Low-Complexity Reconstruction of Covariance Matrix in Hybrid Uniform Circular Array

Spatial covariance matrix(SCM) is essential in many multi-antenna systems such as massive multiple-input multiple-output(MIMO). For multi-antenna systems operating at millimeter-wave bands, hybrid analog-digital structure has been widely adopted to reduce the cost of radio frequency chains.In this situation, signals received at the antennas are unavailable to the digital receiver, and as a consequence, traditional sample average approach cannot be used for SCM reconstruction in hybrid multi-antenna systems. To address this issue, beam sweeping algorithm(BSA) which can reconstruct the SCM effectively for a hybrid uniform linear array, has been proposed in our previous works. However, direct extension of BSA to a hybrid uniform circular array(UCA)will result in a huge computational burden. To this end, a low-complexity approach is proposed in this paper. By exploiting the symmetry features of SCM for the UCA, the number of unknowns can be reduced significantly and thus the complexity of reconstruction can be saved accordingly. Furthermore, an insightful analysis is also presented in this paper, showing that the reduction of the number of unknowns can also improve the accuracy of the reconstructed SCM. Simulation results are also shown to demonstrate the proposed approach.

Empirical Likelihood Statistical Inference for Compound Poisson Vector Processes under Infinite Covariance Matrix

The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to construct confidence regions for the mean vector has been proposed.It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law.The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix.Some simulation results are proposed to illustrate the method of the paper.

Cyclic Beam Direction of Arrival Estimation Method for Ship Propeller Noise

In underwater acoustic applications,the conventional cyclic direction of arrival algorithm faces challenges,including a low signal-to-noise ratio and high bandwidth when compared with modulated frequencies.In response to these issues,this paper introduces a novel,robust,and broadband cyclic beamforming algorithm.The proposed method substitutes the conventional cyclic covariance matrix with the variance of the cyclic covariance matrix as its primary feature.Assuming that the same frequency band shares a common steering vector,the new algorithm achieves superior detection performance for targets with specific modulation frequencies while suppressing interference signals and background noise.Experimental results demonstrate a significant enhancement in the directibity index by 81%and 181%when compared with the traditional Capon beamforming algorithm and the traditional extended wideband spectral cyclic MUSIC(EWSCM)algorithm,respectively.Moreover,the proposed algorithm substantially reduces computational complexity to 1/40th of that of the EWSCM algorithm,employing frequency band statistical averaging and covariance matrix variance.

Optimal Estimation of High-Dimensional Covariance Matrices with Missing and Noisy Data

The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based on complete data. This paper studies the optimal estimation of high-dimensional covariance matrices based on missing and noisy sample under the norm. First, the model with sub-Gaussian additive noise is presented. The generalized sample covariance is then modified to define a hard thresholding estimator , and the minimax upper bound is derived. After that, the minimax lower bound is derived, and it is concluded that the estimator presented in this article is rate-optimal. Finally, numerical simulation analysis is performed. The result shows that for missing samples with sub-Gaussian noise, if the true covariance matrix is sparse, the hard thresholding estimator outperforms the traditional estimate method.

Geomagnetic jerk extraction based on the covariance matrix

We normalize data from 43 Chinese observatories and select data from ten Chinese observatories with most continuous records to assess the secular variations(SVs)and geomagnetic jerks by calculating the deviations between annual observed and CHAOS-6 model monthly means.The variations in the north,east,and vertical eigendirections are studied by using the covariance matrix of the residuals,and we find that the vertical direction is strongly affected by magnetospheric ring currents.To obtain noise-free data,we rely on the covariance matrix of the residuals to remove the noise contributions from the largest eigenvalue or vectors owing to ring currents.Finally,we compare the data from the ten Chinese observatories to seven European observatories.Clearly,the covariance matrix method can simulate the SVs of Dst,the jerk of the northward component in 2014 and that of the eastward component in 2003.5 in China are highly agree with that of Vertically downward component in Europe,compare to CHAOS-6,covariance matrix method can show more details of SVs.

Fast and accurate covariance matrix reconstruction for adaptive beamforming using Gauss-Legendre quadrature

Most of the reconstruction-based robust adaptive beamforming(RAB)algorithms require the covariance matrix reconstruction(CMR)by high-complexity integral computation.A Gauss-Legendre quadrature(GLQ)method with the highest algebraic precision in the interpolation-type quadrature is proposed to reduce the complexity.The interference angular sector in RAB is regarded as the GLQ integral range,and the zeros of the threeorder Legendre orthogonal polynomial is selected as the GLQ nodes.Consequently,the CMR can be efficiently obtained by simple summation with respect to the three GLQ nodes without integral.The new method has significantly reduced the complexity as compared to most state-of-the-art reconstruction-based RAB techniques,and it is able to provide the similar performance close to the optimal.These advantages are verified by numerical simulations.

Coupled Cross-correlation Neural Network Algorithm for Principal Singular Triplet Extraction of a Cross-covariance Matrix

This paper proposes a novel coupled neural network learning algorithm to extract the principal singular triplet (PST) of a cross-correlation matrix between two high-dimensional data streams. We firstly introduce a novel information criterion (NIC), in which the stationary points are singular triplet of the crosscorrelation matrix. Then, based on Newton's method, we obtain a coupled system of ordinary differential equations (ODEs) from the NIC. The ODEs have the same equilibria as the gradient of NIC, however, only the first PST of the system is stable (which is also the desired solution), and all others are (unstable) saddle points. Based on the system, we finally obtain a fast and stable algorithm for PST extraction. The proposed algorithm can solve the speed-stability problem that plagues most noncoupled learning rules. Moreover, the proposed algorithm can also be used to extract multiple PSTs effectively by using sequential method. © 2014 Chinese Association of Automation.

AN IMPROVED SAR-GMTI METHOD BASED ON EIGEN-DECOMPOSITION OF THE SAMPLE COVARIANCE MATRIX

An improved two-channel Synthetic Aperture Radar Ground Moving Target Indication (SAR-GMTI) method based on eigen-decomposition of the covariance matrix is investigated. Based on the joint Probability Density Function (PDF) of the Along-Track Interferometric (ATI) phase and the similarity between the two SAR complex images, a novel ellipse detector is presented and is applied to the indication of ground moving targets. We derive its statistics and analyze the performance of detection process in detail. Compared with the approach using the ATI phase, the ellipse detector has a better performance of detection in homogenous clutter. Numerical experiments on simulated data are presented to validate the improved performance of the ellipse detector with respect to the ATI phase approach. Finally, the detection capability of the proposed method is demonstrated by measured SAR data.

IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean, respectively, are proposed. It is shown that these new estimators dominate the unbiased estimator under the squared error loss function. Finally, some simulation results to compare the performance of the proposed estimators with that of the unbiased estimator are reported. The simulation results indicate that these new shrinkage estimators provide a substantial improvement in risk under most situations.

Two Stage Estimation and Its Covariance Matrix in Multivariate Seemingly Unrelated Regression System

Multivariate seemingly unrelated regression system is raised first and the two stage estimation and its covariance matrix are given. The results of the literatures[1-5] are extended in this paper.

Covariance Matrix Learning Differential Evolution Algorithm Based on Correlation

Differential evolution algorithm based on the covariance matrix learning can adjust the coordinate system according to the characteristics of the population, which makes the search move in a more favorable direction. In order to obtain more accurate information about the function shape, this paper proposes covariance matrix learning differential evolution algorithm based on correlation (denoted as RCLDE) to improve the search efficiency of the algorithm. First, a hybrid mutation strategy is designed to balance the diversity and convergence of the population;secondly, the covariance learning matrix is constructed by selecting the individual with the less correlation;then, a comprehensive learning mechanism is comprehensively designed by two covariance matrix learning mechanisms based on the principle of probability. Finally, the algorithm is tested on the CEC2005, and the experimental results are compared with other effective differential evolution algorithms. The experimental results show that the algorithm proposed in this paper is an effective algorithm.

A New Model for Network Security Situation Assessment of the Industrial Internet

To address the problem of network security situation assessment in the Industrial Internet,this paper adopts the evidential reasoning(ER)algorithm and belief rule base(BRB)method to establish an assessment model.First,this paper analyzes the influencing factors of the Industrial Internet and selects evaluation indicators that contain not only quantitative data but also qualitative knowledge.Second,the evaluation indicators are fused with expert knowledge and the ER algorithm.According to the fusion results,a network security situation assessment model of the Industrial Internet based on the ER and BRB method is established,and the projection covariance matrix adaptive evolution strategy(P-CMA-ES)is used to optimize the model parameters.This method can not only utilize semiquantitative information effectively but also use more uncertain information and prevent the problem of combinatorial explosion.Moreover,it solves the problem of the uncertainty of expert knowledge and overcomes the problem of low modeling accuracy caused by insufficient data.Finally,a network security situation assessment case of the Industrial Internet is analyzed to verify the effectiveness and superiority of the method.The research results showthat this method has strong applicability to the network security situation assessment of complex Industrial Internet systems.It can accurately reflect the actual network security situation of Industrial Internet systems and provide safe and reliable suggestions for network administrators to take timely countermeasures,thereby improving the risk monitoring and emergency response capabilities of the Industrial Internet.

The study of geomagnetic jerk from 2010 to 2021 based on hourly mean data from global geomagnetic observatories

The secular variation in the global geomagnetic field was analyzed in terms of the annual differences in monthly means by using the hourly mean data from 18 foreign(outside China)observatories of the World Data Center(WDC)for Geomagnetism from January 2010 to January 2020 as well as 9 observatories in the Geomagnetic Network of China from January 2015 to April 2021.In addition,according to the correlation of noisy components from the observatories,a covariance matrix was constructed based on residuals between observations and the CHAOS-7.4 model to remove external contamination.Through a comparison before and after denoising,we found that the overall average standard deviations were reduced by 29.97%in China and by 41.4%outside China.Results showed the correlation coefficient between external noise(mainly the magnetosphere ring current)and the Dst index was 0.82,and the correlation coefficient between external noise and the Ring Current(RC)index reached 0.94.A geomagnetic jerk was globally discovered around 2018.0 on the geomagnetic eastward component Y.The jerk timing in China was around 2020.0,and the earliest one was in2018.75,whereas the timing outside China was around 2018.0,and the earliest one was in 2017.67.This 2-year lag may have been caused by the higher electrical conductivity of the deep mantle.After more data were added,this jerk event was found to occur in an orderly manner in the northern hemisphere as the longitude increased and the intensity gradually increased as well.The variations in location of the jerk center were analyzed according to the CHAOS-7.4 model.Results revealed six extreme points distributed nearby the equator.The strongest was near the equator,at 170°E,and the strength gradually decreased as it extended to the northern and southern hemispheres.Another extreme point with the opposite sign was located at the equator,at 20°W,in the south-central part of the Atlantic,and the strength gradually decreased as it extended into Europe.The covariance matrix method can be used to analyze data from the Macao Science Satellite-1 mission in the future,and this method is expected to play a positive role in modeling and separating the large-scale external field.

Efficient Centralized Cooperative Spectrum Sensing Techniques for Cognitive Networks

Wireless Communication is a system for communicating information from one point to other,without utilizing any connections like wire,cable,or other physical medium.Cognitive Radio(CR)based systems and networks are a revolutionary new perception in wireless communications.Spectrum sensing is a vital task of CR to avert destructive intrusion with licensed primary or main users and discover the accessible spectrum for the efficient utilization of the spectrum.Centralized Cooperative Spectrum Sensing(CSS)is a kind of spectrum sensing.Most of the test metrics designed till now for sensing the spectrum is produced by using the Sample Covariance Matrix(SCM)of the received signal.Some of the methods that use the SCM for the process of detection are Pietra-Ricci Index Detector(PRIDe),Hadamard Ratio(HR)detector,Gini Index Detector(GID),etc.This paper presents the simulation and comparative perfor-mance analysis of PRIDe with various other detectors like GID,HR,Arithmetic to Geometric Mean(AGM),Volume-based Detector number 1(VD1),Maximum-to-Minimum Eigenvalue Detection(MMED),and Generalized Likelihood Ratio Test(GLRT)using the MATLAB software.The PRIDe provides better performance in the presence of variations in the power of the signal and the noise power with less computational complexity.

On convergence of covariance matrix of empirical Bayes hyper-parameter estimator

Regularized system identification has become the research frontier of system identification in the past decade.One related core subject is to study the convergence properties of various hyper-parameter estimators as the sample size goes to infinity.In this paper,we consider one commonly used hyper-parameter estimator,the empirical Bayes(EB).Its convergence in distribution has been studied,and the explicit expression of the covariance matrix of its limiting distribution has been given.However,what we are truly interested in are factors contained in the covariance matrix of the EB hyper-parameter estimator,and then,the convergence of its covariance matrix to that of its limiting distribution is required.In general,the convergence in distribution of a sequence of random variables does not necessarily guarantee the convergence of its covariance matrix.Thus,the derivation of such convergence is a necessary complement to our theoretical analysis about factors that influence the convergence properties of the EB hyper-parameter estimator.In this paper,we consider the regularized finite impulse response(FIR)model estimation with deterministic inputs,and show that the covariance matrix of the EB hyper-parameter estimator converges to that of its limiting distribution.Moreover,we run numerical simulations to demonstrate the efficacy of ourtheoretical results.

Co-channel interference rejection for MIMO-OFDM systems

A method based on the maximum a posteriori probability （MAP） criterion is proposed to estimate the channel frequency response （CFR） matrix and interference- plus-noise spatial covariance matrix （SCM） for multiple input and multiple output orthogonal frequency division multiplexing （MIMO-OFDM） systems. An iterative solution is proposed to solve the MAP-based problem and an interference rejection combining （IRC） receiver is derived to suppress co-channel interference （CCI） based on the estimated CFR and SCM. Furthermore, considering the property of SCM, i. e., Hermitian and semi-definite, two schemes are proposed to improve the accuracy of SCM estimation. The first scheme is proposed to parameterize the SCM via a sum of a series of matrices in the time domain. The second scheme measures the SCM on each subcarrier as a low-rank model while the model order can be chosen through the penalized-likelihood approach. Simulation results are provided to demonstrate the effectiveness of the proposed method.

Underdetermined DOA estimation via multiple time-delay covariance matrices and deep residual network

Higher-order statistics based approaches and signal sparseness based approaches have emerged in recent decades to resolve the underdetermined direction-of-arrival(DOA)estimation problem.These model-based methods face great challenges in practical applications due to high computational complexity and dependence on ideal assumptions.This paper presents an effective DOA estimation approach based on a deep residual network(DRN)for the underdetermined case.We first extract an input feature from a new matrix calculated by stacking several covariance matrices corresponding to different time delays.We then provide the input feature to the trained DRN to construct the super resolution spectrum.The DRN learns the mapping relationship between the input feature and the spatial spectrum by training.The proposed approach is superior to existing model-based estimation methods in terms of calculation efficiency,independence of source sparseness and adaptive capacity to non-ideal conditions(e.g.,low signal to noise ratio,short bit sequence).Simulations demonstrate the validity and strong performance of the proposed algorithm on both overdetermined and underdetermined cases.

Direction-of-arrival estimation for uniform circular arrays under small sample size

With a small number of snapshots, performances of uniform circular array (UCA) root-MUSIC based methods for directionof- arrival (DOA) estimation suffer serious degradation, because the beamspace sample covariance matrix (BSCM) severely deviates from the true one. To solve this problem, an iterative technique is proposed. The proposed technique has two key points: transform array data into beamspace data and construct a BSCM; modify the BSCM repeatedly by removing the residual parts. Meanwhile, error and beamspace leakage associated with the BSCM are investigated. The proposed technique can significantly reduce the error and the beamspace leakage which in turn could improve the performance for DOA estimation. Simulation results are given to illustrate the superiority of the proposed technique for uncorrelated and correlated signals. © 2016 Beijing Institute of Aerospace Information.

Mitigation of time-series InSAR turbulent atmospheric phase noise: A review

Synthetic Aperture Radar(SAR)interferometry is one of the most powerful remote sensing tools for ground deformation detection.However,tropospheric delay greatly limits the measurement accuracy of the InSAR technique.While vertically stratified tropospheric delays have been extensively investigated and well tackled,turbulent tropospheric phase noise still remains an intractable issue.In recent years,great efforts have been made to reduce the influence of turbulent atmospheric delay.This contribution is intended to provide a systematic review of the progress achieved in this field.First,it introduces the physical characteristics of atmospheric signals in interferograms.Then,a review of the main mitigation algorithms proposed in the literature is provided.In addition,the strengths and weaknesses of each approach are analyzed to provide guidance for choosing a suitable method accordingly.Finally,sug-gestions for resolving the challenging issues and an outlook for future research are given.

Range walk and array rotation in space-time adaptive processing:effects and compensations

This paper proposes a unified clutter model incorporating the effects of range walk and array rotation for space-time adaptive processing（STAP） in airborne multi-channel early-warning radar.Based on this clutter model,STAP performance is then analyzed from the perspective of covariance matrix tapering（CMT）.For STAP performance degradation due to array rotation,a determinate compensation method is proposed based on the CMT method.Numerical examples are provided to verify the analysis and the proposed compensation method.