Hermite矩阵特征值新的相对扰动界

利用矩阵的Schur三角分解,研究了一类特殊矩阵的扰动问题,得到了Hermite矩阵特征值的扰动界,所得定理推广并彻底改进了以前的结论。     

分析对称微波结构的矩阵特征值方法

本文介绍了特征值和特征矢量的基本性质,以典型的微波网络为例说明特征值方法在微波网络分析中的应用。     

一种利用矩阵特征值的抗干扰算法

信号的自相关矩阵特征值反映每个方向的功率,不同特征值对应不同信号空间,通常在干扰存在的条件下,大特征值对应干扰信号子空间,小特征值对应信号子空间。去除大特征值所对应的干扰子空间就可以去除强干扰信号。基于此,文中提出了一种利用矩阵特征值的抗干扰算法,可以有效消除阻塞性与类单音的各种干扰,与常见的利用FFT进行陷波的算法处理相比,利用矩阵特征值进行抗干扰处理,具有计算量小,逻辑实现简单的优点,降低了抗干扰算法的复杂度。     

遗传算法在矩阵特征值求解中的应用

遗传算法进行全空间并行搜索,并将搜索重点集中于性能高的部分,从而使效率提高且不易陷入局部极小。具有固有的并行性,通过对种群的遗传处理可处理大量的模式,并且容易并行实现。重点研究遗传算法以及混合遗传算法在传统数学中的应用:解决矩阵特征值问题。通过大量的实验研究,证明遗传算法在传统数学的研究问题中有很高的应用价值。     

求解正定矩阵最小和最大特征值对应的特征矢量

本文给出实时求解正定矩阵最小和最大特征值对应特征矢量的神经网络模型。文中的理论分析和模拟结果表明：网络能在电路时常数数量给内给出所求的解，网络给出的解与准确的特征矢量可以任意接近。     

基于随机矩阵特征值比的频谱感知改进算法

针对认知无线电中现有频谱感知方法的不足,利用大维随机矩阵理论分析了随机矩阵的渐近谱特性,研究了接收信号样本协方差矩阵平均特征值的分布特性,提出两种基于随机矩阵特征值比的频谱感知改进算法.改进算法不需要知道主用户信号的先验信息,也不需要知道背景噪声的功率,得到的判决阈值也具有十分简单的闭式表达式.仿真结果表明,在低样本点、低协作用户数、低信噪比和低虚警概率的条件下,改进算法也可以获得很好的感知性能.     

有相对失调光学系统的增广矩阵

使用坐标变换和矩阵方法,推导出了有相对失调光学系统的4×4增广矩阵,并对此作了分析。证明无相对失调系统的4×4增广矩阵可由一般公式简单得出。     

基于Wishart矩阵特征值的频谱感知算法

为了提高频谱感知性能,克服经典算法的缺点,提出了一种新的基于Wishart随机矩阵理论的协作频谱感知算法.根据多个认知用户接收信号样本协方差矩阵特征值的对数分布特性,利用样本协方差矩阵最大特征值与几何平均特征值的比值,得到简单的判决阈值闭式表达式,实现频谱感知判决.该算法不需要知道主用户的任何先验信息,不受噪声不确定性的影响.仿真结果表明,所提算法在协作用户数少、信噪比低、采样点数极少的情况下,仍能获得较高的感知性能.该算法受虚警概率和极端值的影响较小,比同类算法有更好的检测性能.     

一种基于特征值分解的测量矩阵优化方法

测量矩阵是压缩感知中一个很重要的部分,为了减小测量矩阵与稀疏变换矩阵的互相干性,从而改善重建质量,本文首先通过测量矩阵和稀疏变换矩阵的乘积构造得到一个Gram矩阵,然后定义了一种基于Gram矩阵非对角线元素的整体互相干系数,推导出整体互相干系数与Gram矩阵特征值之间的关系。在此基础上,我们提出了一个最优化模型,在不改变Gram矩阵特征值和的前提下,让每个大于零的特征值的大小都为它们和的平均值,使得测量矩阵和稀疏变换矩阵的整体互相干系数达到最小,从而优化了测量矩阵的性能。将该方法用在一些已知的测量矩阵上,实验结果中矩阵的优化速度快,并且用优化矩阵所得的图像的PSNR有所提高,表明本文优化测量矩阵的方法在重建效果和优化速度方面都有一定的优势。      

关于BCH码的广义Hamming重量上,下限

一个线性码的第ｒ广义Ｈａｍｍｉｎｇ重量是它任意ｒ维子码的最小支集大小。本文给出了一般（本原、狭义）ＢＣＨ码的广义Ｈａｍｍｉｎｇ重量下限和一类ＢＣＨ码的广义Ｈａｍｍｉｎｇ重量上限     

Turbo码有效自由距离d2上限的证明

Turbo码是一种新的纠错码,具有十分突出的纠错能力。Turbo码编码器由两个或两个以上的分量码编码器和交织器并行级联而成。S.Benedetto和G.Montersi(1996)中提出了设计Turbo码的新参数有效自由距离d2(Effective Free Distance)。D.Divsalar和R.J.McEliece(1996)给出了有效自由距离的两个上限,但未给出证明。本文从理论上对d2的两个上限进行证明。     

Eigenvalues and Singular Value Decompositions of Reduced Biquaternion Matrices

In this paper, the algorithms for calculating the eigenvalues, the eigenvectors, and the singular value decompositions (SVD) of a reduced biquaternion (RB) matrix are developed. We use the SVD to approximate an RB matrix in the least square sense and define the pseudoinverse matrix of an RB matrix. Moreover, the RB SVD is employed to implement the SVD of a color image. The computational complexity for the SVD of an RB matrix is only one-fourth of that for the SVD of conventional quaternion matrices. Therefore, many useful image-processing methods using the SVD can be extended to a color image without separating the color image into three channels. The numbers of the eigenvalues of an $ntimes n$ RB matrix, the $n^{rm th}$ roots of an RB, and the zeros of an RB polynomial with degree $n$ are all finite and equal to $n^{2}$ , not infinite as those of conventional quaternions.      

Improved Performance Upper Bounds for Terminated Convolutional Codes

In this letter, we propose tight performance upper bounds for convolutional codes terminated with an input sequence of finite length. To obtain the upper bounds, a weight enumerator is defined to represent the relation between the Hamming distance of the coded output and the Hamming distance of the input bits of the code. The upper bounds on frame error rate (FER) and average bit error rate (BER) are obtained from the weight enumerator. A simple method is presented to compute the weight enumerator of a terminated convolutional code based on a modified trellis diagram.     

Eigenvectors and Eigenvalues of 1-D and n-D DFT Matrices

A simple and straightforward derivation of the eigenvectors of the DFT matrix is given. The multiplicity of each of the four eigenvalues of a two-dimensional DFT matrix is then supplied in closed form that is generalizable to higher dimensions.     

稀疏随机矩阵的观测次数下界

压缩感知理论中的稀疏重构问题,要将一个高维信号从它的低维投影中恢复出来,通常选用稠密随机矩阵作为观测矩阵来解决这一问题。而某些稀疏随机矩阵作为观测矩阵也可以达到这一目的。稀疏随机矩阵的特点是,在编码和重构过程中都具有较低的计算复杂度,更新方便,且对存储容量的要求较低。该文基于压缩感知理论,分别对列重固定、行重固定以及一般的稀疏随机矩阵进行了研究,当这些稀疏随机矩阵满足有限等距性质时,推导了观测次数应满足的下界条件,并对三种矩阵的性能进行了分析。以二值稀疏随机矩阵为特例,进行了仿真实验。实验结果显示,结论给出的观测次数下界是比较紧的,并验证了列重固定、行重固定的稀疏随机矩阵作为观测矩阵的可行性和实用性。      

Computation of Upper Bounds for the Solution of Continuous Algebraic Riccati Equations

This paper is considered with the computation of upper bounds for the solution of continuous algebraic Riccati equations (CARE). A parameterized upper bound for the solution of CARE is proposed by utilizing some linear algebraic techniques. Based on this bound, more precise estimation can be achieved by means of carefully choosing the bound’s parameters. Iterative algorithm is also developed to obtain more sharper solution bounds. Comparing with some existing results in the literature, the proposed bounds are less restrictive and more effective. The effectiveness and advantages of the proposed approach are illustrated via a numerical example.     

Upper Bounds on the Partial Correlation of PN Sequences

Upper bounds on the worst case autocorrelation and the worst case cross correlation of linear PN sequences of the same period are obtained. The value of the worst case correlation curve at some specific points is found and using interpolation methods a smooth curve fitting to the correlation curve is formulated.     

Joint Density for Eigenvalues of Two Correlated Complex Wishart Matrices: Characterization of MIMO Systems

In this letter, the joint probability density function (PDF) for the eigenvalues of a complex Wishart matrix and a perturbed version of it are derived. The latter version can be used to model channel estimation errors and variations over time or frequency. As an example, the joint PDF is used to calculate the transition probabilities between modulation states in an adaptive MIMO system. This leads to a Markov model for the system. We then use the model to investigate the modulation state entering rates (MSER), the average stay duration (ASD), and the effects of feedback delay on the accuracy of modulation state selection in mobile radio systems. Other applications of this PDF are also discussed.