Computation of the inverse Hessian matrix using conjugate gradient methods

A method is presented to compute the inverse of the Hessian matrix in an optimization problem using the conjugate gradient algorithm of Hestenes and Stiefel [1]. It is shown how this may be used to refine the solution by a Newton-Raphson iteration for both finite and infinite dimensional optimization problems.     

Propagation modeling over terrain using the parabolic wave equation

We address the numerical solution of the parabolic wave equation over terrain using the Fourier/split-step approach. The method, referred to as a shift map, generalizes that of Beilis and Tappert (1979) who introduced a coordinate transformation technique to flatten the boundary. This technique is extended to a wide-angle form, allowing larger propagation angles with respect to the horizon. A new impedance boundary condition is derived for electromagnetic waves incident on a finitely conducting surface that enables solution of the parabolic wave (PWE) using the previously developed mixed Fourier transform. It is also shown by example that in many cases of interest, the boundary may be approximated by discrete piecewise linear segments without affecting the field solution. A more accurate shift map solution of the PWE for a piecewise linear boundary is, therefore, developed for modeling propagation over digitally sampled terrain data. The shift-map solution is applied to various surface types, including ramps, wedges, curved obstacles, and actual terrain. Where possible, comparisons are made between the numerical solution and an exact analytical form. The examples demonstrate that the shift map performs well for surface slopes as large as 10-15° and discontinuous slope changes on the order of 15-20°. To accommodate a larger range of slopes, it is suggested that the most viable solution for general terrain modeling is a hybrid of the shift map with the well-known terrain masking (knife-edge diffraction) approximation     

Image modeling using inverse filtering criteria with application totextures

Statistical approaches to image modeling have largely relied upon random models that characterize the 2-D process in terms of its first- and second-order statistics, and therefore cannot completely capture phase properties of random fields that are non-Gaussian. This constrains the parameters of noncausal image models to be symmetric and, therefore, the underlying random field to be spatially reversible. Research indicates that this assumption may not be always valid for texture images. In this paper, higher- than second-order statistics are used to derive and implement two classes of inverse filtering criteria for parameter estimation of asymmetric noncausal autoregressive moving-average (ARMA) image models with known orders. Contrary to existing approaches, FIR inverse filters are employed and image models with zeros on the unit bicircle can be handled. One of the criteria defines the smallest set of cumulant lags necessary for identifiability of these models to date, Consistency of these estimators is established, and their performance is evaluated with Monte Carlo simulations as well as texture classification and synthesis experiments.     

Inverse scattering: solution of coupled Gel'fand-Levitan-Marchenkointegral equations using successive kernel approximations

We develop a method of successive kernel approximations to solve coupled Gel'fand-Levitan-Marchenko (1955) integral equations. These equations appear in the synthesis problem of nonuniform and lossy transmission lines, the inversion of absorbing dielectrics and wavenumber-dependent potentials, the design of corrugated waveguide filters, soliton theory, and other applications. We find that our method is easy to apply, more accurate than previously developed methods, and can be used for a larger number of applications when compared to prior work. As an application and example, wavenumber-dependent potentials are reconstructed from scattering data     

Direct synthesis of microwave filters using inverse scatteringtransmission-line matrix method

This paper proposes a new design procedure for planar microwave filters based on the inversion of the one-dimensional transmission-line matrix (TLM) method. The essence of the technique is the solution of the inverse scattering problem using a TLM-based algorithm instead of using equivalent circuits. The procedure consists of determining the geometry of the obstacle that generates the desired scattered field. In the case of filters, this field is the time-domain input reflection coefficient, and the geometry is the impedance profile of the filter. The procedure was validated with the design of low-pass and bandstop filters. It can be used to create filters with arbitrary characteristics     

Broad-band horn-antenna launchers modeling by FDTD and generalized scattering matrix methods

Printed launchers are currently used to feed millimeter broad-band horn antennas. A time-domain procedure, based on the finite-difference time-domain method, is proposed to achieve an accurate model of the launching section. A scattering matrix approach is followed and unidirectional time-domain modal sources are developed for efficient generation of port modes.     

Stable matrix inverse method for array DF using trapezoidal factorisation

An approach to finding the inverse of the covariance matrix required for DF using maximum-likelihood methods (MLM) is to factorise the matrix into LD (lower triangular-diagonal) form. An alternative factorisation, trapezoidal-diagonal (TD) is outlined which is both more stable and, for a small number of signals, more economical.     

Finite element modeling and multigrid preconditioner using adaptive triangular meshes

The letter describes a finite element method (FEM) using adaptive triangular meshes for the modeling of microwave devices. A robust preconditioning technique is provided for the fast solution of the resultant FEM matrix equations. The proposed preconditioner is based on a multigrid scheme for the vector-scalar potential FE formulation of the electromagnetic problem. Numerical experiments demonstrate its superior numerical convergence.     

Numerical analysis of small parabolic antennas using the method of current and change integral equations

The method of current and charge integral equations [1] is applied to numerical electrodynamic analysis of radiation and impedance matching characteristics of parabolic antennas with reflector diameter from 0.5 to 10λ. As a result as opposed to the current method relying on physical optics approximation the influence of feed on reflector’s radiation pattern, the influence of reflector on feed’s impedance matching and the contribution of feed’s rear radiation into reflector’s radiation pattern are all accounted for. A new model of representing a parabolic surface in the form of its square approximation is suggested, which provides almost uniform partitioning grid and has at least 2.5 times less boundary elements that the common revolution surface representation while having the same sampling coefficient. Dependences of antenna’s directivity on reflector dimensions (0.5–10λ) are calculated for six different focus distance to reflector’s diameter ratios using the developed by the authors crystal_U software package. The calculated results are confirmed by good matching with well-known experimental results.     

The inverse of a block-circulant matrix

The inverseA^{-1}of a block-circulant matrix (BCM)Ais given in a closed form, by using the fact that a BCM is a combination of permutation matrices, whose eigenvalues and eigenvectors are found with the help of the complex roots of unity. Special results are also given whenAis block symmetric or symmetric.     

基于像素与子块的背景建模级联算法

针对子块级背景建模方法无法保证所提取前景形状的精确性及像素级背景建模方法无法有效处理非平稳场景的问题,提出了一种背景建模分层模型,首先采用文中子块级建模算法得到较为粗糙的背景区域和前景区域,然后利用混合高斯模型对特定图像区域执行像素级的前景提纯或背景模型更新操作,2种不同层次的算法通过非对称前向反馈机制进行级联。实验结果表明,所提分层模型在能够有效处理非平稳场景的同时保证了所提取前景形状的精确性,且对光照突变不敏感,建模效果优于级联算法中任一独立算法,而处理时间小于2种独立算法处理时间之和,满足了实时处理要求。     

一种圆抛物面天线的有限元分析

应用有限元分析软件ANSYS5．7对一种复合材料圆抛物面天线进行分析计算，确保设计的产品满足使用要求。     

传递矩阵法研究高斯光束经逆抛物型梯度折射率纤维的准直特性

本文采用传递矩阵法研究了高斯光束在一种逆抛物型梯度折射率纤维中的传播规律,得出光斑半径、波面曲率半径与矩阵元之间的关系式。基于此,讨论了这种逆抛物型梯度折射率激光准直元件的原理。     

Numerical modeling of generalized millimeter-wave transmission media with finite element and transmission line matrix methods

In this paper, a general finite element method as well as a graded-mesh TLM procedure for determining the dispersion characteristics, field distribution, pseudo-impedance and losses of generalized millimeter-wave transmission media are described. These methods cover arbitrary cross-sections and account for realistic features (finite metallization thickness, substrate mounting grooves etc.) that are often neglected in theoretical analysis. Dispersion characteristics and characteristic impedances obtained for dielectrically loaded ridged wave-guides compare well with the available data. Conductor and dielectric losses are also computed for these structures. A modified finline structure called “ridged finline” is also analysed. The main advantages of this structure are its large monomode bandwidth and reduced dispersion. The cutoff frequencies of bilateral finlines in circular waveguides are also computed.     

Time-domain wavelet Galerkin modeling of two-dimensionalelectrically large dielectric waveguides

The time-domain wavelet-Galerkin method based on Daubechies' compactly supported scaling functions of high regularity has been applied to the analysis of two-dimensional dielectric slab waveguides that have typical dimensions and material parameters of optical integrated waveguide components, and the results are compared with those obtained with the conventional finite-difference time-domain method. It has been found that the proposed method allows discretization with a much coarser grid than the conventional time-domain analysis techniques due to its local sampling and highly linear numerical dispersion properties. A series of numerical experiments demonstrates the capability of the method to simulate the wave propagation of electrically large inhomogeneous media with reduced computational expenditure     

Design of reduced-rank MMSE multiuser detectors using random matrix methods

Reduced-rank minimum mean-squared error (MMSE) multiuser detectors using asymptotic weights have been shown to reduce receiver complexity while maintaining good performance in long-sequence code-division multiple-access (CDMA) systems. In this paper, we consider the design of reduced-rank MMSE receivers in a general framework which includes fading, single and multiantenna receivers, as well as direct-sequence CDMA (DS-CDMA) and multicarrier CDMA (both uplink and downlink). In all these cases, random matrix results are used to obtain explicit expressions for the asymptotic eigenvalue moments of the interference autocorrelation matrix and for the asymptotic weights used in the reduced-rank receiver.     

一种基于Cholesky分解的快速矩阵求逆方法设计

接收机阵列天线抗干扰可采用直接矩阵求逆的方法实现,但在大维数下,矩阵求逆的用时过长。本文针对协方差矩阵的特殊性—正定赫米特矩阵,采用Cholesky分解求逆方法实现大维数矩阵的求逆,进而对Cholesky矩阵分解求逆进行了高效的流水设计,并在FPGA中进行实现,测试结果表明,该方法实现求逆计算用时极短,是一种高效的实现方法。     

基于滑动平均和逆抛物方程的目标定位法

应用逆抛物方程法进行有源目标定位时,传播空间中的背景散射体会产生高强度的杂波,从而导致其定位精度下降或失效.针对这一问题,使用自适应滑动平均算法进行有效信号提取,研究了不规则地形和不均匀大气媒质环境中的目标定位问题,分析了定位误差和定位门限的选取.通过对离散化的回波数据进行处理,利用运动目标和背景杂波的非相干特性进行信号提取和杂波抑制.仿真结果表明:该方法与逆抛物方程定位算法相比,改善了目标位置的信号聚焦程度和信干噪比.