A systematic design formulation for Butler matrix applied FFT algorithm

A systematic general design formulation for a Butler matrix (Bmatrix) is described. TheBmatrix design problem discussed is used to determine phase shift location and value in a matrix, when the number of beam (elements of array)M = 2^{N}and the scattering matrix for the hybrid couplers are specified. The design formulation presented is based on the fact that aBmatrix design procedure and an FFT algorithm are equivalent in fundamental concepts. It is shown that theBmatrix design procedure can be systematically formulated by the FFT algorithm modifications, which preserves the topological properties of the original signal flow diagram. A simple design formula has been established by this formulation.     

Analysis of Millimeter Wave Scattering by the Infinite Plane Metallic Grating Using PCG-FFT Technique

In this paper, both fast Fourier transformation (FFT) and preconditioned CG technique are introduced into method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. Electromagnetic wave scattering by an infinite plane metallic grating is used as the examples to describe its implementation. For arbitrary incident wave, Helmholz equation and boundary condition are first transformed into new ones so that the impedance matrix elements are calculated by FFT technique. As a result, this Topelitz impedance matrix only requires O(N) memory storage for the conjugate gradient FFT method to solve the current distribution with the computational complexity O(N log N) . Our numerical results show that circulate matrix preconditioner can speed up CG-FFT method to converge in much smaller CPU time than the banded matrix preconditioner.     

GIM 技术在二维介质散射中的应用*

如何利用散射体的几何对称性,使各种矩阵方法求解电磁散射问题所需的存储量和计算时间减少,是当前计算电磁学领域中具有理论和实际意义的重要课题.本文针对谐振频段的TM波对介质柱体的散射问题,采用矩阵方法与GIM(广义镜像法)技术相结合的算法,通过构造虚拟的对称源与反对称源和运用叠加定理,成功地将原问题的求解转化为只在其1/4的边界上进行求解,由此达到了减少矩阵元和节约运算时间的目的.通过理论分析和具体算例的检验,并与MOM计算结果比较,证实了该方法在节约计算时间方面有显著优势.     

Fast algorithm for electromagnetic scattering by buried conductingplates of large size

This letter presents a fast algorithm for electromagnetic scattering by buried conducting plates of large size and arbitrary shape using the conjugate gradient (CG) method combined with the fast Fourier transform (FFT). Due to the use of FFT in handling the cyclic convolutions related to Toeplitz matrices, the Sommerfeld integrals' evaluation for the buried scattering problem, which is usually time consuming, has been reduced to a minimum. The memory required for this algorithm is of the order N-the number of unknowns-and the computational complexity is of order N_iterNlogN (N_iter is the iteration number N_iter≪N for large problems)     

基于紧致字典的基追踪方法在SAR图像超分辨中的应用

基追踪方法是信号稀疏表示领域的一种新方法.它寻求从超完备的基集合(字典)中得到信号的最稀疏的表示,即用尽可能少的基尽可能精确地表示原信号,从而获得信号的内在本质特性.本文将基追踪方法的应用扩展到SAR(Synthetic Aperture Radar)图像的超分辨问题上来.首先在相位历史域依据SAR目标属性散射模型构造了一类紧致字典,从而大大减小了所求解问题的维数,其次设计了一种新的迭代算法进行快速求解,得到SAR图像中各散射中心位置和幅度的高精度估计,最后依据相位历史域SAR目标属性散射模型,生成更大尺度的相位历史数据,对生成的相位历史数据成像即得到更高分辨率的SAR图像.仿真算例和MSTAR实测数据计算表明,基于紧致字典的基追踪方法能够快速稳定实现,同时具有良好的超分辨性能.     

运动目标的时分极化测量研究

运动目标极化特性的测量是极化雷达探测与目标识别等领域非常关心的基础性问题。该文针对时分极化测量雷达,建立了动目标的瞬时极化测量模型。在深入分析目标极化回波的基础上,针对互易性目标,提出了一种基于交叉极化分量相位对齐的散射矩阵校准方法。研究结果表明在一定信噪比条件下,该测量和校准方法可以有效地消除因目标运动而导致的散射矩阵两列元素去相关。     

Block Diagonalization of the Electromagnetic Impedance Matrix of a Symmetric Buried Body Using Group Theory

A major problem with the volume-current integral-equation technique of three-dimensional electromagnetic modeling is the computational time and-storage required to form and solve the impedance matrix equation for the scattering currents. If the horizontal cross sections of a body with vertical sides all possess a certain symmetry, the matrix contains information about the effect of the symmetry on the scattering currents. This information can be deduced easily using group representation theory independent of any numerical computation or particular incident field geometry, and the original matrix, containing redundant informnation, can be replaced by a block-diagonal matrix. A straightforward example is used to illustrate this general technique. The computer storage requirements and solution time for the block-diagonalized matrix equation are significantly smaller than those for the original matrix equation.     

An Effective Multigrid Preconditioned CG Algorithm for Millimeter Wave Scattering by an Infinite Plane Metallic Grating

An effective multigrid based preconditioned conjugate gradient method is developed to solve electromagnetic large matrix problem for millimeter wave scattering application. By using multigrid technique we restrict the large matrix equation to a relative smaller matrix and which can be solved rapidly. The solution is prolonged as the initial guess for the conjugate gradient (CG) method. Numerical results show that our developed method can reach five times improvement of computational complexity.     

Complementary operators: a method to annihilate artificialreflections arising from the truncation of the computational domain inthe solution of partial differential equations

The ease and simplicity with which the finite difference time domain (FDTD) or the finite elements (FE) techniques can handle complex radiation or scattering problems have lead to a remarkable surge in the use of these methods. While execution time is becoming less of an impediment when solving large problems, the biggest constraint remains the memory needed to run the FDTD or the FE methods. It is precisely this limitation that the article addresses. A boundary operation is developed to minimize the artificial reflections that arise when truncating the computational domain of an open region scattering or radiation problem. The method is based on the use of two boundary operators that are complementary in their action. By solving the problem with each of the two operators and then averaging the two solutions, the first-order reflections that arise from the artificial boundary can be completely eliminated. Numerical results are presented to show that this new technique gives significant reduction in the error when compared to other widely used boundary conditions     

On the use of Fourier series/FFT's as global basis functions in thesolution of boundary integral equations for EM scattering

Current methods for the solution of the surface integral equations of interest to practical electromagnetic scattering appear to have reached an impasse. Plagued by disputes concerning the suitability and performance of various competing choices for piecewise basis functions and facing horribly complicated piecewise quadratures for the construction of influence matrix elements, it has become quite commonplace for these methods to be matrix-build-time limited rather than matrix-solve-time limited. An extremely simple alternative to all this is described below and demonstrated, in an introductory sense, on some 2-D problems. In this procedure, the FFT method, the basis functions are all global Fourier series in a suitably chosen parameter, and one attempts to estimate the coefficients describing the unknown surface current directly from the integral equation. This format circumvents all of the shortcomings discussed above-there are no singular integrals to evaluate. Furthermore, since the FFT algorithm is used throughout, the computation is extremely efficient. The results shown below suggest that, so far, this approach is very effective     

Analysis of Millimeter Wave Scattering by an Electrically Large Metallic Grating Using Wavelet-Based Algebraic Multigrid Preconditioned CG Method

An effective wavelet based multigrid preconditioned conjugate gradient method is developed to solve electromagnetic large matrix problem for millimeter wave scattering application. By using wavelet transformation we restrict the large matrix equation to a relative smaller matrix and which can be solved rapidly. The solution is prolonged as the new improvement for the conjugate gradient (CG) method. Numerical results show that our developed wavelet based multigrid preconditioned CG method can reach large improvement of computational complexity. Due to the automaticity of wavelet transformation, this method is potential to be a block box solver without physical background.     

A Spectral Domain Integral Equation Method Utilizing Analytically Derived Characteristic Basis Functions for the Scattering From Large Faceted Objects

A novel technique, based on a spectral domain integral equation method with analytically derived characteristic basis functions, is introduced in this paper. It enables us to treat scattering problems from electrically large faceted bodies in a numerically rigorous and computationally efficient manner, in terms of both time and memory. The analytically derived characteristic basis functions include certain desirable features of the asymptotic schemes and are defined on subdomains that can be electrically large, not being bound to the typical discretization size of the conventional method of moments. By properly weighting through a Galerkin procedure the resulting electric field integral equation, the problem is reduced to a matrix equation having dimensions that do not depend on the size of the scatterer but only on its shape. Electrically large problems can be handled in a computationally efficient manner by using the proposed method since the associated matrix size is relatively small; moreover, all the reduced matrix elements are calculated in the spectral domain without evaluating any convolution products.     

目标电磁散射极点的不变性特征分析

对频域磁场积分方程在离散化的基础上进行了矢量分析，发现离散化后的矩阵方程中含有频率因子的算子矩阵仅包含了反映散射体形状的矢量信息，从而得出极点的分布只依赖于目标的外部形状信息这一结论；然后利用FDTD进行了仿真研究，从不同姿态角(散射方向)的后时响应数据中提取了极点，结果保持了较好的一致，进一步证实了目标姿态角的改变不会影响极点的分布这一特征。     

A systematic treatment of conducting and dielectric bodies witharbitrarily thick or thin features using the method of moments

A systematic procedure for modeling electromagnetic scattering problems involving bodies with electrically thin features is discussed. The scattering bodies are represented using standard surface integral equation formulations and solutions are obtained via the method of moments (MOM). It is demonstrated that accurate evaluation of the moment matrix elements is critical for obtaining accurate solutions for scatterers having thin features. It is also shown (by numerical example) that some of the various surface integral formulations remain valid and can be used to obtain accurate scattering results for arbitrarily thin dielectric and conducting features. The use of the systematic approach for such problems is illustrated by incorporating the procedures into a two-dimensional (MOM) program. Sample results illustrating the technique's utility and validity are provided     

多重网格技术与波恩迭代法 相结合的反演新方法

本文将多重网格技术与波恩迭代法(BIM)相结合,利用时域散射数据对二维无耗非均匀介质剖面进行了反演.在反演迭代过程中,待反演目标区域的离散网格由粗逐渐变细.由于在反演的初期,目标区域离散网格较粗,离散反演积分方程所得到的矩阵方程的维数较小、条件数较低,使得该方法具有稳定性好、更容易收敛到真解的特点.通过反演实例表明,该方法极大地降低了反演过程的计算量,与传统的BIM方法相比能更精确地反演高对比度的散射目标.更为重要的是本文方法简单可行、可以与其它任何反演方法相结合.     

电大尺寸物体电磁辐射与散射特性几种分析方法的比较研究

在一定的规则剖分下，矩量法中的系数矩阵为Ｔｏｅｐｌｉｔｚ矩阵或多重Ｔｏｅｐｌｉｔｚ矩阵。利用这一特征而提出的共轭梯度（ＣＧＭ）和快速付里叶变换（ＦＦＴ）算法已成为目前国际上分析电大尺寸问题的一种有效手段。虽然ＣＧＭ—ＦＦＴ将普通矩量法中正比于Ｎ２（Ｎ为系数矩阵的阶数）的存储量压缩为正比于Ｎ的存储量，但其迭代算法使所花ＣＰＵ时间仍与普通矩量法相当。本文采用基于递推的Ｌｉｖｅｎｓｏｎ算法和一种库软件处理同样的问题，所花ＣＰＵ时间和普通矩量法相比降低两个量级，而且存储量比ＣＧＭ—ＦＦＴ技术还要小。本文以直导线的辐射和散射问题为例介绍了几种算法的基本原理，并对他们的计算时间和存储空间等进行了比较研究，得出了一些重要结论。     

A multilevel matrix decomposition algorithm for analyzingscattering from large structures

A multilevel algorithm is presented for analyzing scattering from electrically large surfaces. The algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics. The algorithm permits a fast matrix-vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks, with each describing the interaction between distant scatterers. The multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast Fourier transform (FFT) and that only relies on well-known algebraic techniques. The computational complexity and the memory requirements of the proposed algorithm are O(N log² N)     

The three-dimensional algorithm of solving the electric fieldintegral equation using face-centered node points, conjugate gradientmethod, and FFT

It has been known for a long time that the accuracy of solving the scattering by a dielectric body using the electric field integral equation (EFIE) is poor when the permittivity of the scatterer becomes large. Recently, this problem has been settled by using a procedure involving face-centered node points. Such a procedure is efficient, since it preserves the convolution property in the EFIE and, hence, the applicability of the fast Fourier transform (FFT). This procedure is generalized to the three-dimensional and anisotropic case. The generalization is quite straightforward in both the formulation and the programming. A calculation for a scatterer with a relative permittivity as high as 100 indicates that the proposed procedure converges quite rapidly, whereas the conventional using the conjugate gradient method approach fails to converge     

The principle of speckle filtering in polarimetric SAR imagery

The principle of speckle reduction in polarimetry is reconsidered. It is shown that polarimetric data can be speckle reduced if and only if all the elements of the Mueller matrix are filtered, which is equivalent to filtering the scattering vector covariance matrix. Assuming that speckle is multiplicative and stationary, the algorithms proposed by S.L.Lee et al. (1991) and S.Goze et al. (1993) are extended to filter the covariance matrix of reciprocal and nonreciprocal targets on one-look and multilook images. The problem of estimation of the first- and second-order statistics of the four-channel speckle vector is discussed, and a solution is proposed for one-look and multilook images     

介质柱电磁极化散射的计算和分析

本文首次给出柱形体的一种有价值的极化散射矩阵Ｓ,定义,Ｓ,具有六个自由度,它包含了柱形体散射的所有信息,并给出计算平行极化ＲＣＳ的垂直极化ＲＣＳ等公式。从Ｓｓ也易于导出线极化基极化散射矩阵Ｓｔ和圆极化基极化散射矩阵Ｓｃ等。在此基础上本文将ＭｏＭ－ＣＧＭ－ＦＦＴ混降低了所需计算机内存和ＣＰＵ,提高了计算效率。本文以介质板柱体的极化散射为例进行了计算,所得结果与理论结果与及其它文献中的精确结果进行比较