A method is presented for calculating a matrix spectrum with a given set of eigenvalues. It can be used to build systems with different spectrums with the aim of choosing desired alternative. It enables a practical im...A method is presented for calculating a matrix spectrum with a given set of eigenvalues. It can be used to build systems with different spectrums with the aim of choosing desired alternative. It enables a practical implementation of control algorithms without resorting to transformation of variables.展开更多
This paper obtains a necessary and sufficient condition for an irreducible complex matrix whose comparison matrix is a singular M-matrix to be singular. This is used to establish a necessary and sufficient condition f...This paper obtains a necessary and sufficient condition for an irreducible complex matrix whose comparison matrix is a singular M-matrix to be singular. This is used to establish a necessary and sufficient condition for a boundary point of Brualdi’s inclusion region of the eigenvalues of an irreducible complex matrix to be an eigenvalue.展开更多
The spectral theory of graph is an important branch of graph theory,and the main part of this theory is the connection between the spectral properties and the structural properties,characterization of the structural p...The spectral theory of graph is an important branch of graph theory,and the main part of this theory is the connection between the spectral properties and the structural properties,characterization of the structural properties of graphs.We discuss the problems about singularity,signature matrix and spectrum of mixed graphs.Without loss of generality,parallel edges and loops are permitted in mixed graphs.Let G1 and G2 be connected mixed graphs which are obtained from an underlying graph G.When G1 and G2 have the same singularity,the number of induced cycles in Gi(i=1,2)is l(l=1,l>1),the length of the smallest induced cycles is 1,2,at least 3.According to conclusions and mathematics induction,we find that the singularity of corresponding induced cycles in G1 and G2 are the same if and only if there exists a signature matrix D such that L(G2)=DTL(G1)D.D may be the product of some signature matrices.If L(G2)=D^TL(G1)D,G1 and G2 have the same spectrum.展开更多
Random Matrix Theory (RMT) is a valuable tool for describing the asymptotic behavior of multiple systems,especially for large matrices. In this paper,using asymptotic random matrix theory,a new cooperative Multiple-In...Random Matrix Theory (RMT) is a valuable tool for describing the asymptotic behavior of multiple systems,especially for large matrices. In this paper,using asymptotic random matrix theory,a new cooperative Multiple-Input Multiple-Output (MIMO) scheme for spectrum sensing is proposed,which shows how asymptotic free property of random matrices and the property of Wishart distribution can be used to assist spectrum sensing for Cognitive Radios (CRs). Simulations over Rayleigh fading and AWGN channels demonstrate the proposed scheme has better detection performance compared with the energy detection techniques even in the case of a small sample of observations.展开更多
Spectrum sensing in a wideband regime for cognitive radio network(CRN) faces considerably technical challenge due to the constraints on analog-to-digital converters(ADCs).To solve this problem,an eigenvalue-based comp...Spectrum sensing in a wideband regime for cognitive radio network(CRN) faces considerably technical challenge due to the constraints on analog-to-digital converters(ADCs).To solve this problem,an eigenvalue-based compressive wideband spectrum sensing(ECWSS) scheme using random matrix theory(RMT) was proposed in this paper.The ECWSS directly utilized the compressive measurements based on compressive sampling(CS) theory to perform wideband spectrum sensing without requiring signal recovery,which could greatly reduce computational complexity and data acquisition burden.In the ECWSS,to alleviate the communication overhead of secondary user(SU),the sensors around SU carried out compressive sampling at the sub-Nyquist rate instead of SU.Furthermore,the exact probability density function of extreme eigenvalues was used to set the threshold.Theoretical analyses and simulation results show that compared with the existing eigenvalue-based sensing schemes,the ECWSS has much lower computational complexity and cost with no significant detection performance degradation.展开更多
The block H-matrices are studied by the concept of G-functions, several concepts of block matrices are introduced. Equivalent characters of block H-matrices are obtained. Spectrum localizations characterized by G-func...The block H-matrices are studied by the concept of G-functions, several concepts of block matrices are introduced. Equivalent characters of block H-matrices are obtained. Spectrum localizations characterized by G-functions for block matrices are got.展开更多
NaI(T1) scintillation detectors have been widely applied for gamma-ray spectrum measurements owing to advantages such as high detection efficiency and low price.However,the mitigation of the limited energy resolution ...NaI(T1) scintillation detectors have been widely applied for gamma-ray spectrum measurements owing to advantages such as high detection efficiency and low price.However,the mitigation of the limited energy resolution of these detectors,which detracts from an accurate analysis of the instrument spectra obtained,remains a crucial need.Based on the physical properties and spectrum formation processes of NaI(T1) scintillation detectors,the detector response to gamma photons with different energies is represented by photopeaks that are approximately Gaussian in shape with unique full-width-at-half-maximum(FWHM) values.The FWHM is established as a detector parameter based on resolution calibrations and is used in the construction of a general Gaussian response matrix,which is employed for the inverse decomposition of gamma spectra obtained from the detector.The Gold and Boosted Gold iterative algorithms are employed to accelerate the decomposition of the measured spectrum.Tests of the inverse decomposition method on multiple simulated overlapping peaks and on experimentally obtained U and Th radionuclide series spectra verify the practicability of the method,particularly in the low-energy region of the spectrum,providing for the accurate qualitative and quantitative analysis of radionuclides.展开更多
A method allowing a desirable matrix spectrum to be constructed as an alternative to the method using matrix transformation to the Frobenius form is stated. It can be applied to implement control algorithms for techni...A method allowing a desirable matrix spectrum to be constructed as an alternative to the method using matrix transformation to the Frobenius form is stated. It can be applied to implement control algorithms for technical systems without executing the variables transformation procedures that are needed for deriving a Frobenius matrix. The method can be used for simulation of systems with different spectrums for choosing an alternative that satisfies to the distinct demands.展开更多
The properties of the transfer-matrix of U(1) lattice gauge theory in the Fourier basis are explored.Among other statements it is shown:(i) the transfer-matrix is block-diagonal,(ii) all consisting vectors of a block ...The properties of the transfer-matrix of U(1) lattice gauge theory in the Fourier basis are explored.Among other statements it is shown:(i) the transfer-matrix is block-diagonal,(ii) all consisting vectors of a block are known based on an arbitrary block vector,(iii) the ground-state belongs to the zero-mode’s block.The emergence of maximum-points in matrix-elements as functions of the gauge coupling is clarified.Based on explicit expressions for the matrix-elements we present numerical results as tests of our statements.展开更多
The Na I(Tl) scintillation detector has a number of unique advantages, including wide use, high light yield,and its low price. It is difficult to obtain the decomposition of instrument response spectrum because of lim...The Na I(Tl) scintillation detector has a number of unique advantages, including wide use, high light yield,and its low price. It is difficult to obtain the decomposition of instrument response spectrum because of limitations associated with the Na I(Tl) scintillation detector's energy resolution. This paper, based on the physical process of c photons released from decay nuclides, generating an instrument response spectrum, uses the Monte Carlo method to simulate c photons with Na I(Tl) scintillation detector interaction. The Monte Carlo response matrix is established by different single energy γ-rays with detector effects. The Gold and the improved Boosted-Gold iterative algorithms have also been used in this paper to solve the response matrix parameters through decomposing tests,such as simulating a multi-characteristic energy c-ray spectrum and simulating synthesized overlapping peaks cray spectrum. An inversion decomposition of the c instrument response spectrum for measured samples(U series, Th series and U–Th mixed sources, among others)can be achieved under the response matrix. The decomposing spectrum can be better distinguished between the similar energy characteristic peaks, which improve the error levels of activity analysis caused by the overlapping peak with significant effects.展开更多
Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the f...Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the first attempt at calculating the energy spectrum for this potential, which was introduced by H. Bahlouli and A. D. Alhaidari and for which they obtained the “potential parameter spectrum”. Our results are also independently verified using a direct method of diagonalizing the Hamiltonian matrix in the J-matrix basis.展开更多
The correlation matrix, which is widely used in eigenvalue decomposition （EVD） or singular value decomposition （SVD）, usually can be denoted by R = E[yiy＇i]. A novel method for constructing the correlation matrix...The correlation matrix, which is widely used in eigenvalue decomposition （EVD） or singular value decomposition （SVD）, usually can be denoted by R = E[yiy＇i]. A novel method for constructing the correlation matrix R is proposed. The proposed algorithm can improve the resolving power of the signal eigenvalues and overcomes the shortcomings of the traditional subspace methods, which cannot be applied to low SNR. Then the proposed method is applied to the direct sequence spread spectrum （DSSS） signal＇s signature sequence estimation. The performance of the proposed algorithm is analyzed, and some illustrative simulation results are presented.展开更多
This paper studies the problem of suboptimal state-feedback H-two/H-infinity control of stochastic systems with spectrum constraint. Concretely speaking, a mixed suboptimal H-two/H-infinity controller synthesis togeth...This paper studies the problem of suboptimal state-feedback H-two/H-infinity control of stochastic systems with spectrum constraint. Concretely speaking, a mixed suboptimal H-two/H-infinity controller synthesis together with placing the spectrum into a strip region is considered, which is achieved via solving a convex optimization problem.展开更多
In cognitive radio networks, the spectrum utilization can be improved by cognitive users opportunistically using the idle channels licensed to the primary users. However, the new arrived cognitive users may not be abl...In cognitive radio networks, the spectrum utilization can be improved by cognitive users opportunistically using the idle channels licensed to the primary users. However, the new arrived cognitive users may not be able to use the channel immediately since the channel usage state is random. This will impose additional time delay for the cognitive users. Excessive waiting delay can make cognitive users miss the spectrum access chances. In this paper, a discrete-time Markov queuing model from a macro point of view is provided. Through the matrix-geometric solution theory, the average sojourn time for cognitive users in the steady state before accessing the spectrum is obtained. Given the tolerant delay of cognitive users, the macro-based throughput is derived and an access control mechanism is proposed. The numerical results show the effects of service completion probability on average sojourn time and throughput. It is confirmed that the throughput can be obviously improved by using the proposed access control mechanism. Finally, the performance evaluations based on users are compared to that based on data packets.展开更多
单主用户信号的出现主要引起多天线接收信号取样协方差矩阵中极值特征值的变化,而多主用户信号的出现则会同时扰动取样协方差矩阵极值特征值和其他特征值,此时,经典的极值特征值检测算法则会表现出次佳的检测性能。针对这一问题,本研究...单主用户信号的出现主要引起多天线接收信号取样协方差矩阵中极值特征值的变化,而多主用户信号的出现则会同时扰动取样协方差矩阵极值特征值和其他特征值,此时,经典的极值特征值检测算法则会表现出次佳的检测性能。针对这一问题,本研究设计了一种基于极值特征值差与特征值几何平均(difference of extreme eigenvalues and geometric average of eigenvalues,DEEGAE)的多主用户信号检测判决规则;提出了一种基于Wishart矩阵特征值统计分布理论的感知判决门限的闭式求解方法。该算法在频谱感知过程中直接利用认知用户的多天线接收数据构造判决规则并实施感知判决,具有全盲检测的优点;通过融合2种极限特征值门限分析结果,提高了非渐近感知条件下感知结果的准确性。Monte-Carlo仿真试验表明,新算法具有比经典的最大最小特征值之比算法和协方差绝对值检测算法更优的多主用户信号检测性能,同时能获得比传统基于最大最小特征值之差及其改进算法更为可靠的检测结果;与此同时,新算法的检测性能随着样本数目以及天线数目的增大而显著提升。展开更多
文摘A method is presented for calculating a matrix spectrum with a given set of eigenvalues. It can be used to build systems with different spectrums with the aim of choosing desired alternative. It enables a practical implementation of control algorithms without resorting to transformation of variables.
文摘This paper obtains a necessary and sufficient condition for an irreducible complex matrix whose comparison matrix is a singular M-matrix to be singular. This is used to establish a necessary and sufficient condition for a boundary point of Brualdi’s inclusion region of the eigenvalues of an irreducible complex matrix to be an eigenvalue.
基金Quality Engineering Project of Anhui Province,China(No.2017zhkt036)
文摘The spectral theory of graph is an important branch of graph theory,and the main part of this theory is the connection between the spectral properties and the structural properties,characterization of the structural properties of graphs.We discuss the problems about singularity,signature matrix and spectrum of mixed graphs.Without loss of generality,parallel edges and loops are permitted in mixed graphs.Let G1 and G2 be connected mixed graphs which are obtained from an underlying graph G.When G1 and G2 have the same singularity,the number of induced cycles in Gi(i=1,2)is l(l=1,l>1),the length of the smallest induced cycles is 1,2,at least 3.According to conclusions and mathematics induction,we find that the singularity of corresponding induced cycles in G1 and G2 are the same if and only if there exists a signature matrix D such that L(G2)=DTL(G1)D.D may be the product of some signature matrices.If L(G2)=D^TL(G1)D,G1 and G2 have the same spectrum.
基金Supported by the National Natural Science Foundation of China (No.60972039)Natural Science Foundation of Jiangsu Province (No.BK2007729)Natural Science Funding of Jiangsu Province (No.06KJA51001)
文摘Random Matrix Theory (RMT) is a valuable tool for describing the asymptotic behavior of multiple systems,especially for large matrices. In this paper,using asymptotic random matrix theory,a new cooperative Multiple-Input Multiple-Output (MIMO) scheme for spectrum sensing is proposed,which shows how asymptotic free property of random matrices and the property of Wishart distribution can be used to assist spectrum sensing for Cognitive Radios (CRs). Simulations over Rayleigh fading and AWGN channels demonstrate the proposed scheme has better detection performance compared with the energy detection techniques even in the case of a small sample of observations.
基金National Natural Science Foundations of China(Nos.61201161,61271335)Postdoctoral Science Foundation of Jiangsu Province of China(No.1301002B)
文摘Spectrum sensing in a wideband regime for cognitive radio network(CRN) faces considerably technical challenge due to the constraints on analog-to-digital converters(ADCs).To solve this problem,an eigenvalue-based compressive wideband spectrum sensing(ECWSS) scheme using random matrix theory(RMT) was proposed in this paper.The ECWSS directly utilized the compressive measurements based on compressive sampling(CS) theory to perform wideband spectrum sensing without requiring signal recovery,which could greatly reduce computational complexity and data acquisition burden.In the ECWSS,to alleviate the communication overhead of secondary user(SU),the sensors around SU carried out compressive sampling at the sub-Nyquist rate instead of SU.Furthermore,the exact probability density function of extreme eigenvalues was used to set the threshold.Theoretical analyses and simulation results show that compared with the existing eigenvalue-based sensing schemes,the ECWSS has much lower computational complexity and cost with no significant detection performance degradation.
文摘The block H-matrices are studied by the concept of G-functions, several concepts of block matrices are introduced. Equivalent characters of block H-matrices are obtained. Spectrum localizations characterized by G-functions for block matrices are got.
基金supported by the National Natural Science Foundation of China(Grant No.11365001)National Major Scientific Equipment Development Projects(Grant No.041514065)+2 种基金the Educational Commission of Jiangxi Province of China(Grant No.GJJ13464)Plan of Science and Technology of Jiangxi Province(Grant No.20141BBE50024)the Fundamental Science on Radioactive Geology and Exploration Technology Laboratory,East China Institute of Technology(Grant No.RGET1316)
文摘NaI(T1) scintillation detectors have been widely applied for gamma-ray spectrum measurements owing to advantages such as high detection efficiency and low price.However,the mitigation of the limited energy resolution of these detectors,which detracts from an accurate analysis of the instrument spectra obtained,remains a crucial need.Based on the physical properties and spectrum formation processes of NaI(T1) scintillation detectors,the detector response to gamma photons with different energies is represented by photopeaks that are approximately Gaussian in shape with unique full-width-at-half-maximum(FWHM) values.The FWHM is established as a detector parameter based on resolution calibrations and is used in the construction of a general Gaussian response matrix,which is employed for the inverse decomposition of gamma spectra obtained from the detector.The Gold and Boosted Gold iterative algorithms are employed to accelerate the decomposition of the measured spectrum.Tests of the inverse decomposition method on multiple simulated overlapping peaks and on experimentally obtained U and Th radionuclide series spectra verify the practicability of the method,particularly in the low-energy region of the spectrum,providing for the accurate qualitative and quantitative analysis of radionuclides.
文摘A method allowing a desirable matrix spectrum to be constructed as an alternative to the method using matrix transformation to the Frobenius form is stated. It can be applied to implement control algorithms for technical systems without executing the variables transformation procedures that are needed for deriving a Frobenius matrix. The method can be used for simulation of systems with different spectrums for choosing an alternative that satisfies to the distinct demands.
基金Supported by the Research Council of the Alzahra University
文摘The properties of the transfer-matrix of U(1) lattice gauge theory in the Fourier basis are explored.Among other statements it is shown:(i) the transfer-matrix is block-diagonal,(ii) all consisting vectors of a block are known based on an arbitrary block vector,(iii) the ground-state belongs to the zero-mode’s block.The emergence of maximum-points in matrix-elements as functions of the gauge coupling is clarified.Based on explicit expressions for the matrix-elements we present numerical results as tests of our statements.
基金supported by National Natural Science Foundation of China(No.11365001)National Major Scientific Equipment Development Projects(No.041514065)+1 种基金Natural Science Foundation of Jiangxi(No.20161BAB201035)Fundamental Science on Radioactive Geology and Exploration Technology Laboratory,East China Institute of Technology(No.RGET1316)
文摘The Na I(Tl) scintillation detector has a number of unique advantages, including wide use, high light yield,and its low price. It is difficult to obtain the decomposition of instrument response spectrum because of limitations associated with the Na I(Tl) scintillation detector's energy resolution. This paper, based on the physical process of c photons released from decay nuclides, generating an instrument response spectrum, uses the Monte Carlo method to simulate c photons with Na I(Tl) scintillation detector interaction. The Monte Carlo response matrix is established by different single energy γ-rays with detector effects. The Gold and the improved Boosted-Gold iterative algorithms have also been used in this paper to solve the response matrix parameters through decomposing tests,such as simulating a multi-characteristic energy c-ray spectrum and simulating synthesized overlapping peaks cray spectrum. An inversion decomposition of the c instrument response spectrum for measured samples(U series, Th series and U–Th mixed sources, among others)can be achieved under the response matrix. The decomposing spectrum can be better distinguished between the similar energy characteristic peaks, which improve the error levels of activity analysis caused by the overlapping peak with significant effects.
文摘Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the first attempt at calculating the energy spectrum for this potential, which was introduced by H. Bahlouli and A. D. Alhaidari and for which they obtained the “potential parameter spectrum”. Our results are also independently verified using a direct method of diagonalizing the Hamiltonian matrix in the J-matrix basis.
文摘The correlation matrix, which is widely used in eigenvalue decomposition （EVD） or singular value decomposition （SVD）, usually can be denoted by R = E[yiy＇i]. A novel method for constructing the correlation matrix R is proposed. The proposed algorithm can improve the resolving power of the signal eigenvalues and overcomes the shortcomings of the traditional subspace methods, which cannot be applied to low SNR. Then the proposed method is applied to the direct sequence spread spectrum （DSSS） signal＇s signature sequence estimation. The performance of the proposed algorithm is analyzed, and some illustrative simulation results are presented.
基金the National Natural Science Foundation of China (No.60174001)Beijing Education Community (No.290122)Specialized Research Fund for the Doctoral Program of Higher Education (No.20050424002)
文摘This paper studies the problem of suboptimal state-feedback H-two/H-infinity control of stochastic systems with spectrum constraint. Concretely speaking, a mixed suboptimal H-two/H-infinity controller synthesis together with placing the spectrum into a strip region is considered, which is achieved via solving a convex optimization problem.
文摘In cognitive radio networks, the spectrum utilization can be improved by cognitive users opportunistically using the idle channels licensed to the primary users. However, the new arrived cognitive users may not be able to use the channel immediately since the channel usage state is random. This will impose additional time delay for the cognitive users. Excessive waiting delay can make cognitive users miss the spectrum access chances. In this paper, a discrete-time Markov queuing model from a macro point of view is provided. Through the matrix-geometric solution theory, the average sojourn time for cognitive users in the steady state before accessing the spectrum is obtained. Given the tolerant delay of cognitive users, the macro-based throughput is derived and an access control mechanism is proposed. The numerical results show the effects of service completion probability on average sojourn time and throughput. It is confirmed that the throughput can be obviously improved by using the proposed access control mechanism. Finally, the performance evaluations based on users are compared to that based on data packets.
文摘单主用户信号的出现主要引起多天线接收信号取样协方差矩阵中极值特征值的变化,而多主用户信号的出现则会同时扰动取样协方差矩阵极值特征值和其他特征值,此时,经典的极值特征值检测算法则会表现出次佳的检测性能。针对这一问题,本研究设计了一种基于极值特征值差与特征值几何平均(difference of extreme eigenvalues and geometric average of eigenvalues,DEEGAE)的多主用户信号检测判决规则;提出了一种基于Wishart矩阵特征值统计分布理论的感知判决门限的闭式求解方法。该算法在频谱感知过程中直接利用认知用户的多天线接收数据构造判决规则并实施感知判决,具有全盲检测的优点;通过融合2种极限特征值门限分析结果,提高了非渐近感知条件下感知结果的准确性。Monte-Carlo仿真试验表明,新算法具有比经典的最大最小特征值之比算法和协方差绝对值检测算法更优的多主用户信号检测性能,同时能获得比传统基于最大最小特征值之差及其改进算法更为可靠的检测结果;与此同时,新算法的检测性能随着样本数目以及天线数目的增大而显著提升。
