Fourth-order Cumulant Research Articles

Localization of Mixed Far-Field and Near-Field Sources via Cumulant Matrix Reconstruction

In this paper, we propose a new localization algorithm using a uniform linear sensor array for scenarios where both the far-field (FF) and near-field (NF) sources may coexist. First, the direction of arrivals (DOAs) of FF sources are obtained using the FF MUSIC spectrum. Then, a special fourth-order cumulant matrix of the array output which is only characterized by the DOAs of sources is constructed. After the kurtosis of FF signals is estimated, the NF cumulant matrix (NFCM) is reconstructed by removing the related FF components. Next, the DOAs of NF sources are estimated by exploiting the reconstructed NFCM and cumulant domain rotational invariance structure. Finally, with the estimated NF DOAs, the ranges of NF sources are estimated via 1-D spectral search. The proposed algorithm does not require NF DOA search and is computationally more efficient than the previous methods. In addition, it realizes a more reasonable classification of the source types. Numerical results show that the proposed algorithm achieves higher estimation accuracy than the traditional methods.

Multi-point Gaussian States, Quadratic–Exponential Cost Functionals, and Large Deviations Estimates for Linear Quantum Stochastic Systems

This paper is concerned with risk-sensitive performance analysis for linear quantum stochastic systems interacting with external bosonic fields. We consider a cost functional in the form of the exponential moment of the integral of a quadratic polynomial of the system variables over a bounded time interval. Such functionals are related to more conservative behaviour and robustness of systems with respect to statistical uncertainty, which makes the challenging problems of their computation and minimization practically important. To this end, we obtain an integro-differential equation for the time evolution of the quadratic–exponential functional, which is different from the original quantum risk-sensitive performance criterion employed previously for measurement-based quantum control and filtering problems. Using multi-point Gaussian quantum states for the past history of the system variables and their first four moments, we discuss a quartic approximation of the cost functional and its infinite-horizon asymptotic behaviour. The computation of the asymptotic growth rate of this approximation is reduced to solving two algebraic Lyapunov equations. Further approximations of the cost functional, based on higher-order cumulants and their growth rates, are applied to large deviations estimates in the form of upper bounds for tail distributions. We discuss an auxiliary classical Gaussian–Markov diffusion process in a complex Euclidean space which reproduces the quantum system variables at the level of covariances but has different fourth-order cumulants, thus showing that the risk-sensitive criteria are not reducible to quadratic–exponential moments of classical Gaussian processes. The results of the paper are illustrated by a numerical example and may find applications to coherent quantum risk-sensitive control problems, where the plant and controller form a fully quantum closed-loop system, and other settings with nonquadratic cost functionals.

The magnetic properties and magneto-caloric effect in the compound MnBi: The Monte Carlo study

In this research paper, we determine and analyze the magnetic properties and the magneto-caloric effect in the compound MnBi. To do so, we firstly establish the magnetic properties of the studied compound by using Monte Carlo simulations method, and then we determine the transition temperature through studying the magnetization, the susceptibility, the specific heat, and the Binder’s fourth-order cumulate of order parameter. This latter result is only one among a number of results attained in this paper. To cite but an example, the plotting of the magnetic entropy change, adiabatic temperature change and the relative cooling power for the different external magnetic field.

Calculation of Higher-Order Moments in the Atmospheric Boundary Layer

The results of analyzing a number of models to calculate the statistical fourth-order moments of turbulent fluctuations of vertical velocity and temperature, which describe diffusion processes in equations for triple correlations in RANS models, are presented. Correct calculation of higher-order moments allows adequate description of the impact of large-scale vortex structures on the vertical flow of turbulence energy, as well as the impact of chemical reactions (in the case of reactive impurities) and/or phase transitions (moisture condensation and evaporation) in the atmospheric boundary layer.Results of calculations with the use of the quasi-normality hypothesis, a number of empirical formulas. and algebraic models for fourth-order cumulants are comparedwith in situ measurements in the convective boundary layer of the atmosphere. It is shown that the secondorder- closure models, which are much more efficient in numerical implementation than the thirdorder models, predict the behavior of the higher-order moments not worse than the latter.

Sparse Method for Direction of Arrival Estimation Using Denoised Fourth-Order Cumulants Vector.

Fourth-order cumulants (FOCs) vector-based direction of arrival (DOA) estimation methods of non-Gaussian sources may suffer from poor performance for limited snapshots or difficulty in setting parameters. In this paper, a novel FOCs vector-based sparse DOA estimation method is proposed. Firstly, by utilizing the concept of a fourth-order difference co-array (FODCA), an advanced FOCs vector denoising or dimension reduction procedure is presented for arbitrary array geometries. Then, a novel single measurement vector (SMV) model is established by the denoised FOCs vector, and efficiently solved by an off-grid sparse Bayesian inference (OGSBI) method. The estimation errors of FOCs are integrated in the SMV model, and are approximately estimated in a simple way. A necessary condition regarding the number of identifiable sources of our method is presented that, in order to uniquely identify all sources, the number of sources K must fulfill . The proposed method suits any geometry, does not need prior knowledge of the number of sources, is insensitive to associated parameters, and has maximum identifiability , where M is the number of sensors in the array. Numerical simulations illustrate the superior performance of the proposed method.

ECG signal filtering based on CEEMDAN with hybrid interval thresholding and higher order statistics to select relevant modes

In this paper, we propose a novel ECG signal enhancement method based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Higher Order Statistics (HOS). In our scheme, the noisy ECG signal is first decomposed adaptively into oscillatory components called intrinsic mode functions (IMFs) by using Empirical Mode Decomposition (EMD) or its variants. Therefore, the obtained modes are separated into two groups of noisy signal modes and one group of useful signal modes, by using a novel criterion derived from the HOS namely the fourth order cumulant or kurtosis. After that, a modified shrinkage scheme based on Interval Thresholding technique is adaptively applied to each selected IMF from the noise-dominant groups in order to reduce the noise and to preserve the QRS complex. The overall filtered ECG signal is then reconstructed by combining the thresholded IMFs and the retained unprocessed lower frequency relevant IMFs. Various tests and simulations are investigated to evaluate the performance of our proposed approach in combination with the EMD, Ensemble EMD (EEMD) and CEEMDAN algorithms. The simulation results carried on MIT-BIH Arrhythmia database, show that CEEMDAN method gives better performance than the two other methods, and outperforms some state-of-the-art methods in terms of Signal to Noise Ratio (SNR) and Root Mean Square Error (RMSE).

A Virtual Array Extension Method for Multiple Partial Discharge Sources Localization Based on Fourth-order Cumulant and Signal Sparse Decomposition

The localization of multiple partial discharges based on UHF signal is difficult to accomplish due to the excessive localization error. A virtual array extension method based on four-order cumulant and signal sparse decomposition is proposed in this paper. The virtually extended array has higher directional resolution and it could detect partial discharge sources with higher accuracy. The 2×2 UHF array that commonly used in existed partial discharge localization methods is virtually extended to 3×3 and 5×5 array. The virtual array extension is accomplished by extending the corresponding steering vector matrix of PD signal spatial spectrum to a overcomplete dictionary, which is then used to realize the sparse decomposition of the PD signal. Eventually the DOA estimation of multiple partial discharge sources is achieved. Simulation and field test results show that the virtually extended UHF array can detect and locate two PD sources simultaneously. The directional angel estimation error is about 6° and the pitch angle error is lower than 4°, which has proved the feasibility of the proposed method.

Adsorption of flexible polymer chains on a surface: Effects of different solvent conditions.

Polymer chains undergoing a continuous adsorption-desorption transition are studied through extensive computer simulations. A three-dimensional self-avoiding walk lattice model of a polymer chain grafted onto a surface has been treated for different solvent conditions. We have used an advanced contact-density chain-growth algorithm, in which the density of contacts can be directly obtained. From this quantity, the order parameter and its fourth-order Binder cumulant are computed, as well as the corresponding critical exponents and the adsorption-desorption transition temperature. As the number of configurations with a given number of surface contacts and monomer-monomer contacts is independent of the temperature and solvent conditions, it can be easily applied to get results for different solvent parameter values without the need of any extra simulations. In analogy to continuous magnetic phase transitions, finite-size-scaling methods have been employed. Quite good results for the critical properties and phase diagram of very long single polymer chains have been obtained by properly taking into account the effects of corrections to scaling. The study covers all solvent effects, going from the limit of super-self-avoiding walks, characterized by effective monomer-monomer repulsion, to poor solvent conditions that enable the formation of compact polymer structures.

Understanding linkages between global climate indices and terrestrial water storage changes over Africa using GRACE products

Africa, a continent endowed with huge water resources that sustain its agricultural activities is increasingly coming under threat from impacts of climate extremes (droughts and floods), which puts the very precious water resource into jeopardy. Understanding the relationship between climate variability and water storage over the continent, therefore, is paramount in order to inform future water management strategies. This study employs Gravity Recovery And Climate Experiment (GRACE) satellite data and the higher order (fourth order cumulant) statistical independent component analysis (ICA) method to study the relationship between terrestrial water storage (TWS) changes and five global climate-teleconnection indices; El Niño-Southern Oscillation (ENSO), North Atlantic Oscillation (NAO), Madden-Julian Oscillation (MJO), Quasi-Biennial Oscillation (QBO) and the Indian Ocean Dipole (IOD) over Africa for the period 2003–2014. Pearson correlation analysis is applied to extract the connections between these climate indices (CIs) and TWS, from which some known strong CI-rainfall relationships (e.g., over equatorial eastern Africa) are found. Results indicate unique linear-relationships and regions that exhibit strong linkages between CIs and TWS. Moreover, unique regions having strong CI-TWS connections that are completely different from the typical ENSO-rainfall connections over eastern and southern Africa are also identified. Furthermore, the results indicate that the first dominant independent components (IC) of the CIs are linked to NAO, and are characterized by significant reductions of TWS over southern Africa. The second dominant ICs are associated with IOD and are characterized by significant increases in TWS over equatorial eastern Africa, while the combined ENSO and MJO are apparently linked to the third ICs, which are also associated with significant increase in TWS changes over both southern Africa, as well as equatorial eastern Africa.

Localisation of mixed near‐field and far‐field sources using the largest aperture sparse linear array

In some applications, the signals received by an array are a mixture of signals emitted by both far-field and near-field sources. This study develops a new cumulant-based multiple signal classification (MUSIC) algorithm for source localisation using a new structural sparse array for scenarios where both far-field and near-field sources coexist. The key feature of this algorithm is that it utilises fourth-order cumulants to compute the virtual covariance matrix and constructs a new special cumulant matrix to acquire the largest number of virtual sensors and the largest array aperture for a given number of sensors. The authors provide a geometric proof to justify the utilisation of the proposed sparse linear array and compute the effective aperture of the array. The proposed algorithm increases resolution ability, direction of arrival (DOA) and range estimation accuracy, and the number of sources to be localised. Moreover, the new method has the main advantage that it does not use the information of all sensors; so that it provides somewhat low computational complexity while it uses many actual and virtual sensors. Monte Carlo simulations are provided to demonstrate the effectiveness of the proposed method.

Redundancy-Removed MUSIC-like Algorithm Based on Single Vector Hydrophone

To reduce the operation time of the MUSIC-like algorithm on a single vector hydrophone, a redundancy-removed MUSIC-like algorithm was proposed. For the extended steering vector, this algorithm removes the repetitive elements directly. For the fourth-order cumulant matrix, the algorithm removes the redundancy using the conjugate symmetry. Simulation experiments show that the proposed algorithm lose a little performance compared with the regular MUSIC-like algorithm. However, the computational cost of the proposed algorithm is reduced greatly.

An improved algorithm for multiple source direction of arrival estimation

Based on MUSIC-LIKE algorithm, an improved algorithm for multiple source direction of arrival estimation was proposed to resolve the problem, the enabled estimation number of source for traditional direction of arrival estimation algorithm restricted by the size of the antenna array. The computations and the matrix dimension were reduced by constructed new fourth cumulate matrix, the number of direction estimation was increased by smoothing computation snapshots based on MFOCMUSIC algorithm. The spatial spectrum measuring error was decreased by smoothing the virtual array extended by fourth order cumulate. Simulation results proved that the proposed algorithm can find more direction of arrival than MFOC-MUSIC algorithm, improve the direction of arrival resolution ratio, and inhibit the influence of gaussian white noise to direction of arrival estimation

Estimation of Modulation Index for Partial Response CPM Signal

Continuous phase modulation (CPM) is a power and bandwidth efficient modulation scheme used in cellular, personal, and satellite communications among other applications. If the modulation index of the CPM waveform used by the transmitter is unavailable at the receiver, serious performance degradation may occur. This paper investigates the problem of modulation index estimation for partial response continuous phase modulation schemes. Specifically, we propose two novel estimators for the CPM signal observed in an additive white Gaussian noise channel. A non-data aided method of moments (MoM) estimator based upon the fourth-order cumulants and a data-aided best linear unbiased estimator (BLUE) based upon an approximate linear phase model of the received CPM signal have been proposed. Modified Cramer-Rao lower bound is derived for the partial response CPM schemes to assess the performance of the estimators. We also perform numerical simulations to compare the mean-squared error (MSE) performance of the proposed MoM and BLUE estimators with previously proposed estimators in the literature. It is shown that the MoM estimator exhibits good MSE performance at low signal-to-noise ratio (SNR) while the BLUE estimator performs very well at high SNRs. Moreover, the proposed estimators have lower complexity than existing methods and are based upon non-iterative algorithms.

Fast Location Algorithm Based on an Extended Symmetry Nested Sensor Model in an Intelligent Transportation System

Vehicle positioning has played an important role in intelligent transportation systems. Previous research has had difficulties in increasing the sensor aperture and reducing the computational complexity of the vehicle positioning algorithm. This paper proposes a new sensor model to extend the sensor aperture, which is similar to the nested sensor model combined with fourth-order cumulants. The proposed algorithm estimates the number of vehicles, which is much higher than the actual number of sensors. An ideal characteristic equation-based method is used to avoid the use of eigenvalue decomposition and spectrum peak search, thereby greatly reducing the computation complexity. In addition, the weighted coefficient matrix is introduced for optimization. Theoretical analysis and simulation results show that the proposed algorithm has lower computational complexity, avoids 2-D parameter matching, and has a high utilization of arrays while still ensuring accurate parameter estimation.

Automatic modulation recognition for DVB-S2 using pairwise support vector machines

In this paper, a support vector machine (SVM) pairwise coupling algorithm is developed for classification of satellite communications signals used in second generation of digital video broadcasting via satellite (DVB-S2) standard. DVB-S2 standard adaptively uses one of QPSK, 8PSK, 16APSK, and 32APSK modulations. The proposed method extracts fourth and sixth order cumulants as features from the received signal. The features are given to a SVM pairwise coupling algorithm in which there is one binary SVM for each pair of modulation types. Finally the algorithm selects the modulation type chosen by the maximal number of pairwise SVMs as final decision. SVMs are trained by samples from different modulation types corrupted by Gaussian noise. The simulation results show that the proposed method allows higher recognition rates in comparison with previous methods, especially at low SNRs.

Automatic modulation recognition for DVB-S2 using pairwise support vector machines

In this paper, a support vector machine (SVM) pairwise coupling algorithm is developed for classification of satellite communications signals used in second generation of digital video broadcasting via satellite (DVB-S2) standard. DVB-S2 standard adaptively uses one of QPSK, 8PSK, 16APSK, and 32APSK modulations. The proposed method extracts fourth and sixth order cumulants as features from the received signal. The features are given to a SVM pairwise coupling algorithm in which there is one binary SVM for each pair of modulation types. Finally the algorithm selects the modulation type chosen by the maximal number of pairwise SVMs as final decision. SVMs are trained by samples from different modulation types corrupted by Gaussian noise. The simulation results show that the proposed method allows higher recognition rates in comparison with previous methods, especially at low SNRs.

The competitive effect of non-magnetic defect and films thickness on the ferromagnetic critical temperature in Ising thin-films

In this work, Monte Carlo simulation was employed to investigate the competitive effect of non-magnetic defects and the thickness on the ferromagnetic behavior of Ising spins in a reduced geometry, i.e. thin-films. The magnetic properties were investigated as functions of temperature, defect concentration, and films’ thickness, especially in the ferromagnetic phase transition region. The finite size scaling was performed via the fourth order cumulant of the magnetization to extract the critical temperatures. From the results, the extracted critical temperatures agree well with previous theoretical investigation, where applicable. With increasing concentration of the nonmagnetic defects, the Ising phase-transition-point slightly shifts towards lower temperature, while the increase of films thickness enhances the critical temperature value. Being confirmed by the main-effect-plot analysis, the increase in thickness has much greater influences on the critical temperature than that of the defect concentration, which could be described in term of the average ferromagnetic interaction spin. As the role of the defect is negligence in the range of considered defect concentration (up to ten percent), it therefore suggests that the preparation of ferromagnetic films can be done in normal operating condition where defects usually occur. It may be not economically worth to aim for the perfectly smooth films when the associated application operates at temperatures away from the critical point.

Single Channel Blind Source Separation for Wind Turbine Aeroacoustics Signals Based on Variational Mode Decomposition

The acquisition of aeroacoustics signals of wind turbines is of great significance in environmental noise assessment and fault monitoring of blades. The single acoustic sensor is simpler and more flexible than the acoustic sensors array but it lacks spatial analysis capability of the acoustic pressure field, and it is difficult to get pure aeroacoustics signals directly. This paper proposes a single channel blind source separation (SCBSS) method based on variational mode decomposition (VMD) which is applied to the separation of the wind turbine aeroacoustics signals acquired by the single acoustic sensors. The variational mode decomposition of the nonlinear and nonstationary signals based on the data itself completely is adaptive. In addition, the problem of mode mixing and “endpoint effect” has been improved. A novel approach combined correlation criterion with an overall index of orthogonality criterion is proposed in this paper to determine the optimal number of decomposition layers of VMD. We transform single channel underdetermined blind source separation to the non-underdetermined problem by establishing virtual multi-channel signals of the observation signals base on VMD, and separate the signals by joint approximate diagonalization of eigen-matrices (JADE) of fourth-order cumulant matrices. The method proposed in this paper has an excellent separation performance for wind turbine aeroacoustics signals, and the analysis of simulation signals indicates it has a 92.23% average recognition proportion, which is better than BSS based on EMD and EEMD, and the method has an extremely shorter computing time than EEMDBSS. The analysis of actual signals shows that the suggested method is adaptive and robust for noise.

Thermodynamic and magnetic properties of a three-state Potts model on a triangular lattice with next-neighbor interactions

Using Monte Carlo calculations, we study the thermodynamic and magnetic properties of 2D structures that can be described by a three-state Potts model on a triangular lattice with nearest- and secondnearest- neighbor interactions characterized by the coupling constants J 1 and J 2, respectively. Analyzing the thermodynamic parameters of heat capacity, the order parameter, the susceptibility, and fourth-order Binder cumulants, we show that the three-state Potts model with coupling constants J 1 > 0 and J 2 < 0 predicts a phase transition of the second kind for 0 ≤ |r| ≤ 1/3, where r = J 2/J 1.

Collectivity from interference

In hadronic collisions, interference between different production channels affects momentum distributions of multi-particle final states. As this QCD interference does not depend on the strong coupling constant αs, it is part of the no-interaction baseline that needs to be controlled prior to searching for other manifestations of collective dynamics, e.g., in the analysis of azimuthal anisostropy coefficients vn at the LHC. Here, we introduce a model that is based on the QCD theory of multi-parton interactions and that allows one to study interference effects in the production of m particles in hadronic collisions with N parton-parton interactions (“sources”). In an expansion in powers of 1/(Nc2 − 1) and to leading order in the number of sources N , we calculate interference effects in the m-particle spectra and we determine from them the second and fourth order cumulant momentum anisotropies vn{2} and vn{4}. Without invoking any azimuthal asymmetry and any density dependent non-linear dynamics in the incoming state, and without invoking any interaction in the final state, we find that QCD interference alone can give rise to values for vn{2} and vn{4}, n even, that persist unattenuated for increasing number of sources, that may increase with increasing multiplicity and that agree with measurements in proton-proton (pp) collisions in terms of the order of magnitude of the signal and the approximate shape of the transverse momentum dependence. We further find that the non-abelian features of QCD interference can give rise to odd harmonic anisotropies. These findings indicate that the no-interaction baseline including QCD interference effects can make a sizeable if not dominant contribution to the measured vn coefficients in pp collisions. Prospects for analyzing QCD interference contributions further and their possible relevance for proton-nucleus and nucleus-nucleus collisions are discussed shortly.