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
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
首先研究了两个线性关系矩阵的乘积等于它们形式乘积的条件,在此基础上得到了线性关系矩阵L_(0)-μI=(A-μI B C D-μI)的Frobenius-Schur分解;其次利用Frobenius-Schur分解,讨论了L_(0)-μI和它的Schur补在单射情况、值域的稠密性以及...首先研究了两个线性关系矩阵的乘积等于它们形式乘积的条件,在此基础上得到了线性关系矩阵L_(0)-μI=(A-μI B C D-μI)的Frobenius-Schur分解;其次利用Frobenius-Schur分解,讨论了L_(0)-μI和它的Schur补在单射情况、值域的稠密性以及逆关系有界性之间的联系;最后刻画了L_(0)的点谱、剩余谱和连续谱。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。
文摘首先研究了两个线性关系矩阵的乘积等于它们形式乘积的条件,在此基础上得到了线性关系矩阵L_(0)-μI=(A-μI B C D-μI)的Frobenius-Schur分解;其次利用Frobenius-Schur分解,讨论了L_(0)-μI和它的Schur补在单射情况、值域的稠密性以及逆关系有界性之间的联系;最后刻画了L_(0)的点谱、剩余谱和连续谱。
