-varying channel in digital communication systems, a novel adaptive decision feedback equalizer (DFE) with the combination of finite impulse response (FIR) filter and functional link neural network (CFFLNNDFE) is introduced in this paper. This convex nonlinear combination results in improving the convergence speed while retaining the lower steady-state error at the cost of a small increasing computational burden. To further improve the performance of the nonlinear equalizer, we derive here a novel simplified modified normalized least mean square (SMNLMS) algorithm. Moreover, the convergence properties of the proposed algorithm are analyzed. Finally, computer simulation results which support analysis are provided to evaluate the performance of the proposed equalizer over the functional link neural network (FLNN), radial basis function (RBF) neural network and linear equalizer with decision feedback (LMSDFE) for time-invariant and time-variant nonlinear channel models in digital communication systems. [Copyright &y& Elsevier]

Abstract: To overcome the computational complexity of the Volterra filter, a novel adaptive joint process filter using pipelined bilinear polynomial architecture (JPBPF) is proposed in this paper. The proposed architecture consists of two subsections: nonlinear subsection performing a nonlinear mapping from the input space to an intermediate space by the bilinear polynomial filter (BPF), and a linear filter performing a linear mapping from the intermediate space to the output space. The corresponding adaptive algorithms are deduced for the nonlinear subsection and linear filter subsection, respectively. To evaluate the performance of the JPBPF, a series of simulations are presented including nonlinear system identification, predicting of speech signals and nonlinear channel equalization. Compared with the conventional second-order Volterra (SOV) filter and BPF, the JPBPF exhibits a slightly better convergence performance in terms of convergence speed and steady-state error. Moreover, since those modules of a JPBPF can be performed simultaneously in a pipelined parallelism fashion, this would lead to a significant improvement in its total computational efficiency. [Copyright &y& Elsevier]

As a new addition to the recursive least squares (RLS) family filters, the state space recursive least squares (SSRLS) filter can achieve desirable performance by conquering some limitations of the standard RLS filter. However, when the system is contaminated by some non-Gaussian noises, the performance of SSRLS will get worse. The main reason for this is that the SSRLS is developed under the well-known minimum mean square error (MMSE) criterion, which is not very suitable for non-Gaussian situations. To address this issue, in this paper, we propose a new state space based linear filter, called the state space least p -power (SSLP) filter, which is derived under the least mean p -power error (LMP) criterion instead of the MMSE. With a proper p value, the SSLP can outperform the SSRLS substantially especially in non-Gaussian noises. Two illustrative examples are presented to show the satisfactory results of the new algorithm. [ABSTRACT FROM AUTHOR]

Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adapt then combine MCC and combine then adapt 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, especially for 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. [ABSTRACT FROM AUTHOR]