This study investigates the convergence behaviors of a family of frequency-domain adaptive filters (FDAFs) under both exact- and under-modeling situations. The stochastic analysis is conducted by transforming the frequency-domain equations into their time-domain counterparts. We discuss the transient and steady-state convergence behaviors of four FDAF versions, i.e., the constrained FDAFs with and without step-normalization, the unconstrained FDAFs with and without step-normalization, and we also present the upper bounds of step size for mean stability and mean-square stability. Starting from the expression for the steady-state mean weight vector, this study investigates whether the FDAFs can converge to unknown system impulse responses and optimum Wiener solutions. Moreover, we provide the closed-form minimum mean-square error (MMSE) that each FDAF can achieve. The difference between the current work and our previous one is threefold. First, the presented time-domain analysis is much easier to handle and has a more explicit physical meaning than that in the frequency domain. Second, we here consider an arbitrary overlap factor between consecutive blocks, while our previous analysis only focuses on 50% overlap. Third, the presented MMSE expressions and excess mean-square error (EMSE) approximations have not been given before. Simulations reveal high consistency between the experimental and theoretical results.

Recently, an affine projection generalized maximum correntropy criterion (APGMCC) algorithm was developed to process the colored input signal and impulsive noise. However, the non-convexity of the generalized correntropic loss (GC-Loss) function causes the APGMCC algorithm suffers from high steady-state misalignment. In this brief, a new robust adaptive filtering algorithm called affine projection kernel risk-sensitive mean <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${p}$ </tex-math></inline-formula> -power error loss (APKRSMPL) is proposed, which is deduced by minimizing the sum of the KRSMPL functions of the a posteriori error vector elements under a bounded energy constraint on the filter weights fluctuation. Since no matrix inversion is required, the proposed APKRSMPL algorithm is computationally efficient. In addition, the convexity of the KRSMPL function ensures faster convergence and lower steady-state misalignment of the APKRSMPL algorithm. Then, the mean-square stability as well as the steady-state excess mean square error (EMSE) of the APKRSMPL algorithm are analyzed and an approximate steady-state EMSE solution is derived. Finally, system identification and acoustic echo cancellation (AEC) computer simulations verify the accuracy of the steady-state EMSE solution and the effectiveness of the proposed APKRSMPL algorithm.

Robust augmented space recursive least-constrained-squares algorithms

Recently, maximum Versoria criterion-based adaptive algorithms have been introduced as a new solution for robust adaptive filtering. This paper studies the steady-state tracking analysis of an adaptive filter with maximum Versoria criterion (MVC) in a non-stationary (Markov time-varying) system. Our analysis relies on the energy conservation method. Both Gaussian and general non-Gaussian noise are considered, and for both cases, the closed-form expression for steady-state excess mean square error (EMSE) is derived. Regardless of noise type, unlike the stationary environment, the EMSE curves are not increasing functions of step-size parameter. The validity of the theoretical results is justified via simulation.

The adaptive filtering algorithms based on the arctangent cost function framework have shown robustness against impulsive noise. In this brief, the standard least mean square (LMS) algorithm under this framework is concentrated on, which is called the arctangent LMS (ATLMS) algorithm. The steady-state excess mean square error (EMSE) and mean square deviation (MSD) of the ATLMS algorithm are analyzed using the energy conservation relation. In stationary environment, both Gaussian and non-Gaussian situations are discussed. The closed-form expressions of the steady-state EMSE and MSD are obtained using Taylor’s expansion. In non-stationary environment, a first-order random-walk model is used for modeling the time-varying optimal weight. Theoretical steady-state performance and the optimal step size are derived. Simulation results under different noise environments verify the validity of our theoretical findings.

Steady-state mean-square performance analysis of the block-sparse maximum Versoria criterion

A reference free non-negative adaptive learning system for health care monitoring and adaptive physiological artifact elimination in brain waves

Robust kernel adaptive filtering for nonlinear time series prediction

In recent years, the hyperbolic family of adaptive algorithms have been widely used to combat impulsive noise. The novel exponential hyperbolic sine adaptive filters (EHSAF) and the normalized exponential hyperbolic sine adaptive filter (NEHSAF) suitable for impulsive noise environments are proposed in this brief. The cost function is based on the exponential hyperbolic sine-based error function. The stability condition based on the learning rate and the steady-state analysis are investigated too. Additionally, a variable scheme for the scaling parameter is proposed to remove the tradeoff between convergence speed and steady-state excess mean square error (EMSE). The computational complexity is presented too. The simulation results in the context of unknown system identification and echo cancellation application have been performed to prove the performance improvement of the proposed algorithms.

Bias-compensated augmented complex-valued NSAF algorithm and its low-complexity implementation

Performance analysis of the augmented complex-valued least mean kurtosis algorithm

A distributed FxLMS algorithm for narrowband active noise control and its convergence analysis

The Least Mean Square (LMS) algorithm has a slow convergence rate as it is dependent on the eigenvalue spread of the input correlation matrix. In this research, we solved this problem by introducing a novel adaptive filtering algorithm for complex domain signal processing based on q-derivative. The proposed algorithm is based on Wirtinger calculus and is called as q- Complex Least Mean Square (q-CLMS) algorithm. The proposed algorithm could be considered as an extension of the q-LMS algorithm for the complex domain. Transient and steady-state analyses of the proposed q-CLMS algorithm are performed and exact analytical expressions for mean analysis, mean square error (MSE), excess mean square error (EMSE), mean square deviation (MSD) and misadjustment are presented. Extensive experiments have been conducted and a good match between the simulation results and theoretical findings is reported. The proposed q-CLMS algorithm is also explored for whitening applications with satisfactory performance. A modification of the proposed q-CLMS algorithm called Enhanced q-CLMS (Eq-CLMS) is also proposed. The Eq-CLMS algorithm eliminates the need for a pre-coded value of the q-parameter thereby automatically adapting to the best value. Extensive experiments are performed on system identification and channel equalization tasks and the proposed algorithm is shown to outperform several benchmark and state-of-the-art approaches namely Complex Least Mean Square (CLMS), Normalized Complex Least Mean Square (NCLMS), Variable Step Size Complex Least Mean Square (VSS-CLMS), Complex FLMS (CFLMS) and Fractional-ordered-CLMS (FoCLMS) algorithms.

This paper presents a spline-based Hammerstein model for adaptive filtering based on a sign algorithm with the normalised orthogonal gradient algorithm. Spline-based Hammerstein architecture consists of an interpolation spline-based adaptive lookup table in the part of nonlinear filter and an adaptive finite impulse response filter used in the part of linear filter. Hammerstein spline adaptive filter (HSAF) is a nonlinear filter for the nonlinear systems among the advantages in the low computational cost and high performance. An adaptive lookup table and spline control points are determined and derived with the orthogonal gradient-based mechanism. Performance analysis in terms of convergence properties and mean square analysis based on the mean square error (MSE) constraint are proven by using the Taylor series expansion of the estimation error in the form of the excess MSE. Experimental results indicate the robust performance of the proposed algorithm can provide the better performance than the other models based on the conventional least mean square Hammerstein spline adaptive filtering algorithm.

Proportionate Maximum Versoria Criterion (P-MVC) based adaptive algorithms for unknown sparse system identification problem are proposed in this brief. The conventional proportionate type algorithms used for sparse system identification can work well only under Gaussian assumption due to the dependency on the least mean square error. However, in many real cases, the algorithms have to be also robust in impulsive noise environments. The Maximum Versoria Criteria based adaptive algorithms were found to have good robustness against impulsive noise while the proportionate term in the adaptive algorithm exploits the sparse nature to improve the convergence speed. Hence, to simultaneously have robustness under impulsive environment and improved convergence speed, the P-MVC algorithm and an improved tracking P-MVC version are proposed. The performance analysis indicates that the Excess Mean Square Error (EMSE) is the same as that of MVC adaptive algorithm. Furthermore, simulations in the context of sparse system identification scenario reveal that the proposed algorithms have both robustness and improved performance in impulsive noise environment.

An improved mean-square performance analysis of the diffusion least stochastic entropy algorithm

On the behavior of a combination of adaptive filters operating with the NLMS algorithm in a nonstationary environment

A robust diffusion algorithm using logarithmic hyperbolic cosine cost function for channel estimation in wireless sensor network under impulsive noise environment

In distributed wireless networks, the adaptation process depends on the information being shared between various nodes. The global minimum, is therefore, likely to be affected when the information shared between the nodes gets corrupted. This could happen due to several reasons namely link failure, noisy environment and erroneous data etc. In this research, we propose a computationally efficient robust incremental least mean square (RILMS) algorithm to resolve the aforementioned issues. Essentially, a fusion step is introduced in the framework of the incremental least mean square (ILMS). Prior to adaptation at a node, the information shared by the neighbouring node is fused with the temporally preceding information of the node using an efficient combiner. An adaptive fusion strategy is proposed resulting in dynamic weight assignment for the fusion step. Closed form expression for the steady-state excess mean square error (EMSE) is derived and the performance of the proposed algorithm is evaluated for the noisy link environments and compared to the existing algorithms. Extensive experiments show the efficacy of the proposed approach compared to the contemporary methods. The proposed algorithm is found to be robust against the link failure and local node divergence problems. The improved performance of the proposed RILMS algorithm comes with a significant reduction in computational complexity compared to the convex combination based ILMS (CILMS) approach.

The Thoracic Electrical Bioimpedance (TEB) helps to determine the stroke volume during cardiac arrest. While measuring cardiac signal it is contaminated with artifacts. The commonly encountered artifacts are Baseline wander (BW) and Muscle artifact (MA), these are physiological and non-stationary. As the nature of these artifacts is random, adaptive filtering is needed than conventional fixed coefficient filtering techniques. To address this, a new block based adaptive learning scheme is proposed to remove artifacts from TEB signals in clinical scenario. The proposed block least mean square (BLMS) algorithm is mathematically normalized with reference to data and error. This normalization leads, block normalized LMS (BNLMS) and block error normalized LMS (BENLMS) algorithms. Various adaptive artifact cancellers are developed in both time and frequency domains and applied on real TEB quantities contaminated with physiological signals. The ability of these techniques is measured by calculating signal to noise ratio improvement (SNRI), Excess Mean Square Error (EMSE), and Misadjustment (Mad). Among the considered algorithms, the frequency domain version of BENLMS algorithm removes the physiological artifacts effectively then the other counter parts. Hence, this adaptive artifact canceller is suitable for real time applications like wearable, remove health care monitoring units.