Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method

The non-Gaussianity of quantum states incarnates an important resource for improving the performance of continuous-variable quantum information protocols.We propose a novel criterion of non-Gaussianity for single-mode rotationally symmetric quantum states via the squared Frobenius norm of higher-order cumulant matrix for the quadrature distribution function.As an application,we study the non-Gaussianities of three classes of single-mode symmetric non-Gaussian states:a mixture of vacuum and Fock states,single-photon added thermal states,and even/odd Schr¨odinger cat states.It is shown that such a criterion is faithful and effective for revealing non-Gaussianity.We further extend this criterion to two cases of symmetric multi-mode non-Gaussian states and non-symmetric single-mode non-Gaussian states.

Wigner function of optical cumulant operator and its dissipation in thermo-entangled state representation

To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion.

基于RARE-Cumulant的互耦校正和DOA估计

基于四阶累计量及RARE(RAnk reducee quation)变换,结合均匀线阵互耦矩阵的特殊性,提出了一种新的互耦校正及波达方向估计算法。虽然四阶累计量比传统的二阶方法算法复杂,却扩展了阵列孔径,提高了在色噪声背景下DOA估计精度,而互耦系数并未因增加了虚拟阵元而增多。RARE变换将互耦系数与波达方向参量分离,有效地实现了多维参数估计的降维处理,减小了多维参量估计的计算量。仿真实验表明,在高斯色噪声背景下,本文方法计算量小,而且估计能力明显优于二阶去耦算法和传统的四阶方法。

Joint estimation of DOA, frequency, and polarization based on cumulants and UCA

A joint estimation algorithm of direction of arrival （DOA）, frequency, and polarization, based on fourth-order cumulants and uniform circular array （UCA） of trimmed vector sensors is presented for narrowband non-Gaussian signals. The proposed approach, which is suitable for applications in arbitrary Gaussian noise environments, gives a closed-form representation of the estimated parameters, without spectral peak searching. An efficient method is also provided for elimination of cyclic phase ambiguities. Simulations are presented to show the performance of the algorithm.

CLASSIFICATION OF MPSK SIGNALS USING CUMULANT INVARIANTS

A new feature based on higher order statistics is proposed for classification of MPSKsignals, which is invariant with respect to translation (shift), scale and rotation transforms of MPSK signal constellations, and can suppress additive color or white Gaussian noise. Application of the new feature to classification of MPSK signals, at medium signal-to-noise ratio with specified sample size, results in high probability of correct identification. Finally, computer simulations and comparisons with existing algorithms are given.

Non-Gaussianity dynamics of two-mode squeezed number states subject to different types of noise based on cumulant theory

We provide a measure to characterize the non-Gaussianity of phase-space function of bosonic quantum states based on the cumulant theory. We study the non-Gaussianity dynamics of two-mode squeezed number states by analyzing the phase-averaged kurtosis for two different models of decoherence： amplitude damping model and phase damping model.For the amplitude damping model, the non-Gaussianity is very fragile and completely vanishes at a finite time. For the phase damping model, such states exhibit rich non-Gaussian characters. In particular, we obtain a transition time that such states can transform from sub-Gaussianity into super-Gaussianity during the evolution. Finally, we compare our measure with the existing measures of non-Gaussianity under the independent dephasing environment.

Identification of multiple inputs single output errors-in-variables system using cumulant

A higher-order cumulant-based weighted least square（HOCWLS） and a higher-order cumulant-based iterative least square（HOCILS） are derived for multiple inputs single output（MISO） errors-in-variables（EIV） systems from noisy input/output data. Whether the noises of the input/output of the system are white or colored, the proposed algorithms can be insensitive to these noises and yield unbiased estimates. To realize adaptive parameter estimates, a higher-order cumulant-based recursive least square（HOCRLS） method is also studied. Convergence analysis of the HOCRLS is conducted by using the stochastic process theory and the stochastic martingale theory. It indicates that the parameter estimation error of HOCRLS consistently converges to zero under a generalized persistent excitation condition. The usefulness of the proposed algorithms is assessed through numerical simulations.

CONVERGENCE PROPERTIES OF HIGHER-ORDER MOMENT AND CUMULANT ESTIMATES

The sample estimates of higher-order statistics are studied. Under certain conditions, the almost sure convergence of the third- and fourth-order moment and cumulant estimates of stationary processes is established. The rate of almost sure convergence is obtained for the sample estimates of third- and fourth-order moment and cumulant. Additionally, it is shown that the third- and fourth-order moment and cumulant estimates are asymptotic normal.

Application of Three Order Cumulants in Fault Diagnosis

The three-order cumulants’ complex forms of different definitions include different coupling information of signals, and the information can be used to diagnose fault. In the experiment of pressure reducing valve’s fault diagnosis, through these different coupling information, the features of fault signals and normal signals were extracted by wavelet in different directions, then these features were inputted to diagnose the fault. The experiment shows that this method can achieve a satisfactory result.

Signal Classification Method Based on Support Vector Machine and High-Order Cumulants

In this paper, a classification method based on Support Vector Machine (SVM) is given in the digital modulation signal classification. The second, fourth and sixth order cumulants of the received signals are used as classification vectors firstly, then the kernel thought is used to map the feature vector to the high dimensional feature space and the optimum separating hyperplane is constructed in space to realize signal recognition. In order to build an effective and robust SVM classifier, the radial basis kernel function is selected, one against one or one against rest of multi-class classifier is designed, and method of parameter selection using cross- validation grid is adopted. Through the experiments it can be concluded that the classifier based on SVM has high performance and is more robust.

Recognition Analysis and Simulation Implementation Based on High-Order Cumulants of Wireless Digital Modulation Mode

This paper mainly studies the data characteristics of high order cumulants using digitally modulated signals, and constructs the identification feature parameters that can distinguish the signal modulation type by the high-order cumulants data of the digital modulation signal. Set the identification signal modulation type determination threshold based on the value of the identification feature parameter. The identification feature parameter value of the signal modulation type is compared with the set determination threshold, to realize the recognition of digital modulation signal. This identification method is implemented based on MATLAB design, with a 2ASK (2-ary Amplitude Shift Keying) signal, 4ASK (4-ary Amplitude Shift Keying) signal, 2PSK (2-ary Phase Shift Keying) signal, 4PSK (4-ary Phase Shift Keying) signal, 2FSK (2-ary Frequency Shift Keying) signal, 4FSK (4-ary Frequency Shift Keying) signal. The second, fourth and sixth order cumulants of the six signals were analyzed. Calculate the selected identification feature parameter value and the determination threshold to identify the six signals. The six signals have made MATLAB identification simulation. Simulation results show that this method is feasible and has high recognition rate. Simulation results verify that such recognition methods maintain a high recognition rate under conditions with low signal-to-noise ratio. This identification method can be extended to more MASK (M-ary Amplitude Shift Keying), MPSK (M-ary Phase Shift Keying), MFSK (M-ary Frequency Shift Keying), MQAM (M-ary Quadrature Amplitude Modulation) signal identification.

BLIND AND COMPLETE MODELING OF LINEAR SYSTEMS USING THIRD ORDER CUMULANTS

This paper presents a novel approach to structure determination of linear systems along with the choice of system orders and parameters. AutoRegressive （AR）, Moving Average （MA） or AutoRegressive-Moving Average （ARMA） model structure can be extracted blindly from the Third Order Cumulants （TOC） of the system output ts, where the unknown system is driven by an unobservable stationary independent identically distributed （i.i.d.） non-Gaussian signal. By means of the system order recursion, whether the system has an AR structure or has AR part of an ARMA structure is firstly investigated. MA features in the TOC domain is then applied as a threshold to decide if the system is an MA model or has MA part of an ARMA model. Numerical simulations illustrate the generality of the proposed blind structure identification methodology that may serve as a guideline for blind, linear system modeling.

A Cumulant-Based Beamforming Algorithm for CDMA Frequency-nonselective Fading Channel

A cumulant-based beamforing technique for synchronous CDMA system with decorrelator is presented. With decorrelating detector the proposed algorithm has the advantages that the steering vector of desired user’s can be estimated independently by eliminating all the other resolved signal interferences. Furthermore employing cumulant-based signal processing technique the steering vector of the decoupled signals can be estimated blindly. Simulation results show that the cumulant-based beamformer demonstrates excellent performance.

ADAPTIVE ALGORITHM FOR CONSISTENTMA PARAMETER ESTIMATION VIATHIRD ORDER CUMULANT

This paper addresses the problem of adaptive,consistent parameter estimation for a MA model from the 3rd order cumulant of the system output. The proposed adaptive algorithm is derived by using the new linear equation system (J. K. Tugnait, 1990), which is proved to have unique solution,and hence guarantees the consistence of the MA parameters. Simulation results are provided to show the performance of the new algorithm.

THE FOURTH-ORDER CUMULANTS BASED SPECTRALESTIMATION METHOD AND ITS APPLICATIONTO DIRECTION-FINDING

Traditional approaches of spatial spectral estimation are usually based on the second-order statistics. The higher-order cumulants and the poly-spectrum contain more information and are capable of reducing the Gaussian noise. In this paper, we present a new spectrum estimation method for direction-finding, the FOMUSIC algorithm, which is based on the eigen-structure analysis of the fourth-order cumulants. The derivation of the algorithm is given in detail and its performance is illustrated by both the computer simulations and the experiments of a direction-finding system. The obtained results demonstrate that the fourth-order cumulants based method outperforms the traditional methods, especially when the noise is an unknown colored one.

Cumulative effects of excess high-normal alanine aminotransferase levels in relation to new-onset metabolic dysfunction-associated fatty liver disease in China

BACKGROUND Within the normal range,elevated alanine aminotransferase(ALT)levels are associated with an increased risk of metabolic dysfunction-associated fatty liver disease(MAFLD).AIM To investigate the associations between repeated high-normal ALT measurements and the risk of new-onset MAFLD prospectively.METHODS A cohort of 3553 participants followed for four consecutive health examinations over 4 years was selected.The incidence rate,cumulative times,and equally and unequally weighted cumulative effects of excess high-normal ALT levels(ehALT)were measured.Cox proportional hazards regression was used to analyse the association between the cumulative effects of ehALT and the risk of new-onset MAFLD.RESULTS A total of 83.13%of participants with MAFLD had normal ALT levels.The incidence rate of MAFLD showed a linear increasing trend in the cumulative ehALT group.Compared with those in the low-normal ALT group,the multivariate adjusted hazard ratios of the equally and unequally weighted cumulative effects of ehALT were 1.651[95%confidence interval(CI):1.199-2.273]and 1.535(95%CI:1.119-2.106)in the third quartile and 1.616(95%CI:1.162-2.246)and 1.580(95%CI:1.155-2.162)in the fourth quartile,respectively.CONCLUSION Most participants with MAFLD had normal ALT levels.Long-term high-normal ALT levels were associated with a cumulative increased risk of new-onset MAFLD.

A MODIFIED HIGH-ORDER CUMULANT MUSIC ALGORITHM FOR SIGNAL DOA ESTIMATION

This paper gives a MUSIC signal DOA estimation algorithm based on the modified high-order cumulant matrix which is constructed by the recieved data and their conjugate rearrangements. When the snapshot number is limited, this algorithm can improve the signal DOA estimation performances obviously, and its computational complexity scarcely increases. Finally, some simulation results to verify the theoretical analyses are presented.

Harmonic Retrieval Embedded in Hybrid Colored Noise: a Novel Pisarenko Method Based on Cross high order Cumulant

Spectral estimation method is an effective method in the case of parameter estimation of sinusoid signal in noises.It always applies cross spectral estimation theory and high order self spectral estimation methods up to now.Yule Walker equation based on cross fourth order cumulant is developed and Pisarenko method is provided in this paper.Simulation results show that the method is effective to retrieve sinusoid signal frequencies from hybrid colored noises and has good performance.

ANALYSIS OF A CUMULANT-BASED 2D-RAKE RECEIVER FOR CDMA SYSTEM OVER FREQUENCY-SELECTIVE FADING CHANNELS

The conventional 2D Rake receivers for code division multiple access (CDMA) system over frequency selective fading channels are generally based on the second order statistics while assuming perfect array conditions. However, the sensor response, location uncertainty, and the use of sample statistics can severely degrade the performance of second order statistics processing. And in practical application, it is impossible to calibrate the array frequently. In this paper a cumulant based 2D Rake receiver for synchronous CDMA system with decorrelator is presented. Decorrelating is a multi user detection approach that not only provides a fundamental solution to the mutual interference problem in CDMA communications but also makes it convenient for the decoupled signal to be processed spatially and temporally. High order signal processing has some inherent advantages over that of second order. Employing second order statistics it is impossible to estimate source steering vector blindly, while employing higher than second order cumulants, this purpose can be achieved. The performance analysis shows that employing cumulant based signal processing technique the proposed 2D Rake receiver is blind and demonstrates excellent performance.

Photon number cumulant expansion and generating function for photon added-and subtracted-two-mode squeezed states

For the first time, we derive the photon number cumulant for two-mode squeezed state and show that its cumulant expansion leads to normalization of two-mode photon subtracted-squeezed states and photon added- squeezed states. We show that the normalization is related to Jacobi polynomial, so the cumulant expansion in turn represents the new generating function of Jacobi polynomial.