Analysis of adaptive step-size Correlation Phase-Newton Algorithm

This paper first reviews Correlation Phase Algorithm (CPhA) for adaptive filters to be used in digital Quadrature Amplitude Modulation (QAM) systems in radio communications. Stochastic models are presented for two types of impulse noise that are found in adaptive filtering systems: one in observation noise and another at filter input. To improve the filter convergence speed, we propose a new Adaptive Step-Size (ASS) control algorithm to be combined with the CPhA. Rigorous performance analysis of the ASS-CPhA is developed for calculating transient and steady-state convergence behavior. Through numerical experiments, we demonstrate faster convergence and high robustness of the proposed ASS-CPhA in the presence of both types of impulsive noise. Good agreement between simulated and theoretical filter convergence shows the validity of the analysis.

This paper proposes a new adaptation algorithm named normalized correlation-Newton (NC-Newton) algorithm and a novel variable q-norm control method (NC-Newton-Varq-norm) for complex-domain adaptive filters. First, stochastic models are presented for two types of impulse noise intruding adaptive filters: one is present in observation noise and another at filter input. After reviewing q-norm and NC-Newton algorithm, we propose a variable q-norm control method. Analysis of the NC-Newton-Varq-norm algorithm is developed for theoretically calculating transient and steady-state convergence behavior. Through experiment with some examples, we demonstrate effectiveness of the proposed variable q-norm control method in improving filter convergence speed while preserving robustness of the NC-Newton algorithm in impulsive noise environments. Good agreement between simulated and theoretical convergence behavior validates the analysis.

This paper proposes Adaptive Step-Size Least Mean Modulus (ASS-LMM) algorithm for fast convergent and robust adaptive filtering in the presence of impulse noise. The ASS-LMM algorithm for use in adaptive filters defined in the complex-number domain is basically the LMM algorithm combined with a new adaptive step-size control algorithm to improve the convergence speed of the LMM algorithm while preserving its robustness against additive impulsive observation noise. Through analysis and experiment, we demonstrate effectiveness of the proposed ASS-LMM algorithm in making adaptive filters fast convergent and highly robust in the presence of impulse noise. Good agreement between simulated and theoretical convergence behavior in the transient phase and in the steady state proves the validity of the analysis.

The generalized maximum correntropy criterion (GMCC) has been widely applied for robust adaptive filtering (AF) algorithm. The gradient-based GMCC (GB-GMCC) algorithm realizes good filtering performance for system identification under impulsive noise environments. However, the highly colored input signal can damage the convergence rate of GB-GMCC. Therefore, based on the data-reusing method, we propose a robust AF algorithm, called as data-reusing GMCC (DR-GMCC) algorithm, which uses the information of the latest <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> input data to remedy the convergence limitation of GB-GMCC. In addition, to enhance the filtering performance of DR-GMCC, we use a random strategy to select the past <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> input data leading to a new algorithm, named as random DR-GMCC (RDR-GMCC). Furthermore, for RDR-GMCC, we also analyze the mean-square convergence and computational complexity. Compared with existing algorithms, simulation results verify that RDR-GMCC achieves better filtering accuracy and faster convergence rate.

In order to realize the high-resolution multipath Time Difference Of Arrival (TDOA) estimation which is not limited by the resolution limit of correlation method under impulsive noise environment, a Correntropy Expectation-Maximum (CEM) high resolution multipath TDOA estimation algorithm is proposed based on the Maximum Correntropy Criterion (MCC). The multipath TDOA is estimated by transforming multi-dimensional optimization problems into multiple one-dimensional optimization problems. The simulation results show that the CEM algorithm has good estimation performance under strong impulsive noise and low SNR environment, and the selection of kernel size in CEM algorithm is not depend on the prior information of the impulsive noise.

This paper presents an adaptive filtering system where impulse noise is present at filter input. To study adverse, or favorable, effects of such impulse noise on adaptive filter performance, we develop transient and steady-state analysis of adaptive filters using the LMS algorithm (LMSA) and signed regressor LMS algorithm (SRA). Through analysis and experiment, we find that the SRA exhibits significantly higher robustness against the impulse noise than the LMSA. For the SRA, we find that mean square tap weight misalignment (MSTWM) decreases as the impulse noise variance increases, attaining a minimum before the filter diverges.

In this paper, a new robust adaptive FIR filter algorithm with variable forgetting factor for time-varying parameters estimation in the presence of impulsive noise is discussed. The proposed algorithm is based on the robust recursive least square and extended prediction error variable forgetting factor adaptation algorithms. The feasibility of the approach is demonstrated in a system identification simulation using a FIR filter application.

A robust direction-of-arrival estimation method for impulsive noise environments

Automatic modulation classification plays an essential role in cognitive communication systems. Traditional automatic modulation classification approaches are primarily developed under Gaussian noise assumptions. Nevertheless, recent empirical studies show that the impulsive noise has emerged in numerous wireless communication systems. The bursty nature of impulsive noise fundamentally challenges the applicability of traditional automatic modulation classification approaches. In order to accurately identify the modulation schemes in impulsive noise environment, in this paper, we propose a novel modulation classification approach through using hyperbolic-tangent cyclic spectrum and multi-branch attention shuffle neural networks. First, based on the designed hyperbolic-tangent autocorrelation function, hyperbolic-tangent cyclic spectrum is proposed to effectively suppress impulsive noise and extract the discriminating features. Then, based on the hyperbolic-tangent cyclic spectrum, a novel deep shuffle neural network is proposed as a classifier to perform the modulation classification through multi-branch attention mechanism to reweight all features. Both numerical and real-data experimental results demonstrate that the proposed algorithm can correctly classify modulation schemes with high accuracy and robustness in impulsive noise.

Channel estimation in Underwater Acoustic Communication (UAC) faces significant challenges due to the non-Gaussian, impulsive noise in ocean environments and the inherent high dimensionality of the estimation task. This paper introduces a robust channel estimation algorithm by solving an l1−l1 optimization problem via the Alternating Direction Method of Multipliers (ADMM), effectively exploiting channel sparsity and addressing impulsive noise outliers. A non-monotone backtracking line search strategy is also developed to improve the convergence behavior. The proposed algorithm is low in complexity and has robust performance. Simulation results show that it exhibits a small performance deterioration of less than 1 dB for Channel Impulse Response (CIR) estimation in impulsive noise environments, nearly matching its performance under Additive White Gaussian Noise (AWGN) conditions. For Delay-Doppler (DD) doubly spread channel estimation, it maintains Bit Error Rate (BER) performance comparable to using ground truth channel information in both AWGN and impulsive noise environments. At-sea experimental validations for channel estimation in Orthogonal Frequency Division Multiplexing (OFDM) systems further underscore the fast convergence speed and high estimation accuracy of the proposed method.

In this paper, an efficient Fast Block LMS (FBLMS) algorithm is proposed for removing artifacts preserving the low frequency components and tiny features of the ECG. The proposed implementation is suitable for applications requiring large signal to noise ratios with fast convergence rate. The FBLMS algorithm, being the solution of the steepest descent strategy for minimizing the mean squared error in a complete signal occurrence, is shown to be steady-state unbiased and with a lower variance than the LMS algorithm. Finally, we have applied this algorithm on ECG signals from the MIT-BIH data base and compared its performance with the conventional LMS algorithm. The results show that the performance of the FBLMS algorithm is superior than the LMS algorithm. I. INTRODUCTION The extraction of high-resolution ECG signals from record- ings contaminated with background noise is an important issue to investigate. The goal for ECG signal enhancement is to separate the valid signal components from the undesired artifacts, so as to present an ECG that facilitates easy and accurate interpretation. Many approaches have been reported in the literature to address ECG enhancement using adaptive filters (2)-(3), which permit to detect time varying potentials and to track the dynamic variations of the signals. In (3), Thakor et al. proposed an LMS based adaptive recurrent filter to acquire the impulse response of normal QRS complexes, and then applied it for arrhythmia detection in ambulatory ECG recordings. The reference inputs to the LMS algorithm are deterministic functions and are defined by a periodically extended, truncated set of orthonormal basis functions. In these papers, the LMS algorithm operates on an instantaneous basis such that the weight vector is updated every new sample within the occurrence, based on an instantaneous gradient estimate. There are certain clinical applications of ECG signal processing that require adaptive filters with large number of taps. In such applications the conventional LMS algorithm is computationally expensive to implement. The block processing of data samples can significantly reduce the computational complexity. By applying this strategy, a special implementa- tion of the LMS algorithm is called the block LMS algorithm. In a recent study, however, a steady state convergence analysis for the LMS algorithm with deterministic reference inputs showed that the steady-state weight vector is biased, and thus, the adaptive estimate does not approach the Wiener solution. To handle this drawback another strategy was considered for estimating the coefficients of the linear expansion, ie., the BLMS algorithm (8), in which the coefficient vector is updated only once every occurrence based on a block gradient estimation. The BLMS algorithm has been proposed in the case of random reference inputs and has, when the input is stationary, the same steady state misadjustment and convergence speed as the LMS algorithm. A major advantage of the block, or the transform domain, LMS algorithm is that the input signals are approximately uncorrelated. Moreover, the filter output and the weight update terms can be evaluated faster using FFT-based fast BLMS (FBLMS) algorithm. The advantage of this algorithm is less computational complexity and good filtering capability. These characteristics may plays a vital role in biotelemetry, where extraction of noise free ECG signal for efficient diagnosis and fast computations, high data transfer rate are needed to avoid overlapping of pulses and to resolve ambiguities. To the best of our knowledge, transform domain has not been considered previously within the context of filtering artifacts in ECG signals. In this paper, we present a FBLMS algorithm to remove the artifacts from ECG. Such a realization is intrinsically less complex than its BLMS based counterpart. This algorithm enjoys less compu- tational complexity and good filtering capability. To study the performance of the proposed algorithm to effectively remove the noise from the ECG signal, we carried out simulations on MIT-BIH database for different artifacts. The simulation results shows that the proposed algorithm performs better than the LMS counterpart to eliminate the noise from ECG.

The sequential-LMS (S-LMS) family of algorithms are designed for partial update adaptive filtering. Like the LMS algorithm, their performance will be severely degraded by impulsive noises. In this paper, we derive the nonlinear least mean M-estimate (LMM) versions of the S-LMS family from robust M-estimation. The resultant algorithms, named the S-LMM family, have the improved performance in impulsive noise environment. Using the Pricepsilas theorem and its extension, the mean and mean square convergence behaviors of the S-LMS and S-LMM families of algorithms are derived both for Gaussian and contaminated Gaussian (CG) additive noises.

Constrained least lncosh adaptive filtering algorithm

In this paper, we propose a modified time-domain channel estimation algorithm for OFDM systems working under impulsive noise conditions. The proposed method employs two time-domain windows to reduce additive white Gaussian noise and impulsive noise components included in the estimated channel impulse response (CIR). Meanwhile, the impulse noise equalizer further eliminates the impulse noise. As a result, the modified algorithm can overcome the mean-square error (MSE) floor caused by the conventional method in impulsive noise environment. Simulation results demonstrate that the proposed algorithm can significantly improve the MSE performance compared with the conventional estimation method, and provides about 3dB improvement in SNR for the same BER values in DVB system.

Nonlinear system identification in noisy environments presents a significant challenge in adaptive filtering, particularly when dealing with impulsive noise, non-Gaussian distributions, and complex system dynamics. Traditional filtering approaches, including Least Mean Squares (LMS) and Recursive Least Squares (RLS), often exhibit performance degradation due to their reliance on second-order statistical assumptions. The Maximum Correntropy Criterion (MCC) has shown promise in improving robustness; however, it suffers from limitations in capturing highly nonlinear system behaviors. This study proposes a Generalized Maximum Correntropy Criterion (GMCC) with Spline Adaptive Filtering, leveraging B-spline basis functions to enhance function approximation and noise resilience. The GMCC framework was evaluated against LMS, RLS, and conventional MCC-based adaptive filtering methods across Gaussian, Laplacian, and impulsive noise environments. Experimental results demonstrate that GMCC consistently achieves lower Mean Squared Error (MSE) values across all noise scenarios, outperforming conventional approaches in both accuracy and convergence stability. Statistical analysis using ANOVA confirmed performance consistency, though differences were not statistically significant at the 95% confidence level. Practical applications include biomedical signal processing, financial modeling, radar tracking, and autonomous systems, where robust nonlinear filtering is essential. Future research should focus on optimizing computational efficiency, incorporating deep learning enhancements, and extending real-time implementations for IoT and edge computing applications.