An Incremental Self-Learning Algorithm with Robustness against Impulsive Noise

Accurate channel-estimation algorithms are critical for enhancing the throughput of wireless communication systems, including millimetre wave (mmWave) multiple-input multiple-output (MIMO) systems, where precise channel knowledge enables reliable signal detection and beamforming. In practical wireless environments, impulsive non-Gaussian noise with unknown statistics often occurs due to electromagnetic interference and harsh propagation conditions, significantly degrading estimation accuracy and overall system performance. In this context, the maximum correntropy criterion (MCC) has emerged as an attractive solution for robust channel estimation that outperforms state-of-the-art algorithms. However, the MCC-based algorithm’s performance is sensitive to the tuning of hyperparameters, which is challenging in the presence of non-Gaussian noise, such as impulsive noise (IN). Furthermore, a recent genre of kernel width sampling methods makes MCC hyperparameter-free and allows for asymptotic convergence to the squared-error performance of MCC with the ideal kernel width. To ensure their practical applicability, convergence analysis is essential to theoretically guarantee stability and performance under various IN scenarios. This study presents convergence analysis of hyperparameter-free MCC-based channel estimation for mmWave MIMO systems considering various IN scenarios. To validate the theoretical analysis, simulations are conducted on practical mmWave MIMO system models. Simulation results closely match the analytical findings, which confirms the accuracy and effectiveness of the analysis we here present.

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.

Nonlinear system identification has been studied under the assumption that the noise has finite second and higher order statistics. In many practical applications, impulsive measurement noise severely weakens the effectiveness of conventional methods. In this paper, /spl alpha/-stable noise is used as a noise model. In such case, the minimum mean square error (MMSE) criterion is no longer an appropriate metric for estimation error due to the lack of finite second-order statistics of the noise. Therefore, we adopt minimum dispersion criterion, which in turn leads to the adaptive least mean pth power (LMP) algorithm. It is shown that the LMP algorithm under the /spl alpha/-stable noise model converges as long as the step size satisfies certain conditions. The effect of p on the performance is also investigated. Compared with conventional methods, the proposed method is more robust to impulsive noise and has better performance.

Cyclostationary analysis has several applications in communications, e.g., spectral sensing, signal parameter estimation, and modulation classification. Most of them consider the additive white Gaussian noise (AWGN) channel model, although wireless communication systems may also be subject to non-Gaussian interference and impulsive noise. In this context, the communication channel can be better modeled by heavy-tailed distributions, such as the non-Gaussian alpha-stable one. Some applications of the cyclostationary approach based on the spatial sign cyclic correlation function (SSCCF), fractional lower-order cyclic autocorrelation function (FLOCAF), and cyclic correntropy function (CCF) demonstrate that these are promising solutions for the analysis of signals in the presence of impulsive non-Gaussian noise. However, the investigation of functions above applied to digital modulation recognition in impulsive environments, and the comparison among them are topics that did not adequately explore yet. This work demonstrates that SSCCF is a particular case of the FLOCAF. Besides, a detailed analysis of the use of the FLOCAF and CCF is presented to obtain cyclostationary descriptors for the recognition of digital modulations BPSK, QPSK, 8-QAM, 16-QAM, and 32-QAM. Automatic modulation classification (AMC) architectures, based on the functions mentioned above, are also proposed. Besides, another contribution showed is that both the FLOCAF and CCF allow the symbol rate parameter estimation. The performances of AMC architectures were evaluated in the scenario with modulated signals contaminated with additive non-Gaussian alpha-stable noise. The results demonstrate that both architectures can classify signals in different contamination scenarios. However, the architecture based on the CCF is more efficient than the FLOCAF-based one.

A blocked proportionate normalized maximum correntropy criterion (PNMCC) is presented to improve the estimation behavior of the traditional maximum correntropy criterion (MCC) algorithm for identifying the blocked sparse systems. The proposed blocked MCC is implemented by constructing a new cost function based on a hybrid-norm constraint (HNC) of the filter coefficient vector to adaptively utilize the cluster-sparse characteristic of unknown systems, denoting as hybrid-norm constrained PNMCC (HNC-PNMCC). The proposed HNC-PNMCC algorithm is achieved by using the basis pursuit. Various simulations are brought out to confirm the validity of the HNC-PNMCC. Simulation results indicate that the HNC-PNMCC is better than the PNMCC, MCC, and sparse MCC with respect to the estimation performance for the cluster-sparse system identification under the impulsive noises.

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.

Nonlinear dynamics are inherent in a wide range of industrial processes and mechatronic systems, where impulsive noise—arising from sensor faults, switching transients, or electromagnetic interference—poses serious challenges to accurate measurement, system identification, and subsequent control performance. To address these challenges, this work presents a robust Hammerstein spline adaptive filtering method, termed HSAF-lncosh-MVC, aimed at achieving reliable nonlinear system identification in impulsive environments. The nonlinear module employs an lncosh-based adaptation mechanism that constrains the update direction within a bounded gradient region, thereby ensuring stable parameter estimation. Concurrently, the linear module integrates a maximum versoria criterion (MVC) that suspends weight updates in the presence of pronounced outliers, thus improving resilience against impulsive disturbances. This hybrid strategy of nonlinear and linear components is implemented through stochastic gradient operations without introducing significant additional computational cost. Theoretical analysis establishes the algorithm’s convergence and steady state characteristics. Extensive simulations, covering Gaussian, symmetric α-stable, and Cauchy noise scenarios as well as complex nonlinear dynamical systems, demonstrate that the proposed method achieves accelerated convergence and reduced steady state error relative to conventional Hammerstein spline filters, while maintaining computational efficiency. These results highlight the potential of HSAF-lncosh-MVC as an effective tool for robust signal processing and nonlinear system identification in measurement and instrumentation systems operating under impulsive noise conditions.

Improved proportionate-type sparse adaptive filtering under maximum correntropy criterion in impulsive noise environments

This paper investigates the kernel entropy based extended Kalman filter (EKF) as the navigation processor for the Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS). The algorithm is effective for dealing with non-Gaussian errors or heavy-tailed (or impulsive) interference errors, such as the multipath. The kernel minimum error entropy (MEE) and maximum correntropy criterion (MCC) based filtering for satellite navigation system is involved for dealing with non-Gaussian errors or heavy-tailed interference errors or outliers of the GPS. The standard EKF method is derived based on minimization of mean square error (MSE) and is optimal only under Gaussian assumption in case the system models are precisely established. The GPS navigation algorithm based on kernel entropy related principles, including the MEE criterion and the MCC will be performed, which is utilized not only for the time-varying adaptation but the outlier type of interference errors. The kernel entropy based design is a new approach using information from higher-order signal statistics. In information theoretic learning (ITL), the entropy principle based measure uses information from higher-order signal statistics and captures more statistical information as compared to MSE. To improve the performance under non-Gaussian environments, the proposed filter which adopts the MEE/MCC as the optimization criterion instead of using the minimum mean square error (MMSE) is utilized for mitigation of the heavy-tailed type of multipath errors. Performance assessment will be carried out to show the effectiveness of the proposed approach for positioning improvement in GPS navigation processing.

In this work, we perform an analysis, in the context of channel equalization, of two criteria that can be considered central to the field of information theoretic learning (ITL): the minimum error entropy criterion (MEEC) and the maximum correntropy criterion (MCC). An original derivation of the exact cost function of these criteria in the scenario of interest is provided and used to analyze their robustness and efficiency from a number of relevant standpoints. Another important feature of the paper is an study of the estimated versions of these cost functions, which raises several aspects regarding parameters of the canonical Parzen window estimator. The study is carried out for distinct channel and noise models, both in the combined response and parameter spaces, and also employs as benchmarks crucial metrics like the probability of bit error. The conclusions indicate under what conditions ITL criteria are particularly reliable and a number of factors that can lead to suboptimal performance.

Non-orthogonal multiple access (NOMA) has emerged as a promising multiple-access technique capable of accommodating many users over limited time-frequency resources. Among several NOMA techniques, sparse code multiple access (SCMA) has emerged as viable due to its promise of high coding-gain by appropriate codebook-design and simplistic detection using message-passing algorithm (MPA). However, the performance of classic SCMA based systems are severely impaired by impulsive noise (IN), which causes outages and therefore non-negligible degradations to the bit-error-rate (BER) performance. Exploiting the robustness of the maximum correntropy criterion (MCC) to non-Gaussian noise processes, an MPA based detector is formulated with message-functions derived from the MCC criterion. Based on the said MCC criterion, concurrent-adaptation of the MCC’s spread-parameter is proposed in this letter. Lastly, analytical results for the proposed approach’s BER performance are presented with corresponding validation by computer-simulations.

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

Most of the existing SHM damage detection methodologies are based on the changes in the system parameters estimated by the linear model fitted to the structure. However, real-life structures exhibit nonlinearity even in their healthy state due to complex joints, interfaces, etc. Nonlinear identification and damage identification are very challenging inverse engineering problems. In this paper, a nonlinear system identification methodology using empirical Slow-Flow Model has been presented. A dynamical system described by slowly varying amplitudes and phases is obtained through performing partition between slow and flow dynamics of the system using the well known complexification-averaging technique. By using the theoretical link between the measured instantaneous parameters through Hilbert transform and slow-flow equations of a system, the system parameters are identified using the classical least square procedure. A numerical simulation study has been conducted on a beam with breathing crack to demonstrate the effectiveness of the proposed algorithm.

To date, most linear and nonlinear Kalman filters (KFs) have been developed under the Gaussian assumption and the well-known minimum mean square error (MMSE) criterion. In order to improve the robustness with respect to impulsive (or heavy-tailed) non-Gaussian noises, the maximum correntropy criterion (MCC) has recently been used to replace the MMSE criterion in developing several robust Kalman-type filters. To deal with more complicated non-Gaussian noises such as noises from multimodal distributions, in this article, we develop a new Kalman-type filter, called minimum error entropy KF (MEE-KF), by using the minimum error entropy (MEE) criterion instead of the MMSE or MCC. Similar to the MCC-based KFs, the proposed filter is also an online algorithm with the recursive process, in which the propagation equations are used to give prior estimates of the state and covariance matrix, and a fixed-point algorithm is used to update the posterior estimates. In addition, the MEE extended KF (MEE-EKF) is also developed for performance improvement in the nonlinear situations. The high accuracy and strong robustness of MEE-KF and MEE-EKF are confirmed by experimental results.

Kernel recursive maximum correntropy