non-Gaussian Impulsive Noise Research Articles

Kernel Least Mean $p$-Power Algorithm

This letter proposes a novel kernel least mean $p$ -power (KLMP) algorithm for nonlinear system identification in the presence of additive non-Gaussian impulsive noises, modeled by a symmetric $\alpha$ -stable distribution with heavy tail. The KLMP algorithm based on the fractional lower order statistics error criterion can effectively scale down the dynamic recursive weight coefficients affected by the impulsive estimation error to avoid the significant performance degradation. Simulation results demonstrate that the proposed algorithm has favorable convergence properties than the classical kernel least-mean-square algorithm using a conventional error criterion in the non-Gaussian impulsive environment.

Cyclostationary Features Based Modulation Classification in Presence of Non Gaussian Noise Using Sparse Signal Decomposition

Automatic modulation classification (AMC) is a salient component in the area of cognitive radio, signal detection, interference identification, electronic warfare, spectrum management and surveillance. The majority of the existing signals detection and classification methods presume that the received signal is corrupted by additive white Gaussian noise. The performance of the modulation classification algorithms degrades severely under the non-Gaussian impulsive noise. Hence, in this paper, we introduce a robust algorithm to identify the modulation type of digital signal contaminated with non-Gaussian impulse noise and additive white Gaussian noise (AWGN) using a sparse signal decomposition on hybrid dictionary. The algorithm first detects and removes the impulse noise using sparse signal decomposition thereafter it classifies the modulation schemes using cyclostationary feature extraction algorithm. Simulation results demonstrate the superiority of the proposed method under different non-Gaussian impulse noise and AWGN conditions. The performance of the proposed classifier is evaluated using well known classifiers available in the literature.

Constrained maximum correntropy adaptive filtering

Constrained adaptive filtering algorithms have been extensively studied in many applications. Most existing constrained adaptive filtering algorithms are developed under the mean square error (MSE) criterion, which is an ideal optimality criterion under Gaussian noises. This assumption however fails to model the behavior of non-Gaussian noises found in practice. Motivated by the robustness and simplicity of maximum correntropy criterion (MCC) for non-Gaussian impulsive noises, this paper proposes a new adaptive filtering algorithm called constrained maximum correntropy criterion (CMCC). Specifically, CMCC incorporates a linear constraint into a MCC filter to solve a constrained optimization problem explicitly. The proposed adaptive filtering algorithm is easy to implement, has low computational complexity, and can significantly outperform those MSE based constrained adaptive algorithms in heavy-tailed impulsive noises. Additionally, the mean square convergence behaviors are studied under energy conservation relation, and a sufficient condition to ensure the mean square convergence and the steady-state mean square deviation (MSD) of the CMCC algorithm are obtained. Simulation results confirm the theoretical predictions under both Gaussian and non-Gaussian noises, and demonstrate the excellent performance of the novel algorithm by comparing it with other conventional methods.

Subspace-based Localization Approach for Near-field Source in Impulse Noise Environment

In this paper, we propose a subspace-based matching (SBM) approach based on fractional lower order moment (FLOM) matrix to estimate the location of near-field acoustic signals in additive nonGaussian impulsive noise environment. By matching the subspace in the fingerprint database and the subspace computed from the current received signals, we associate the received signal with its transmission location with high accuracy. The proposed algorithm has two advantages: firstly, it can locate multiple sources without estimating bearing and range of sources. Secondly, it is more robust to multipath, environment changing and noise level. The simulation results show the efficacy of our proposed algorithm.

Type of active impulse noise suppressing method based on double‐loop antennas in very low frequency/ultra‐low frequency coupling communications

Very low frequency/ultra-low frequency coupling communication systems suffer from severe disturbance from non-Gaussian impulsive noises which producing significant long tails. Considering the significant in-band parts of the impulse, traditional noise-suppression methods are not adequate in improving the signal-to-noise ratio (SNR), and the performance of existing dipole–loop double antennas active noise suppression systems are limited to a low level due to the different directionality of the antennas. A new double-loop antennas active noise suppressing system was proposed, in which one multi-turn loop antenna was employed to receive the useful signals, and one single-turn loop was employed as the noise reference antenna. A mathematical morphology processor and a time-switch filter were employed to extract the impulsive noise, and the digital equivalent model of the multi-turn loop antenna was established filtering the extracted impulsive noise to obtain a duplicate transient, which is highly correlated with the transients received from the multi-turn loop antenna. The system SNR was improved by subtracting the transient duplicate from the received signals. Simulations were carried out with Monte Carlo method, showing that the SNR can be improved with the gain of about 18 dB with communication error rate extremely reduced by orders of magnitude. Experiment system was also designed and established to verify the feasibility and efficiency, and a 50 m communication experiment in an industrial environment showed that the error rate can be decreased from 0.2 to 0.06% while employing the proposed noise suppression method.

State space maximum correntropy filter

The state space recursive least squares (SSRLS) filter is a new addition to the well-known recursive least squares (RLS) family filters, which can achieve an excellent tracking performance by overcoming some limitations of the standard RLS algorithm. However, when the underlying system is disturbed by some heavy-tailed non-Gaussian impulsive noises, the performance of SSRLS will deteriorate significantly. The main reason for this is that the SSRLS is derived under the minimum mean square error (MMSE) criterion, which is not well-suited to estimation problems under non-Gaussian noises. To overcome this issue, we propose in this paper a novel linear filter, called the state space maximum correntropy (SSMC) filter, which is derived under the maximum correntropy criterion (MCC) instead of the MMSE. Since MCC is very suited to non-Gaussian signal processing, the SSMC performs very well in non-Gaussian noises especially when the signals are corrupted by impulsive noises. A simple illustrative example is presented to demonstrate the desirable performance of the new algorithm.

Binormalized data-reusing adaptive filtering algorithm for active control of impulsive sources

The main objective of active noise control (ANC) is to provide attenuation for the environmental acoustic noise. The adaptive algorithms for ANC systems work well to attenuate the Gaussian noise; however, their performance may degrade for non-Gaussian impulsive noise sources. Recently, we have proposed variants of the most famous ANC algorithm, the filtered-x least mean square (FxLMS) algorithm, where an improved performance has been realized by thresholding the input data or by efficiently normalizing the step-size. In this paper, we propose a modified binormalized data-reusing (BNDR)-based adaptive algorithm for impulsive ANC. The proposed algorithm is derived by minimizing a modified cost function, and is based on reusing the past and present samples of data. The main contribution of the paper is to develop a practical DR-type adaptive algorithm, which incorporates an efficiently normalized step-size, and is well suited for ANC of impulsive noise sources. The computer simulations are carried out to demonstrate the effectiveness of the proposed algorithm. It is shown that an improved performance has been realized with a reasonable increase in the computational complexity.

An Accurate Kernelized Energy Detection in Gaussian and non-Gaussian/Impulsive Noises

Motivated by the simplicity of energy detector and capability of higher order and fractional lower order statistics in non-Gaussian signal processing, this paper proposes a new spectrum sensing method based on kernel theory, referred to as Kerenlized Energy Detector (KED), which exhibits a moderate complexity, it is easy to implement, and it compares favourably against competing solutions in the case of various Gaussian and non-Gaussian impulsive noises. The incorporation of the nonlinear kernel function in the KED test statistic allows for the development of a nonlinear algorithm capable of considering both higher order and fractional lower order moments (FLOMs) in the sensing task. We show that the proposed KED detector can serve as an optimal spectrum sensing method under both Gaussian and non-Gaussian noise scenarios. In addition, the detection performance of the proposed KED scheme is analyzed by employing U-statistics theory. The Kernel parameter selection for the KED method has been discussed in both theoretical and practical points of view. Potential of considering the KED scheme in either single user multi-antennas or cooperative spectrum sensing is investigated.

A family of threshold based robust adaptive algorithms for active impulsive noise control

The common active noise control (ANC) algorithm, namely the filtered-x least mean square (FxLMS) algorithm, becomes unstable for the non-Gaussian impulsive noise. This is because the typical FxLMS algorithm is based on the minimization of variance of the error signal (the second order moment in L2 space), which does not exist for the non-Gaussian impulsive noise. In this study, a family of threshold based algorithms is proposed by minimizing several robust objective error functions as well as thresholding the reference signal to further refine the robustness of the ANC system for impulsive noise. The proposed algorithms are also expected to generalize the existing adaptive algorithms for impulsive noise control. These robust error functions are typically represented by (1) robust space vectors: Lp and Log space; and (2) re-descending M-estimators: Huber, Fair and Hampel threshold functions. The threshold parameters in the reference signal and those M-estimators can be determined by using online and/or offline statistical estimation approaches. Numerical simulations are carried out to verify the performance of proposed algorithms by using synthesized impulsive noise following symmetric α-stable (SαS) distribution. Results show the improved robustness and convergence performance of the proposed algorithms for ANC of impulsive noises as compared to the conventional algorithms.

Enhanced filtered-x least mean M-estimate algorithm for active impulsive noise control

Abstract Applying the typical active noise control (ANC) algorithm, namely the filtered-x least mean square (FxLMS) algorithm, to the non-Gaussian impulsive noise will experience difficulty. This is because the FxLMS algorithm is based upon the minimization of variance of the error signal, which is normally with the assumption of Gaussian distribution. To deal with this issue, the filtered-x least mean M-estimate (FxLMM) algorithm has been proposed based on the robust statistics theory to minimize the objective M-estimator error function. The Hampel’s three-part M-estimator has been applied to provide thresholds for detecting and rejecting the outliers/impulses in the error signal. To further enhance the robustness of the conventional FxLMM algorithm, in this study a modified FxLMM (MFxLMM) algorithm is proposed, where the reference signal is fed through another Hampel’s three-part M-estimator by setting thresholds for the impulsive samples. Numerous computer simulations are performed to validate the performance of the proposed algorithm. The generic impulsive noise is synthesized by using the contaminated Gaussian (CG) noise model, where certain number of impulses with different amplitudes and widths can be added in the background white Gaussian noise to represent different impulsive characteristics. In addition, extensive laboratory tests are carried out to further demonstrate the enhanced efficacy of the algorithm in a real-time environment. Results indicate that the proposed MFxLMM algorithm with online-threshold estimation is a very promising alternative for ANC of impulsive noise, and it shows similar convergence performance as the prevalent FxLMS algorithm for noise not corrupted by impulses.

Bearings Fault Detection in Gas Compressor in Presence of High Level of Non-Gaussian Impulsive Noise

The paper deals with the local damage detection in rolling element bearings in presence of a high level non-Gaussian noise. In many theoretical signal processing papers and engineering application related to damage detection, a simple model of the vibration is assumed. Basically it consists of signal of interest (SOI) and some unwanted (deterministic and/or random) components masking SOI in acquired observation. So, damage detection problem has to concern filtering, decomposition or extraction issue. Unfortunately, in the most of the industrial systems mentioned unwanted sources are in fact not Gaussian, so many of de-noising techniques cannot be applied directly or at least might give unexpected results. In this paper an industrial example will be discussed and novel approach based on advanced cyclostationary-based technique will be proposed. In the paper disturbances include periodic impacts in reciprocating compressor on an oil rig. Existing classical detection techniques (statistics in time domain, analysis of envelope spectrum, time-frequency decompositions) are insufficient to perform the task due to high power of disturbance contribution in comparison to damage signature. In the proposed technique, the Spectral Coherence Density Map (SCDM) is estimated first. Next step is related to analysis of SCDM contents and selection of informative part. If informative and non-informative components lay in separate frequency regions, such selection should fix the problem immediately

Particle Filtering for Acoustic Source Tracking in Impulsive Noise With Alpha-Stable Process

NonGaussian impulsive noises distort the source signal and cause problems for direction of arrival (DOA) estimation of an acoustic source. In this paper, a Bayesian framework and its particle filtering (PF) implementation for DOA tracking in the presence of complex symmetric alpha-stable noise process are developed. A constant velocity model is employed to model the source dynamics, and spatial spectra are exploited to formulate a pseudo likelihood of particles. Since the second-order statistics of alpha-stable processes do not exist, the fractional lower order moment matrix of the received data is used to replace the covariance matrix in calculating the spatial spectra. The noise usually spreads and distorts the mainlobe of the likelihood function and the particles cannot be weighted accurately. Hence, the likelihood function is exponentially weighted to emphasize the particles in a high likelihood area and thus enhance the resampling efficiency. The performance of the proposed tracking algorithm is extensively studied under simulated alpha-stable noise environments. The results show that the proposed algorithm significantly outperforms the existing PF tracking approach and the traditional localization approaches in DOA estimation.

Robust sparse channel estimation and equalization in impulsive noise using linear programming

In this paper, an algorithm for sparse channel estimation, called ℓ1-regularized least-absolutes (ℓ1-LA), and an algorithm for equalization, called linear least-absolutes (LLA), in non-Gaussian impulsive noise are proposed. The proposed approaches are based on the minimization of the absolute error function, rather than the squared error function. By replacing the standard modulus with the ℓ1-modulus of complex numbers, the resulting optimization problem can be efficiently solved through linear programming. The selection of an appropriate regularization parameter is also addressed. Numerical results demonstrate that the proposed algorithms, compared with the classical methods, are more robust to impulsive noise and have a superior accuracy.

Support Vector Machines Regression for MIMO-OFDM Channel Estimation

In this paper, we propose a robust highly selective nonlinear channel estimator for Multiple -Input Multiple-Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) system using complex Support Vector Machines Regression (SVR) and applied to Long Term Evolution (LTE) downlink under high mobility conditions .The new method uses the information provided by the pilot signals to estimate the total frequency response of the channel in two phases: learning phase and estimation phase. The estimation algorithm makes use of the reference signals to estimate the total frequency response of the highly selective multipath channel in the presence of non-Gaussian impulse noise interfering with pilot signals. Thus, the algorithm maps trained data into a high dimensional feature space and uses the Structural Risk Minimization (SRM) principle to carry out the regression estimation for the frequency response function of the highly selective channel. The simulations show the effectiveness of the proposed method which has good performance and high precision to track the variations of the fading channels compared to the conventional LS method and it is robust under high mobility conditions.

SIMO-OFDM Channel Estimation based on Nonlinear Complex LS-SVM

In this contribution, we propose a robust highly selective nonlinear channel estimator for Single -Input Multiple-Output (SIMO) Orthogonal Frequency Division Multiplexing (OFDM) system using complex Least Squares Support Vector Machines (LS-SVM) and applied to Long Term Evolution (LTE) downlink under high mobility conditions .The new method uses the information provided by the pilot signals to estimate the total frequency response of the channel in two phases: learning phase and estimation phase. The estimation algorithm makes use of the reference signals to estimate the total frequency response of the highly selective multipath channel in the presence of non-Gaussian impulse noise interfering with pilot signals. Thus, the algorithm maps trained data into a high dimensional feature space and uses the Structural Risk Minimization (SRM) principle to carry out the regression estimation for the frequency response function of the highly selective channel. The simulations show the effectiveness of the proposed method which has good performance and high precision to track the variations of the fading channels compared to the conventional LS method and it is robust at high speed mobility.

Time-difference-of-arrival estimation algorithms for cyclostationary signals in impulsive noise

In this paper, new signal-selective methods for the estimation of time-difference-of-arrival in the presence of interfering signals and non-Gaussian symmetric α-stable impulsive noise are introduced. First, the performance degradation of the conventional approaches based on second-order cyclic statistics is presented. Then, two new classes of robust algorithms are developed using the theory of stable distributions and the cyclostationary property, including the pth-order cyclostationarity methods and the fractional lower-order cyclostationarity methods. It is shown that these new methods are tolerant to interference and robust in both Gaussian and non-Gaussian impulsive noise environments. The improved performance is demonstrated through detailed theoretical analysis and simulations.

Complex Support Vector Machine Regression for Robust Channel Estimation in Lte Downlink System

In this paper, the problem of channel estimation for LTE Downlink system in the environment of high mobility presenting non-Gaussian impulse noise interfering with reference signals is faced. The estimation of the frequency selective time varying multipath fading channel is performed by using a channel estimator based on a nonlinear complex Support Vector Machine Regression (SVR) which is applied to Long Term Evolution (LTE) downlink. The estimation algorithm makes use of the pilot signals to estimate the total frequency response of the highly selective fading multipath channel. Thus, the algorithm maps trained data into a high dimensional feature space and uses the structural risk minimization principle to carry out the regression estimation for the frequency response function of the fading channel. The obtained results show the effectiveness of the proposed method which has better performance than the conventional Least Squares (LS) and Decision Feedback methods to track the variations of the fading multipath channel.

Active noise control with on-line estimation of non-Gaussian noise characteristics

Active noise control (ANC) is a methodology for attenuating noise based on adaptive signal processing algorithms. ANC is well assessed for the attenuation of Gaussian noise, but the rejection of non-Gaussian impulsive noise signals represents a much more critical task that may even impair algorithm convergence. To overcome this problem the adaptive filter weight update process must be modified by discarding or discounting samples associated with impulsive noise. This can be done either by modeling the impulsive noise with a non-Gaussian distribution such as the Symmetric α -stable ( S α S ) distribution or by applying an outlier detection method. With both approaches the accuracy in the noise description appears to be crucial for effective noise reduction. This paper proposes two novel approaches for the attenuation of impulsive noise both for invariant and time-varying noise distributions. The first one is based on the on-line estimation of an S α S model of the noise probabilistic description. The second relies on a simple on-line recursive procedure that reliably estimates amplitude thresholds for outlier detection. Both methods compare favorably with competitor approaches, while maintaining a sufficiently low algorithm complexity. Several examples are shown to demonstrate the algorithms' effectiveness.

Nonlinear Channel Estimation for OFDM System by Complex Ls-SVM Under High Mobility Conditions

A nonlinear channel estimator using complex Least Square Support Vector Machines (LS-SVM) is proposed for pilot-aided OFDM system and applied to Long Term Evolution (LTE) downlink under high mobility conditions. The estimation algorithm makes use of the reference signals to estimate the total frequency response of the highly selective multipath channel in the presence of non-Gaussian impulse noise interfering with pilot signals. Thus, the algorithm maps trained data into a high dimensional feature space and uses the structural risk minimization (SRM) principle to carry out the regression estimation for the frequency response function of the highly selective channel. The simulations show the effectiveness of the proposed method which has good performance and high precision to track the variations of the fading channels compared to the conventional LS method and it is robust at high speed mobility.

Adaptive recursive M-robust system parameter identification using the QQ-plot approach

A new adaptive algorithm for the robust estimation of parameters of linear dynamic discrete-time systems in the presence of non-Gaussian impulsive noise within a measurement sequence is proposed in this study. Starting from the theory of robust estimation, a simple, adaptive, practically applicable robust approximate maximum likelihood algorithm is derived that, in the cases of contaminated normal distribution of measurement noise, demonstrates a high level of efficiency. The QQ-plot technique, combined with data cleaning based on the robustified winsorisation technique, is used as a framework for the classification of sorted data into the class of regular normally distributed data and the class of irregular data belonging to the contaminating distribution with a variance that is much greater than nominal. The link between the QQ-plot technique and a specific linear regression is established, so that the estimation of statistical parameters of the contaminated measurement distribution is performed using the least-squares technique. Then, the suboptimal maximum likelihood criterion is defined, and the system parameter estimation problem is solved robustly, using the proposed recursive robust parameter estimation scheme. Simulation results illustrate the discussion and show the efficiency of the proposed adaptive recursive parameter estimation algorithm in the presence of glint spikes or outliers.