Fractional Lower Order Moments Research Articles

The Phase Fractional Lower-Order Moment Based DPD Algorithm of Non-circular Sources for Nested Array Under Impulsive Noise

The Phase Fractional Lower-Order Moment Based DPD Algorithm of Non-circular Sources for Nested Array Under Impulsive Noise

A Novel DOA Estimation Algorithm Based on Robust Mixed Fractional Lower-Order Correntropy in Impulsive Noise

The estimation of direction of arrival (DOA) is paramount in the realm of practical array signal processing systems. Nevertheless, traditional estimation methods often rely heavily on the Gaussian noise assumption, rendering them ineffective in achieving high-precision estimates in environments plagued by strong impulsive noise. To address this challenge, this paper introduces a novel DOA estimation algorithm that leverages mixed fractional lower-order correntropy (MFLOCR) in the context of Alpha-stable distributed impulsive noise. Correntropy is used as a measure of the similarity of the signals, using a Gaussian function to smooth extreme values and provide greater robustness against impulsive noise. By utilizing diverse kernel lengths to jointly regulate the kernel function, the concept of correntropy is expanded and implemented in the fractional lower-order moment (FLOM) algorithm for received signals. Subsequently, the MFLOCR is derived by adjusting the resulting form of correntropy. Finally, an enhanced DOA estimation algorithm is proposed that combines the MFLOCR operator with the MUSIC algorithm, specifically tailored for impulsive noise environments. Furthermore, a proof of boundedness is provided to validate the effectiveness of the proposed approach in such noisy conditions. Simulation experiments confirmed that the proposed method outperforms existing DOA estimation methods in the context of intense impulsive noise, a low generalized signal-to-noise ratio (GSNR), and a smaller number of snapshots.

Direction of Arrival Estimation Method Based on Eigenvalues and Eigenvectors for Coherent Signals in Impulsive Noise

In this paper, a Toeplitz construction method based on eigenvalues and eigenvectors is proposed to combine with traditional denoising algorithms, including fractional low-order moment (FLOM), phased fractional low-order moment (PFLOM), and correntropy-based correlation (CRCO) methods. It can improve the direction of arrival (DOA) estimation of signals in impulsive noise. Firstly, the algorithm performs eigenvalue decomposition on the received covariance matrix to obtain eigenvectors and eigenvalues, and then the Toeplitz matrix is created according to the eigenvectors corresponding to its eigenvalues. Secondly, the spatial averaging method is used to obtain an unbiased estimate of the Toeplitz matrix, which is then weighted and added based on the corresponding eigenvalues. Next, the noise subspace of the Toeplitz matrix is reconstructed to obtain the one that has less angle information. Finally, the DOA of the coherent signal is estimated using the Multiple Signal Classification (MUSIC) algorithm. The improved method based on the Toeplitz matrix can not only suppress the effect of impulsive noise but can also solve the problem of aperture loss due to its decoherence. A series of simulations have shown that they have better performances than other algorithms.

Variable step size VLF/ELF nonlinear channel adaptive filtering algorithm based on Sigmoid function

The signals received by very low-frequency/extremely low-frequency nonlinear receivers are frequently affected by intense atmospheric pulse noise stemming from thunderstorms and global lightning activity. Current noise processing algorithms designed for nonlinear channels within these frequency ranges, which are predicated on fractional p-order moment alpha stable distribution criteria (where 0 < p < α < 2, and p and α denote distinct characteristic indices of alpha stable distribution noise), are constrained by their reliance on limited p-order moment statistics. As a result, the performance of low-frequency nonlinear channel receivers experiences significant degradation when confronted with robust pulse noise interference (0 < p < α < 2). To tackle this challenge, the present study introduces a novel variable step robust mixed norm (RMN) adaptive filtering algorithm, designated as SVS-RMN, which is based on the Sigmoid function. Leveraging the nonlinearity of the Sigmoid function and building upon the power function Hammerstein nonlinear channel model, the algorithm aims to enhance the RMN algorithm by deriving new cost functions and adaptive iteration formulas. The performance of the proposed algorithm is evaluated in comparison to conventional RMN algorithms based on fractional low-order moment (FLOM) criteria (0 < p < 2), as well as other algorithms employing variable step sizes and either FLOM or radial basis function (RBF) criteria, across various intensities of pulse noise and mixed signal-to-noise ratios. The experimental results reveal the following: (1) The proposed algorithm effectively mitigates strong pulse noise interference and significantly enhances the tracking performance of the RMN algorithm compared to conventional RMN algorithms based on FLOM criteria. (2) In terms of computational efficiency, simplicity of structure, convergence speed, and stability, the proposed algorithm surpasses other algorithms based on FLOM or RBF criteria.

Fractional-order ascent maximum mixture correntropy criterion for FLANNs based multi-channel nonlinear active noise control

The filtered-s maximum correntropy criterion (FsMCC) algorithm was developed for nonlinear active noise control (NANC) in impulsive noise environments with the use of functional linked artificial neural networks (FLANNs) structure. However, the kernel-width of the FsMCC is constant, which is dull and cannot self-regulate to achieve both the fast convergence and low steady-state error performance. For better convergence ability, in this paper, a fractional-order gradient ascent filtered-s maximum correntropy criterion algorithm (FGA-FsMCC) is presented for multi-channel NANC system. The fractional lower-order moments supersede the non-existent second-order moments. To come up with a more reliable algorithm, by merging two kernels with complementary width, the fractional-order gradient ascent filtered-s mixture correntropy criterion (FGA-FsMMCC) was presented. The computational complexity and convergence conditions are analyzed. To verify the robustness of proposed algorithms, simulations are carried out to discuss parameters and control effects of algorithms for alpha-stable noise in different nonlinear environments.

Robust Localization for Near- and Far-Field Signals with an Unknown Number of Sources

Source location is a constant issue of importance of both theoretical study and practical engineering. Many pioneers have put out the corresponding solutions for near- or far-field signals, and preferred contributions are suggested. To our best knowledge, there are currently few focused approaches to the complicated situation where both near- and far-field signals exist with an unknown number of sources. Additionally, the robustness of the method must be taken into account when the additive background noise does not follow Gaussian or super-Gaussian distribution. To solve these problems, a novel method based on phased fractional lower-order moment (PFLOM) is proposed to simultaneously better preserve the signal and suppress the noise. Secondly, the whole procedure of the method containing direction of arrival (DOA) estimation, range estimation, separation of near-and far-field sources, and crucial parameter settings are studied in detail. Finally, comprehensive Monte Carlo experiments are carried out in the simulation to demonstrate the superiority of the proposed method compared to the existing competitive methods. Due to the novel method’s effectiveness with an unknown number of sources and robustness against various noises, it is believed that it could be fully utilized in more fields.

A signal enhancement method based on the reverberation statistical information

This paper proposes a reverberation suppression algorithm utilizing fractional lower-order moments based on statistical properties. As fractional lower-order moments can only be applied on symmetric α-stable random variables, the energy redistribution method is used, so reverberation signals can obtain the characteristic exponents of the symmetric α-stable distribution. To evaluate the proposed algorithm, an experiment involving simulated linear frequency modulation reverberation with the proposed method and comparison methods is performed and discussed. Moreover, an experiment is conducted using reverberation as measured from the lake. The results show that the proposed algorithm can achieve better reverberation suppression and signal enhancement performance compared with other methods.

Graph denoising of impulsive EEG signals and the effect of their graph representation

As the field of brain monitoring is evolving rapidly, there is an increasing demand for innovative approaches to handle relevant signals. Recently, graph signal processing, which enables the treatment of signal ensembles, emerges as a powerful alternative to a per-signal analysis. This is especially the case for electroencephalogram (EEG) signals that naturally admit graph representations, with each electrode corresponding to one graph node. These signals are often corrupted by impulsive noise best characterized by heavy-tailed statistics, thus driving conventional denoising techniques to failure. To address this problem, we propose an efficient regularized graph filtering method based on fractional lower-order moments, which better adapt to heavy-tailed statistics. An experimental evaluation on real EEG measurements, including the publicly available P300 dataset and epilepsy signals, reveals a superior denoising performance of our method when compared against well-established EEG signal denoising methods.

Time Delay Estimation Method Used Median Filter in Low Signal to Noise Ratio Pulse Environment

In practice, the collected signal often contains impulsive noise. The classical time delay estimation algorithm based on the second-order statistics of Gaussian distribution will degrade or even be unreliable, so that it cannot be used. Although the fractional low-order signal processing method can be better adapted to signal processing in the impulse noise environment, the determination of the order p value of the fractional low-order moment depends on the prior knowledge or estimation of the characteristic index α value of the pulse, and when the pulse is stronger or the signal-to-noise ratio is low, the performance cannot meet the requirements well. The paper adopted the method of median filter preprocessing. First, the abnormal points (pulse points) are removed in the noise and return the noise to the Gaussian model distribution; next, use the time delay estimation algorithm under the second-order statistics to avoid the estimate of p-value. Computer simulation experiments show that the method proposed in this paper has better estimation performance in low snr pulse environment.

Generalized covariance for non-Gaussian signal processing and GC-MUSIC under Alpha-stable distributed noise

Direction of arrival (DOA) estimation is one of the most important techniques applied in many practical engineering applications. Multiple signal classification (MUSIC) has gained increasing attention due to its high resolution in space. Many methods have been studied to handle the noise of Alpha-stable distribution within the framework of non-Gaussian signal processing. Inspired by a state-of-the-art concept, bounded nonlinear covariance (BNC), a more generalized concept, named generalized covariance (GC), is proposed. A series of existing concepts based on the fractional lower-order moment (FLOM), the correntropy, and the BNC are unified in the name of GC. Then, the convergence of GC under Alpha-stable distributed random variables is addressed. Furthermore, four different types of nonlinear functions are introduced for GC and BNC to handle impulsive noise, including sigmoid functions, score functions, FLOM mapping, Gaussian-like functions. These curves with different parameters are also exhibited in detail to illustrate their capabilities to suppress outliers. Also, GC-MUSIC is proposed, and its performances are compared with other 6 MUSIC-like algorithms in the presence of heavy-tailed impulsive noise. Besides, Cramer-Rao bound (CRB) of root mean squared error is also deduced and exhibited. Through Monte-Carlo simulations, the superiority of GC-MUSIC and BNC-MUSIC under Alpha-stable distributed noise is demonstrated.

A Covert Digital Communication System Using Skewed α-Stable Distributions for Internet of Things

Information security is a key issue involved in the utilization of different technological innovations, such as the Internet of Things (IoT). This study proposes a new covert communication scheme in which the transmitted waveform modulated by the covert bit is statistically similar to the background noise to achieve information security. The impulsive noise in many communication fields can be well modeled with a symmetrical α -stable distribution. Thus, the proposed scheme exploits skewed α -stable distributions to conduct the covert bit. The polarity transition of the skewness parameter within the first and second halves of a bit period represents a covert bit. The resultant signal exhibits a near-symmetrical behavior similar to ambient interference to achieve concealment. The sample skewness estimator based on the signed fractional lower order moment is used to determine the binary message at the receiver. Then, the expression of the skewness estimator and its probability density function are derived. With the aid of the hard decision, the theoretical expression of the bit error rate of the proposed communication system is obtained. The proposed scheme works at the physical layer with the advantages of simple structure, easy implementation, and extreme suitability with low-cost, resource-limited IoT devices exhibiting low-rate transmission.

Median-Difference Correntropy for DOA under the Impulsive Noise Environment

The source localization using direction of arrival (DOA) of target is an important research in the field of Internet of Things (IoTs). However, correntropy suffers the performance degradation for direction of arrival when the two signals contain the similar impulsive noise, which cannot be detected by the difference between two signals. This paper proposes a new correntropy, called the median-difference correntropy, which combines the generalized correntropy and the median difference. The median difference is defined as the deviation between the sampling value and the median of the signal, and it intuitively reflects the abnormality of impulsive noise. Then, the median difference is combined with the generalized correntropy to form a new weighting factor that can effectively suppress the amplitude level of impulsive noise. To improve the robustness of the algorithm, an adaptive kernel size is also integrated into the weighting factor to obtain the optimal local feature. The influence of adaptive kernel sizes on the proposed algorithm is simulated, and the comparison between three typical direction-of-arrival estimation algorithms is conducted. The results show that the accuracy of the median-difference correntropy is significantly superior to the correntropy-based correlation and the phased fractional lower-order moment for a wide range of alpha-stable distribution noise environments.

DOA Tracking Based on Unscented Transform Multi-Bernoulli Filter in Impulse Noise Environment.

Aiming at the problem of multiple-source direction of arrival (DOA) tracking in impulse noise, this paper models the impulse noise by using the symmetric α stable (SαS) distribution, and proposes a DOA tracking algorithm based on the Unscented Transform Multi-target Multi-Bernoulli (UT-MeMBer) filter framework. In order to overcome the problem of particle decay in particle filtering, UT is adopted to select a group of sigma points with different weights to make them close to the posterior probability density of the state. Since the α stable distribution does not have finite covariance, the Fractional Lower Order Moment (FLOM) matrix of the received array data is employed to replace the covariance matrix to formulate a MUSIC spatial spectra in the MeMBer filter. Further exponential weighting is used to enhance the weight of particles at high likelihood area and obtain a better resampling. Compared with the PASTD algorithm and the MeMBer DOA filter algorithm, the simulation results show that the proposed algorithm can more effectively solve the issue that the DOA and number of target are time-varying. In addition, we present the Sequential Monte Carlo (SMC) implementation of the UT-MeMBer algorithm.

Unilateral left‐tail Anderson Darling test‐based spectrum sensing with Laplacian noise

This paper focuses on spectrum sensing under Laplacian noise. To remit the negative effects caused by heavy-tailed behavior of Laplacian noise, the fractional lower order moments (FLOM) technology is employed to pre-process the received samples before spectrum sensing. Via exploiting the asymmetrical difference between the distribution for the FLOM of received samples in the absence and presence of primary users, we formulate the spectrum sensing problem under Laplacian noise as a unilateral goodness-of-fit (GoF) test problem. Based on this test problem, we propose a new GoF-based detector which is called unilateral left-tail Anderson Darling (ULAD) detector. The analytical expressions for the theoretical performance, in terms of false-alarm and detection probabilities, of the ULAD are derived. Moreover, a closed-form expression for the optimal detection threshold is also derived to minimize the total error rate. Simulation results are provided to validate the theoretical analyses and to demonstrate the superior performance of the proposed detector than others.

Compressive Sensing Using Symmetric Alpha-Stable Distributions for Robust Sparse Signal Reconstruction

Traditional compressive sensing (CS) primarily assumes light-tailed models for the underlying signal and/or noise statistics. Nevertheless, this assumption is not met in the case of highly impulsive environments, where non-Gaussian infinite-variance processes arise for the signal and/or noise components. This drives the traditional sparse reconstruction methods to failure, since they are incapable of suppressing the effects of heavy-tailed sampling noise. The family of symmetric alpha-stable (SαS) distributions, as a powerful tool for modeling heavy-tailed behaviors, is adopted in this paper to design a robust algorithm for sparse signal reconstruction from linear random measurements corrupted by infinite-variance additive noise. Specifically, a novel greedy reconstruction method is developed, which achieves increased robustness to impulsive sampling noise by solving a minimum dispersion (MD) optimization problem based on fractional lower-order moments. The MD criterion emerges naturally in the case of additive sampling noise modeled by SαS distributions, as an effective measure of the spread of reconstruction errors around zero, due to the lack of second-order moments. The experimental evaluation demonstrates the improved reconstruction performance of the proposed algorithm when compared against state-of-the-art CS techniques for a broad range of impulsive environments.

Phased Fractional Lower-Order Cyclic Moment Processed in Compressive Signal Processing

In signal processing research, cyclostationarity and fractional lower-order statistics (FLOS) are two important solutions to non-stationary signals and non-Gaussian noises, respectively. In the last five years, many methodologies combining the two technologies were proposed to achieve the two tasks simultaneously. Unfortunately, these methodologies need to be based on the Shannon/Nyquist sampling theorem. As phased fractional lower-order cyclic moment (PFLOCM) theoretically cooperates with compressive signal processing (CSP), this paper studies PFLOCM to apply in CSP at sub-Nyquist sampling rates. Using this technical foundation, a complete procedure is novelly proposed to rebuild phased fractional lower-order cyclic moment spectrum (PFLOCMS), which functions as a crucial factor in signal detection, system identification, parameter estimation, and other applications. In addition, various experiments verify the performance of the proposed procedure. It is believed that this paper will have implications for non-stationary and non-Gaussian signal processing at sub-Nyquist sampling rates.

Performance analysis of spectrum sensing schemes based on fractional lower order moments for cognitive radios in symmetric α-stable noise environments

Abstract Spectrum sensing schemes based on fractional lower order moment (FLOM) are often used in impulsive noise environments in which traditional energy detectors are not applicable. The performance of FLOM-based detectors operating in an α-stable noise environment is difficult to evaluate. This is because α-stable random variables can usually only be modeled by the characteristic function since closed-form expressions are not available, except for the special values of the characteristic exponent that correspond to the Cauchy and Gaussian noise distributions. In this paper, we derive closed-form expressions for the probability density function (PDF) and corresponding complementary cumulative distribution function (CDF) for a symmetric α-stable random variable with an arbitrary characteristic exponent α (0

Nonparametric Blind Signal Detection Based on Logarithmic Moments in Very Impulsive Noise

The detection problem in impulsive noise modeled by the symmetric alpha stable SαS distribution is studied. The traditional detectors based on the second or higher order moments fail in SαS noise, and the method based on the fractional lower order moments (FLOMs) performs poorly when the noise distribution has small values of characteristic exponent. In this paper, a detector based on the logarithmic moments is investigated. The analytical expressions of the false alarm and detection probabilities are derived in nonfading channels as well as Rayleigh fading channels. The effect of noise uncertainty on the performance is discussed. Simulation results show that the logarithmic detector performs better than the FLOM and Cauchy detectors in very impulsive noise. In addition, the logarithmic detector is a nonparametric method and avoids estimating the parameter of the noise distribution, which makes the logarithmic detector easier to implement than the FLOM detector.

Modeling of non-Gaussian colored noise and application in CR multi-sensor networks

Motivated by the practical and accurate demand of intelligent cognitive radio (CR) sensor networks, a new modeling method of practical background noise and a novel sensing scheme are presented, where the noise model is the non-Gaussian colored noise based on α stable process and the sensing method is improved fractional low-order moment (FLOM) detection algorithm with balance parameter. First, we establish the non-Gaussian colored noise model through combining α-distribution with a linear system represented by a matrix. And a fitting curve of practical noise data is given to verify the validity of the proposed model. Then we present a parameter estimation method with low complexity to obtain the balance parameter, which is an important part of the detection algorithm. The balance parameter-based FLOM (BP-FLOM) detector does not require any a priori knowledge about the primary user signal and channels. Monte Carlo simulations clearly demonstrate the performance of the proposed method versus the generalized signal-to-noise ratio, the characteristic exponent α, and the number of detectors in sensing networks.

Localization by Fusing a Group of Fingerprints via Multiple Antennas in Indoor Environment

Most existing fingerprints-based indoor localization approaches are based on some single fingerprint, such as received signal strength (RSS), channel impulse response, and signal subspace. However, the localization accuracy obtained by the single fingerprint approach is rather susceptible to the changing environment, multipath, and non-line-of-sight propagation. In this paper, we propose a novel localization framework by Fusing A Group Of fingerprinTs (FAGOT) via multiple antennas for the indoor environment. We first build a GrOup Of Fingerprints (GOOF), which includes five different fingerprints, namely, RSS, covariance matrix, signal subspace, fractional low-order moment, and fourth-order cumulant, which are obtained by different transformations of the received signals from multiple antennas in the offline stage. Then, we design a parallel GOOF multiple classifiers based on AdaBoost (GOOF-AdaBoost) to train each of these fingerprints in parallel as five strong multiple classifiers. In the online stage, we input the corresponding transformations of the real measurements into these strong classifiers to obtain independent decisions. Finally, we propose an efficient combination fusion algorithm, namely, MUltiple Classifiers mUltiple Samples (MUCUS) fusion algorithm to improve the accuracy of localization by combining the predictions of multiple classifiers with different samples. As compared with the single fingerprint approaches, our proposed approach can improve the accuracy and robustness of localization significantly. We demonstrate the feasibility and performance of the proposed algorithm through extensive simulations as well as via real experimental data using a Universal Software Radio Peripheral platform with four antennas.