广义逆矩阵在OFDM系统信道估计中的应用

介绍了矩阵知识在计算卷积中的应用、广义逆矩阵的概念以及应用广义逆矩阵在OFDM系统中进行时域信道估计的方法,并对此方法进行了仿真。在仿真结果的基础上对时域信道估计方法和频域信道估计方法作了定性的评估。总结了广义逆矩阵进行时域信道估计的优缺点。     

一种基于拟牛顿法的CS投影矩阵优化算法

压缩感知(Compressed Sensing,CS)理论中,投影矩阵优化是一类通过提高观测数据信息量而改善性能的方法.由于投影矩阵与稀疏字典内积构造的Gram矩阵必定奇异,基于广义逆矩阵求解方法存在计算精度的问题.本文提出了一种利用拟牛顿法的CS投影矩阵优化算法.该算法分为两步:一是利用阈值函数约束Gram矩阵非对角线元素,使投影矩阵与稀疏字典的互相关系数逼近Welch界;二是采用秩2校正得到Hessian阵逆近似去修正梯度搜索方向.两个步骤交替执行,直到解出符合优化要求的投影矩阵.该算法始终保持下降性,具有超线性收敛速度,避免了矩阵函数二阶导数复杂的计算,计算量较小.实验结果表明,当信号稀疏度或观测数据相同时,本文算法的重构结果优于其他算法.     

泛延拓矩阵的QR分解

考虑泛延拓矩阵的QR分解与广义逆,导出了泛延拓矩阵的QR分解与广义逆的公式,讨论了系统参数估计问题.结果显示所给方法既减少了计算量与存储量,又不会降低数值精度.同时推广和优化了文献[8,9]的研究结果,拓宽了实际应用领域的范围.     

低复杂度大规模MIMO信号检测算法研究

原有的信号检测算法ZF(迫零)和MMSE(最小均方误差)不可避免地要对矩阵求逆,但是大规模MIMO中天线数量可能是上百根,复杂度随着天线数量呈指数增加,所以在大规模MIMO系统中直接对矩阵求逆任何机器都无法承担的。因此在不损失性能的前提下,提出一种通过迭代计算对矩阵近似求逆的方法来取代传统的矩阵精确求逆,从而起到算法复杂度降低的效果。     

基于边界像素的模糊模型复原研究

针对水平方向匀速直线运动模糊一般模型进行复原时存在明显周期干扰的问题,从分析边缘像素的角度出发,提出了基于零边界像素的复原模型和基于Neumann边界像素的复原模型,有效的减轻了周期干扰.通过广义逆矩阵进行运动模糊图像的复原,从实验结果来看,本文的复原方法简单可行,并具有较好的复原效果.     

频变交叉耦合带通滤波器的耦合矩阵综合研究

综合代表滤波器拓扑结构和特性的耦合矩阵是交叉耦合滤波器设计的重点。提出了一种基于广义特征值的优化综合方法,通过非线性最小二次求解,将耦合矩阵的广义特征值逼近至广义切比雪夫响应多项式传输函数零极值参考点,优化求解出带有频变交叉耦合带通滤波器的耦合矩阵。通过3个数值实例演示了该方法,并验证其有效性。这是对经典带通滤波器耦合矩阵综合方法的补充,为频变交叉耦合滤波器的设计建立了基础。     

用于MIMO-OFDM系统信号检测的简化V-BLAST方法

V-BLAST是一种用于MIMO-OFDM系统的有效检测方法,但具有较大的计算复杂度.基于MIMO-OFDM系统相邻子载波信道矩阵的充分接近这一特性,本文提出了一种简化V-BLAST方法.在该方法中,系统先对一些子载波信道进行常规V-BLAST检测,然后将由这些检测计算出的信道矩阵的广义逆用于其相邻子载波信道矩阵广义逆的近似计算,从而相当程度地降低了MIMO-OFDM系统进行V-BLAST检测的计算量.简化V-BLAST与常规V-BLAST检测性能比较的仿真实验结果显示,简化V-BLAST方法在相当程度地降低了计算时间的同时取得了非常接近于常规V-BLAST检测的误码性能.     

开关电容网络（SCN）广义节点方程的直接形成

本文提出一种形态含独立电压源、ＶＣＶＳ、零极子、开关、电容的多相周期性ＳＣＮ广义节点议程的有效算法，该算法利用ＳＣＮ每个相位定义的两个向量，直接形成具有最低维数的ＳＣＮ广义节点方程的矩阵，而不需在高阶矩阵求逆后形成ＳＣＮ节点方程，或利用矩阵行列运算形成ＳＣＮ广义节点方程，具有较低的时空复杂度。     

广义传输矩阵

本文在广义逆矩阵的基础上定义了一类广义传输矩阵,推导出散射矩阵与该矩阵之间的变换式,并指出该矩阵在分析一般多端口(非2m端口)网络的广义级联时的优越性和局限性。     

对基于广义逆矩阵密钥协商协议及其改进的攻击

E.Dawson和Chuan-KuanWu在文献犤1犦中提出了基于广义逆矩阵的密钥协商方案。王永传等、雷信生、王锦玲分别在文献犤2犦、犤3犦、犤4犦中对其作了补充、攻击、改进。笔者对以上方案提出一种攻击方法,指出基于广义逆矩阵的以上密钥协商方案是不安全的,同时给出建议。     

On matrix integrators for real-time simulation

A matrix integration method is generalized to systems with zero eigenvalues. It is shown that the regression coefficients of the integrator can be determined without explicitly computing the inverse of the system Jacobian. This is done by transforming the original system into a new system whose Jacobian is in block upper triangular form. A numerical example is included for illustrative purposes     

An inverse problem for line and strip sources of electromagnetic field above an imperfectly conducting ground plane

An analytic method of solving the inverse problem of determining the optimal excitation of line and strip sources of electromagnetic fields generating given directional functions above an imperfectly conducting ground plane is presented. The method used is based upon algebraization of the problem. The overdetermined system of equations obtained is solved by the method of generalized matrix inverse and the method of regularization of Tikhonov. An error estimate, criteria for the choice of parameters, and an experimental procedure are given. Numerical examples related to airborne radionavigation illustrate the application of the theory.     

On the use of SVD-improved point matching in the current-modelmethod [EM scattering]

An approach which uses the singular value decomposition (SVD) to improve the accuracy of the numerical solution obtained with fictitious current models is introduced. In this approach, the SVD is essentially facilitating a systematic way to optimally reduce the generalized inverse matrix used in the solution to a submatrix of smaller rank. This reduction strikes a balance between the fulfillment of the boundary conditions at the matching points and that between them. Clearly, the boundary conditions errors at the matching points are no longer strictly zero. However, the previously discernible errors between the matching points are markedly suppressed. The approach is efficacious not only when the impedance matrix is inherently singular or highly ill conditioned, but also when this matrix is entirely well conditioned. It can be generalized and implemented in any method of moments code which uses point matching for testing. The approach has been incorporated into an existing solution based on the current-model method for the problem of scattering from periodic sinusoidal surfaces, and is shown to render the solution more accurate     

基于矩阵变换的图像置乱逆问题求解

 基于矩阵变换的图像置乱用周期性对图像恢复,代价高昂;而通过逆变换恢复,已有方法未解决 Z _N上逆阵求解问题.针对此问题,通过构造映射规则,将伴随矩阵求逆方法推广到 Z _N,解决了n维矩阵变换的逆问题.为减小该方法计算代价,将杜里特尔分解和克劳特分解求逆推广到 Z _N,解决了变换阵顺阶主子式模N互质,矩阵变换的逆问题.为弱化扩展杜里特尔分解和克劳特分解求逆条件,将高斯-约当消去法推广到 Z _N,给出了任意变换阵在 Z _N上求逆算法和简化求逆算法.所提方法可用于得到任意变换阵在 Z _N上的逆变换阵,从而可直接对图像恢复,而不必计算可恢复周期.实验表明所提方法的可行性和有效性.     

基于神经网络广义逆两电机同步控制研究

基于神经网络广义逆系统,提出二自由度的内模控制。来改善两电机同步系统的解耦控制性能和鲁棒性能。提出先对原来系统的数学模型进行广义逆的存在性分析,进而推出原系统广义逆的数学模型,再用神经网络逼近广义逆,接在原系统前组成具有等价效果的伪线性系统,来实现系统的解耦线性化。有利于系统的综合。然后对广义伪线性系统引入二自由度内模控制,以保证系统的鲁棒稳定性。     

MIMO OFDM排序判决反馈检测方法

一般多天线系统的判决反馈检测方法中,是顺序检测每用户天线端接收信号,其缺点是若从前面若干幅接收天线检测出的信号误差较大,则会降低后续天线端检测性能.为解决该问题,本文提出一种排序判决反馈检测方法,其思想先对待检测的用户天线支路排序,利用计算预测误差获得的待检测天线支路对应信道逆阵向量是已检测天线支路对应信道逆阵向量的线性组合特征,应用正交变换求解获得用户天线支路的检测顺序,使当前待检测用户天线端的迫零向量与已检测用户天线支路的迫零向量正交,这样可使由已检测用户天线支路带来的判决反馈误差最小,进而提高了检测性能.     

Complete Gabor transformation for signal representation

Properties of the Gabor transformation used for image representation are discussed. The properties can be expressed in matrix notation, and the complete Gabor coefficients can be found by multiplying the inverse of the Gabor (1946) matrix and the signal vector. The Gabor matrix can be decomposed into the product of a sparse constant complex matrix and another sparse matrix that depends only on the window function. A fast algorithm is suggested to compute the inverse of the window function matrix, enabling discrete signals to be transformed into generalized nonorthogonal Gabor representations efficiently. A comparison is made between this method and the analytical method. The relation between the window function matrix and the biorthogonal functions is demonstrated. A numerical computation method for the biorthogonal functions is proposed.     

The effects of errors in assumed conductivities and geometry onnumerical solutions to the inverse problem of electrocardiography

Here, the authors used a previously proposed model problem to examine the effects of inhomogeneities on four techniques for numerically solving the inverse problem of electrocardiography. The layered inhomogeneous eccentric spheres system contains three regions representing the lungs, muscle, and subcutaneous fat, and is numerically modeled using finite elements. The authors simulated both anterior and posterior spherical cap activation fronts. They examined inverse solutions based on zero order Tikhonov regularization, truncated singular value decomposition, their new generalized eigensystem approach, and a modification of the generalized eigensystem approach. The effects on the inverse solutions of geometrical errors, errors in the assumed conductivities, and homogeneous torso assumptions were examined     

严重拖尾复合高斯杂波中目标的自适应极化检测

该文研究极化高分辨雷达在动态变化的杂波场景中自适应检测小目标的问题.将统计特性严重拖尾的杂波建模为纹理分量为逆伽马分布的复合高斯过程,借助于广义似然比检验和辅助数据得到了自适应极化检测器,并推导了该检测器的虚警概率表达式,证明了该检测器对协方差矩阵结构具有恒虚警特性.最后,利用仿真杂波数据验证了检测器检测性能的有效性.