该文针对非等功率信号波达方向(DOA)估计问题,提出一种基于噪声子空间特征值重构(Eigenvalue Reconstruction of Noise Subspace,ERNS)的超分辨算法。算法对接收信号自相关矩阵进行特征值分解,通过重构噪声空间特征值以及引入虚拟信源...该文针对非等功率信号波达方向(DOA)估计问题,提出一种基于噪声子空间特征值重构(Eigenvalue Reconstruction of Noise Subspace,ERNS)的超分辨算法。算法对接收信号自相关矩阵进行特征值分解,通过重构噪声空间特征值以及引入虚拟信源来构造新的接收信号自相关矩阵,对该矩阵进行特征值分解得到新的噪声空间特征值。当虚拟信源与实际信源入射方向相同时,新噪声空间特征值与重构后噪声空间特征值保持不变,利用这一特性来估计信源入射方向。该文给出算法的原理及实现步骤,并通过仿真进行原理验证与性能分析,仿真结果表明与其他子空间算法和MUSIC算法相比,ERNS算法能够提高弱信号估计成功的概率。展开更多
针对数字通信信号的信噪比盲估计问题,提出了一种基于子空间理论的盲信噪比估计方法。该方法首先根据信号自相关序列构建特定维数的信号自相关矩阵,并根据实际工程应用需求,利用坐标旋转数字计算(Coordinate rotation digital computer,...针对数字通信信号的信噪比盲估计问题,提出了一种基于子空间理论的盲信噪比估计方法。该方法首先根据信号自相关序列构建特定维数的信号自相关矩阵,并根据实际工程应用需求,利用坐标旋转数字计算(Coordinate rotation digital computer,CORDIC)算法实现Jacobi旋转来完成自相关矩阵的特征值分解,避免了实际实现时对硬件乘法器的调用。并以6种常用的数字通信信号为例,在加性高斯白噪声(AWGN)信道条件下,实际信噪比在-10～30dB范围内时对其信噪比估计性能进行仿真分析。仿真表明,当实际信噪比为-5～22dB时,信噪比估计标准偏差小于0.5dB,且提出的信噪比估计器具有渐近无偏特性,证明了该方法是一种进行盲信噪比估计的有效方法。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
We consider a Hamiltonian of a system of two fermions on a three-dimensional lattice Z<sup>3</sup> with special potential <img alt="" src="Edit_56564354-6d65-4104-9126-d4657fa750af.png&qu...We consider a Hamiltonian of a system of two fermions on a three-dimensional lattice Z<sup>3</sup> with special potential <img alt="" src="Edit_56564354-6d65-4104-9126-d4657fa750af.png" />. The corresponding Shrödinger operator <em>H</em>(<strong>k</strong>) of the system has an invariant subspac <span style="white-space:nowrap;"><span><em>L</em></span><sup>-</sup><sub style="margin-left:-10px;">123</sub>(T<sup>3</sup>)</span> , where we study the eigenvalues and eigenfunctions of its restriction <span style="white-space:nowrap;"><span><em>H</em></span><sup>-</sup><sub style="margin-left:-10px;">123</sub></span><span style="white-space:nowrap;">(<strong>k</strong>)</span>. Moreover, there are shown that <span style="white-space:nowrap;"><span><em>H</em></span><sup>-</sup><sub style="margin-left:-10px;">123</sub>(<em>k</em><sub>1</sub>, <em>k</em><sub>2</sub>, π)</span> has also infinitely many invariant subspaces <img alt="" src="Edit_4955ffad-4b18-434a-8c99-ff14779f2812.bmp" />, where the eigenvalues and eigenfunctions of eigenvalue problem <img alt="" src="Edit_01b218d2-fa3e-4f39-bc2d-ce736205db93.bmp" />are explicitly found.展开更多
We propose a quadratically convergent algorithm for computing the invariant subspaces of an Hermitian matrix. Each iteration of the algorithm consists of one matrix-matrix multiplication and one QR decomposition. We p...We propose a quadratically convergent algorithm for computing the invariant subspaces of an Hermitian matrix. Each iteration of the algorithm consists of one matrix-matrix multiplication and one QR decomposition. We present an accurate convergence analysis of the algorithm without using the big O notation. We also propose a general framework based on implicit rational transformations which allows us to make connections with several existing algorithms and to derive classes of extensions to our basic algorithm with faster convergence rates. Several numerical examples are given which compare some aspects of the existing algorithms and the new algorithms.展开更多
Let A be a C~*-algebra and x an element in A. the following invariant subspace problem is considered: Does there exist an irreducible representation π of A such that π(x) has a non-trivial invarint subspace? And a p...Let A be a C~*-algebra and x an element in A. the following invariant subspace problem is considered: Does there exist an irreducible representation π of A such that π(x) has a non-trivial invarint subspace? And a positive solution of the problem for finite separable matroid C~*-algebras is given. Also the eigenvalues Of elements in C~*-algebras is considered. Some versions of Fredholm Alternatives are given.展开更多
文摘该文针对非等功率信号波达方向(DOA)估计问题,提出一种基于噪声子空间特征值重构(Eigenvalue Reconstruction of Noise Subspace,ERNS)的超分辨算法。算法对接收信号自相关矩阵进行特征值分解,通过重构噪声空间特征值以及引入虚拟信源来构造新的接收信号自相关矩阵,对该矩阵进行特征值分解得到新的噪声空间特征值。当虚拟信源与实际信源入射方向相同时,新噪声空间特征值与重构后噪声空间特征值保持不变,利用这一特性来估计信源入射方向。该文给出算法的原理及实现步骤,并通过仿真进行原理验证与性能分析,仿真结果表明与其他子空间算法和MUSIC算法相比,ERNS算法能够提高弱信号估计成功的概率。
文摘针对数字通信信号的信噪比盲估计问题,提出了一种基于子空间理论的盲信噪比估计方法。该方法首先根据信号自相关序列构建特定维数的信号自相关矩阵,并根据实际工程应用需求,利用坐标旋转数字计算(Coordinate rotation digital computer,CORDIC)算法实现Jacobi旋转来完成自相关矩阵的特征值分解,避免了实际实现时对硬件乘法器的调用。并以6种常用的数字通信信号为例,在加性高斯白噪声(AWGN)信道条件下,实际信噪比在-10～30dB范围内时对其信噪比估计性能进行仿真分析。仿真表明,当实际信噪比为-5～22dB时,信噪比估计标准偏差小于0.5dB,且提出的信噪比估计器具有渐近无偏特性,证明了该方法是一种进行盲信噪比估计的有效方法。
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.
文摘We consider a Hamiltonian of a system of two fermions on a three-dimensional lattice Z<sup>3</sup> with special potential <img alt="" src="Edit_56564354-6d65-4104-9126-d4657fa750af.png" />. The corresponding Shrödinger operator <em>H</em>(<strong>k</strong>) of the system has an invariant subspac <span style="white-space:nowrap;"><span><em>L</em></span><sup>-</sup><sub style="margin-left:-10px;">123</sub>(T<sup>3</sup>)</span> , where we study the eigenvalues and eigenfunctions of its restriction <span style="white-space:nowrap;"><span><em>H</em></span><sup>-</sup><sub style="margin-left:-10px;">123</sub></span><span style="white-space:nowrap;">(<strong>k</strong>)</span>. Moreover, there are shown that <span style="white-space:nowrap;"><span><em>H</em></span><sup>-</sup><sub style="margin-left:-10px;">123</sub>(<em>k</em><sub>1</sub>, <em>k</em><sub>2</sub>, π)</span> has also infinitely many invariant subspaces <img alt="" src="Edit_4955ffad-4b18-434a-8c99-ff14779f2812.bmp" />, where the eigenvalues and eigenfunctions of eigenvalue problem <img alt="" src="Edit_01b218d2-fa3e-4f39-bc2d-ce736205db93.bmp" />are explicitly found.
文摘We propose a quadratically convergent algorithm for computing the invariant subspaces of an Hermitian matrix. Each iteration of the algorithm consists of one matrix-matrix multiplication and one QR decomposition. We present an accurate convergence analysis of the algorithm without using the big O notation. We also propose a general framework based on implicit rational transformations which allows us to make connections with several existing algorithms and to derive classes of extensions to our basic algorithm with faster convergence rates. Several numerical examples are given which compare some aspects of the existing algorithms and the new algorithms.
文摘Let A be a C~*-algebra and x an element in A. the following invariant subspace problem is considered: Does there exist an irreducible representation π of A such that π(x) has a non-trivial invarint subspace? And a positive solution of the problem for finite separable matroid C~*-algebras is given. Also the eigenvalues Of elements in C~*-algebras is considered. Some versions of Fredholm Alternatives are given.
