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 struc...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.展开更多
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 o...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.展开更多
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 con...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.展开更多
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 high...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.展开更多
The knowledge of subnuclear localization in eukaryotic cells is indispensable for under-standing the biological function of nucleus, genome regulation and drug discovery. In this study, a new feature representation wa...The knowledge of subnuclear localization in eukaryotic cells is indispensable for under-standing the biological function of nucleus, genome regulation and drug discovery. In this study, a new feature representation was pro-posed by combining position specific scoring matrix (PSSM) and auto covariance (AC). The AC variables describe the neighboring effect between two amino acids, so that they incorpo-rate the sequence-order information;PSSM de-scribes the information of biological evolution of proteins. Based on this new descriptor, a support vector machine (SVM) classifier was built to predict subnuclear localization. To evaluate the power of our predictor, the benchmark dataset that contains 714 proteins localized in nine subnuclear compartments was utilized. The total jackknife cross validation ac-curacy of our method is 76.5%, that is higher than those of the Nuc-PLoc (67.4%), the OET- KNN (55.6%), AAC based SVM (48.9%) and ProtLoc (36.6%). The prediction software used in this article and the details of the SVM parameters are freely available at http://chemlab.scu.edu.cn/ predict_SubNL/index.htm and the dataset used in our study is from Shen and Chou’s work by downloading at http://chou.med.harvard.edu/ bioinf/Nuc-PLoc/Data.htm.展开更多
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...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.展开更多
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 ...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.展开更多
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...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.展开更多
Differential evolution algorithm based on the covariance matrix learning can adjust the coordinate system according to the characteristics of the population, which make<span style="font-family:Verdana;"&g...Differential evolution algorithm based on the covariance matrix learning can adjust the coordinate system according to the characteristics of the population, which make<span style="font-family:Verdana;">s</span><span style="font-family:Verdana;"> the search move in a more favorable direction. In order to obtain more accurate information about the function shape, this paper propose</span><span style="font-family:Verdana;">s</span><span style="font-family:;" "=""> <span style="font-family:Verdana;">covariance</span><span style="font-family:Verdana;"> matrix learning differential evolution algorithm based on correlation (denoted as RCLDE)</span></span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">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,</span><span style="font-family:;" "=""> </span><span style="font-family:;" "=""><span style="font-family:Verdana;">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 </span><span style="font-family:Verdana;">an effective algorithm</span><span style="font-family:Verdana;">.</span></span>展开更多
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 t...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.展开更多
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 ...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.展开更多
In this paper,we consider the limiting spectral distribution of the information-plus-noise type sample covariance matrices Cn=1/N(Rn+σXn)(Rn+σXn),under the assumption that the entries of Xn are independent but...In this paper,we consider the limiting spectral distribution of the information-plus-noise type sample covariance matrices Cn=1/N(Rn+σXn)(Rn+σXn),under the assumption that the entries of Xn are independent but non-identically distributed random variables.It is proved that,almost surely,the empirical spectral distribution of Cn converges weakly to a non-random distribution whose Stieltjes transform satisfies a certain equation.Our result extends the previous one with the entries of Xn are i.i.d.random varibles to a more general case.The proof of the result mainly employs the Stein equation and the cumulant expansion formula of independent random variables.展开更多
In many applications, such as in multivariate meta-analysis or in the construction of multivariate models from summary statistics, the covariance of regression coefficients needs to be calculated without having access...In many applications, such as in multivariate meta-analysis or in the construction of multivariate models from summary statistics, the covariance of regression coefficients needs to be calculated without having access to individual patients’ data. In this work, we derive an alternative analytic expression for the covariance matrix of the regression coefficients in a multiple linear regression model. In contrast to the well-known expressions which make use of the cross-product matrix and hence require access to individual data, we express the covariance matrix of the regression coefficients directly in terms of covariance matrix of the explanatory variables. In particular, we show that the covariance matrix of the regression coefficients can be calculated using the matrix of the partial correlation coefficients of the explanatory variables, which in turn can be calculated easily from the correlation matrix of the explanatory variables. This is very important since the covariance matrix of the explanatory variables can be easily obtained or imputed using data from the literature, without requiring access to individual data. Two important applications of the method are discussed, namely the multivariate meta-analysis of regression coefficients and the so-called synthesis analysis, and the aim of which is to combine in a single predictive model, information from different variables. The estimator proposed in this work can increase the usefulness of these methods providing better results, as seen by application in a publicly available dataset. Source code is provided in the Appendix and in http://www.compgen.org/tools/regression.展开更多
针对传统的自适应波束形成算法在目标导向矢量失配及接收数据的协方差矩阵存在误差时,性能急剧下降的问题,提出了一种基于小快拍场景的联合协方差矩阵重构,及导向矢量优化的稳健波束形成算法。对不确定集约束求解得到干扰导向矢量,根据...针对传统的自适应波束形成算法在目标导向矢量失配及接收数据的协方差矩阵存在误差时,性能急剧下降的问题,提出了一种基于小快拍场景的联合协方差矩阵重构,及导向矢量优化的稳健波束形成算法。对不确定集约束求解得到干扰导向矢量,根据稀疏干扰来向的导向矢量近似正交,求出干扰导向矢量对应的干扰功率,从而完成协方差矩阵重构;对期望信号来向及其邻域进行权值求解,对加权后的数据特征分解,利用多信号分类(Multiple Signal Classification, MUSIC)谱估计算法对信号区域积分得到信号协方差矩阵,将其主特征值近似为期望信号的导向矢量完成重新估计。仿真结果表明,在无误差时,算法输出信干噪比(Signal to Interference Plus Noise Ratio, SINR)接近理论最优;在多种误差环境下输出性能随信噪比(Signal to Noise Ratio, SNR)的变化均具有较好的稳健性,并且在信号来向可精准形成波束;在小快拍时可以较快收敛至理论最优值。展开更多
基金supported by National Key Research and Development Program of China under Grant 2020YFB1804901State Key Laboratory of Rail Traffic Control and Safety(Contract:No.RCS2022ZT 015)Special Key Project of Technological Innovation and Application Development of Chongqing Science and Technology Bureau(cstc2019jscx-fxydX0053).
文摘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.
文摘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.
基金Characteristic Innovation Projects of Ordinary Universities of Guangdong Province,China(No.2022KTSCX150)Zhaoqing Education Development Institute Project,China(No.ZQJYY2021144)Zhaoqing College Quality Project and Teaching Reform Project,China(Nos.zlgc202003 and zlgc202112)。
文摘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.
基金supported by the National Natural Science Foundation of China(618711496197115962071144)。
文摘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.
文摘The knowledge of subnuclear localization in eukaryotic cells is indispensable for under-standing the biological function of nucleus, genome regulation and drug discovery. In this study, a new feature representation was pro-posed by combining position specific scoring matrix (PSSM) and auto covariance (AC). The AC variables describe the neighboring effect between two amino acids, so that they incorpo-rate the sequence-order information;PSSM de-scribes the information of biological evolution of proteins. Based on this new descriptor, a support vector machine (SVM) classifier was built to predict subnuclear localization. To evaluate the power of our predictor, the benchmark dataset that contains 714 proteins localized in nine subnuclear compartments was utilized. The total jackknife cross validation ac-curacy of our method is 76.5%, that is higher than those of the Nuc-PLoc (67.4%), the OET- KNN (55.6%), AAC based SVM (48.9%) and ProtLoc (36.6%). The prediction software used in this article and the details of the SVM parameters are freely available at http://chemlab.scu.edu.cn/ predict_SubNL/index.htm and the dataset used in our study is from Shen and Chou’s work by downloading at http://chou.med.harvard.edu/ bioinf/Nuc-PLoc/Data.htm.
基金Supported by the Aviation Science Fund (No. 20080152004)China Postdoctoral Foundation (No. 20090461119)
文摘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.
基金supported by the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (0506011200702)National Natural Science Foundation of China+2 种基金Tian Yuan Special Foundation (10926059)Foundation of Zhejiang Educational Committee (Y200803920)Scientific Research Foundation of Hangzhou Dianzi University(KYS025608094)
文摘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.
基金supported by National Natural Science Foundation of China(61174207,61374120,61074072,11405267)
文摘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.
文摘Differential evolution algorithm based on the covariance matrix learning can adjust the coordinate system according to the characteristics of the population, which make<span style="font-family:Verdana;">s</span><span style="font-family:Verdana;"> the search move in a more favorable direction. In order to obtain more accurate information about the function shape, this paper propose</span><span style="font-family:Verdana;">s</span><span style="font-family:;" "=""> <span style="font-family:Verdana;">covariance</span><span style="font-family:Verdana;"> matrix learning differential evolution algorithm based on correlation (denoted as RCLDE)</span></span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">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,</span><span style="font-family:;" "=""> </span><span style="font-family:;" "=""><span style="font-family:Verdana;">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 </span><span style="font-family:Verdana;">an effective algorithm</span><span style="font-family:Verdana;">.</span></span>
基金supported in part by the National Natural Science Foundation of China(No.62273287)by the Shenzhen Science and Technology Innovation Council(Nos.JCYJ20220530143418040,JCY20170411102101881)the Thousand Youth Talents Plan funded by the central government of China.
文摘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.
基金supported by the Program for Innovative Research Groups of the Hunan Provincial Natural Science Foundation of China(2019JJ10004)。
文摘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.
基金supported by the National Natural Science Foundation of China(11071213,11101362)Natural Science Foundation of Zhejiang Province(R6090034)Specialized Research Foundation for the Doctor Program of Higher Education(20100101110001)
文摘In this paper,we consider the limiting spectral distribution of the information-plus-noise type sample covariance matrices Cn=1/N(Rn+σXn)(Rn+σXn),under the assumption that the entries of Xn are independent but non-identically distributed random variables.It is proved that,almost surely,the empirical spectral distribution of Cn converges weakly to a non-random distribution whose Stieltjes transform satisfies a certain equation.Our result extends the previous one with the entries of Xn are i.i.d.random varibles to a more general case.The proof of the result mainly employs the Stein equation and the cumulant expansion formula of independent random variables.
文摘In many applications, such as in multivariate meta-analysis or in the construction of multivariate models from summary statistics, the covariance of regression coefficients needs to be calculated without having access to individual patients’ data. In this work, we derive an alternative analytic expression for the covariance matrix of the regression coefficients in a multiple linear regression model. In contrast to the well-known expressions which make use of the cross-product matrix and hence require access to individual data, we express the covariance matrix of the regression coefficients directly in terms of covariance matrix of the explanatory variables. In particular, we show that the covariance matrix of the regression coefficients can be calculated using the matrix of the partial correlation coefficients of the explanatory variables, which in turn can be calculated easily from the correlation matrix of the explanatory variables. This is very important since the covariance matrix of the explanatory variables can be easily obtained or imputed using data from the literature, without requiring access to individual data. Two important applications of the method are discussed, namely the multivariate meta-analysis of regression coefficients and the so-called synthesis analysis, and the aim of which is to combine in a single predictive model, information from different variables. The estimator proposed in this work can increase the usefulness of these methods providing better results, as seen by application in a publicly available dataset. Source code is provided in the Appendix and in http://www.compgen.org/tools/regression.
文摘针对传统的自适应波束形成算法在目标导向矢量失配及接收数据的协方差矩阵存在误差时,性能急剧下降的问题,提出了一种基于小快拍场景的联合协方差矩阵重构,及导向矢量优化的稳健波束形成算法。对不确定集约束求解得到干扰导向矢量,根据稀疏干扰来向的导向矢量近似正交,求出干扰导向矢量对应的干扰功率,从而完成协方差矩阵重构;对期望信号来向及其邻域进行权值求解,对加权后的数据特征分解,利用多信号分类(Multiple Signal Classification, MUSIC)谱估计算法对信号区域积分得到信号协方差矩阵,将其主特征值近似为期望信号的导向矢量完成重新估计。仿真结果表明,在无误差时,算法输出信干噪比(Signal to Interference Plus Noise Ratio, SINR)接近理论最优;在多种误差环境下输出性能随信噪比(Signal to Noise Ratio, SNR)的变化均具有较好的稳健性,并且在信号来向可精准形成波束;在小快拍时可以较快收敛至理论最优值。