一种MIMO-OFDM系统信道估计简化方法

提出了一种基于MMSE准则的MIMO-OFDM系统信道估计简化方法。该方法将信道估计问题转化为TBT线性方程求解问题,然后利用快速求解算法避免了复杂的矩阵求逆和矩阵相乘,大大降低了实现复杂度。仿真结果表明,相比于传统MMSE算法,该简化算法在降低复杂度的同时仅带来微弱的性能损失。     

基于LDL算法的大规模矩阵求逆加速器设计及其FPGA实现

矩阵求逆是工程计算中的基本问题，在大规模MIMO系统、阵列信号处理以及图像信号处理等应用中，大规模矩阵求逆的处理速度对系统性能至关重要，但传统矩阵求逆方法运算复杂度高、并行性低且消耗大量存储空间，不利于硬件加速。针对大规模矩阵求逆硬件加速问题，文中研究了基于LDL分解的矩阵求逆算法，并提出了一种基于该算法的大规模矩阵求逆加速架构。利用LDL分解后三角矩阵对角线元素全为1的特点，对矩阵进行分块迭代设计，减少了求逆运算的计算量，提高了计算速度。文中基于Xilinx Virtex7 FPGA设计实现了该加速器，实验结果表明，在128阶矩阵下，吞吐量达105.2 Inv·s^-1,最高时钟频率达200 MHz。与现有矩阵求逆加速方案相比，该设计占用的硬件资源更少，且具有更高的性能。     

线性方程的列初等变换求解算法

引入了任意（ｍ，ｎ）－矩阵的准下三角阵、最简准下三角阵和准标准形新概念，得到了用系数矩阵的列初等变换求基础解系的几个定理，适用于任意线性方程的求解定理，进而给出了计算机化求解算法和实用程序。纠正了文［１］等“只用列初等变换或用行、列初等交换不能解线性方程组”的错误结论。     

不完全非负矩阵分解的加速算法

非负矩阵分解(NMF)已成为数据分析与处理的一种日益流行的方法.当数据矩阵不完全时,可用加权非负矩阵分解(WNMF)来分解矩阵.但是在WNMF算法中,对于给定的搜索方向,步长的选取一般来说不是最优的.本文研究了不完全非负矩阵分解(INMF)问题,提出了加速算法(AINMF).首先,将INMF问题转化为交替地求解两个非负...     

改进的牛顿法确定大气消光系数边界值

在用激光雷达方程反演大气消光系数时,大气消光系数边界值对反演精度影响较大,而在低层大气中该值较难确定。文中提出了一种基于改进牛顿法的大气消光系数边界值确定方法,其核心思想是,把确定大气消光系数边界值的问题转化为求非线性方程的数值解。首先,根据大气消光系数边界值与激光雷达回波信号功率以及大气光学厚度之间的关系,假设大气消光系数边界值为x,构建一个非线性方程。其次,采用改进的牛顿法求非线性方程的数值解,得到大气消光系数边界值。使用香港天文台装置在香港国际机场的多普勒激光雷达回波信号数据,对该方法的可行性和可靠性进行了验证。结果表明:利用该方法确定边界值,可以较为准确地反演出低层大气消光系数。该方法收敛速度快,迭代次数少,并且不需要计算导数值,极大地减少了运算量,具有较强的实际应用价值。     

关于二阶线性微分方程的特色公式及其在无线电技术中的应用

本文应用连环术解的方法给出了求二阶常系数线性非齐次方程的一个特解公式。并把该公式推广到某些变系数的二阶线性方程中去，推出相应的求解公式，最后给出了在物理及无线电技术中应用的例子。     

非系统卷积码前馈逆及校验矩阵的求解法

本文从不变因子定理和线性自动机理论出发，给出了卷积码前馈逆的三种系统求法。在求逆的同时求出了校验矩阵，从而使非系统卷积码可用简单求逆电路恢复。也可利用校验矩阵是数逻辑译码，在高信噪比情况下有实际应用价值。     

一种基于约化因子上三角矩阵求逆的FPGA实现方法

矩阵运算广泛应用于实时性要求的各类电路中，其中矩阵求逆运算最难以实现。基于现场可编程门阵列(FPGA)实现矩阵求逆能够充分发挥硬件的速度与并行性优势，加速求逆运算过程。基于改进的脉动阵列的计算架构，采用一种约化因子求逆的优化算法，将任意一个n×n阶上三角矩阵转换成对角线为1的上三角矩阵，使得除法运算与乘加运算分离开来，大大简化矩阵求逆运算过程。以一个4×4阶上三角矩阵求逆为例，在Xilinx ISE平台下，采用Virtex5 FPGA完成算法实现与功能验证，在14个周期内，使用了2个除法器，3个乘法器与4个加法器实现整个矩阵求逆运算。相比于经典的脉动阵列架构，仅占用近一半资源的同时，性能提升了26.43%；相比于集成更多处理单元(PE)的脉动阵列实现方式，在性能近乎不变的情况下，耗费的资源缩减到1/4，大幅度提升了资源利用率。     

线性监督分类器的瓶颈与能力

本文研究了线性前馈网络用于监督分类的瓶颈问题，证明隐层节点数小于内间散布矩阵秩的所有网络，其隐层都可以实现前级模式的Ｆｉｓｈｅｒ线性变换，并揭示了这种分类器出现颈的原因和解决办法，最后，作为这种分类器能力探讨之一，提出了将其用于解决非奇异阵求逆问题，所给算例表明，所提线性求逆网络是非常有效的。     

非线性方程法确定低空探测机载激光雷达消光系数边界值

提出了机载激光雷达进行低空探测时确定消光系数边界值的非线性方程法。首先根据机载激光雷达方程推导出消光系数边界值与机载激光雷达回波信号之间的函数关系,构建一个以消光系数边界值为变量的非线性方程。然后采用改进Jarratt法求此非线性方程的数值解,得到消光系数边界值。使用地基激光雷达真实回波信号数据模拟得到的机载激光雷达回波信号,进行了实验验证,并与斜坡法进行了比较。结果表明,本方法确定边界值的相对误差比斜坡法减小5.9%,由于其具有六阶的收敛特性,迭代次数仅为3次。该方法不需辅助测量设备,精度较高,收敛速度快,迭代次数少,具有良好的应用前景。     

利用Thompson距离研究非线性矩阵方程

首先介绍Thompson距离的基本性质,在此基础上利用压缩原理来研究非线性矩阵方程X-A*X-1/2A=I。证明了矩阵方程有唯一的正定解。给出了一种求正定解的数值方法,同时指出了此算法的误差估计。     

PMD的统计特性及其对光脉冲传播的影响

由耦合非线性薛定谔方程可以得出与光纤参数有关的琼斯矩阵。文章采用此法得到的琼斯矩阵法研究了一阶偏振模色散(PMD)的统计特性,并通过求解耦合非线性薛定谔方程仿真了PMD对于光脉冲传输的影响。     

Explicit calculation of N-soliton solutions of the nonlinearSchroedinger equation

The method of inverse scattering is used to calculate N-soliton solutions of the nonlinear Schroedinger equation. The solution of the inverse problem is proposed as a simple matrix equation. The exact 3-soliton solution is calculated and a simple equation for the calculation of the power proposed     

Determination of the steady state of an oscillator by a combinedtime-frequency method

A novel method for the computation of the steady state of nonlinear oscillators including distributed elements is presented which exploits advantages of both time-domain and frequency-domain simulation. The oscillator network is divided into a linear subnetwork described by a hybrid matrix in the frequency domain and a nonlinear differential equation solved in the time domain. The periodic steady state of the oscillator is shown to be equivalent to the solution of a boundary value problem, where the boundary conditions are given at a set of points along the time axis. For the solution of the boundary value problem the multiple shooting algorithm is applied. It is shown that the bandwidth in the nonlinear subnetwork can be chosen arbitrarily high regardless of the number of harmonics at the ports connecting the subnetworks. In order to demonstrate the feasibility of the method and to discuss the error mechanisms it is applied to two examples: a Clapp oscillator including a piecewise-linear characteristic and an integrated GaAs MESFET oscillator at 10.7 GHz     

纯方位目标跟踪极坐标模型的状态空间变换方法

在纯方位目标跟踪定位研究领域里,采用极坐标模型,可以实现可观测状态和不可观测状态的分离,但非线性的系统方程使算法的具体实现非常困难。利用状态空间的变换,可避免直接计算非线性函数雅可比矩阵的值,减小了计算量,提高了滤波稳定性。     

对一类过滤生成器的攻击

为了对过滤生成器实施攻击,提出一种求解概率方程组的算法,此算法利用系数矩阵的逆矩阵选取概率方程组的解;然后分析一类支撑集具有特殊结构的过滤函数,得到一条间断序列,再结合求解概率方程组的算法对过滤生成器实施攻击.分析结论可知,得到的攻击方法具有较好的灵活性和可行性.     

Toward a More Robust and Accurate CEM Fast Integral Equation Solver for IC Applications

We review recent advances in fast algorithms for fast integral equation solvers that are useful for IC applications. We review fast solvers for Laplace's equation, which is about 10 times faster than the conventional fast multipole method. Then we review the physics of low-frequency electromagnetics, and the relevant low-frequency method of moments. We describe a fast solver that allows us to solve over one million unknowns on a workstation recently. In addition, we demonstrate the applications of these fast integral equation solvers to the lithography problem. In addition, we propose a scheme whereby we first characterize blocks of linear circuits with network S, Y, or Z parameters. Then a fast real-time convolution scheme is used to calculate the interaction of a linear circuit with nonlinear terminations such as transistors and diodes. Such a scheme requires no model-order reduction of the circuits.     

Exciton enhancement effect on the third harmonic generation in ZnS/CdSe quantum dot quantum well

Exciton enhancement effect on the third-order optical nonlinearities of a ZnS/CdSe quantum dot quantum well (QDQW) has been theoretically studied. The wave functions and eigenenergies of excitons in QDQW have been calculated under the effective-mass approximation. By solving a three-dimensional nonlinear Schrödinger equation and by means of compact density matrix method, the third-order nonlinear susceptibilities for third-harmonic generation (THG) have been calculated in a two energy levels model of QDQW. Firstly, we studied the size effect on THG in QDQW. Then we compared the value of THG with the case that only considering electron states. The results show that the THG is greatly enhanced when compared with the condition just considering electron states.     

A priori bound for optimal stochastic control problem with multiplicative noise

An easy-to-evaluate lower bound on the spectral norm of the solution to a nonlinear matrix equation arising in control of linear systems with state and control dependent noise is found. The result enables one to speculate as to the magnitude of the solution matrix.     

Investigation of the mathematical properties of a new negative resistance oscillator model

A new negative resistance oscillator model was proposed by Walker and Connelly. We investigate the mathematical properties of the associated nonlinear differential equation for a single-mode LCR network oscillator. In particular, we prove that under suitable conditions, small-amplitude stable limit-cycle oscillations can occur. The method of harmonic balance is used to calculate an analytic approximation to the limit-cycle parameters. Also, the general properties of trajectories in phase-space are presented. These predictions are compared with the results obtained by numerical integration of the differential equation.This research was supported in part by ARO.