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.     

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.     

分析无限平面金属栅电磁散射问题的一种新方法

本文基于直线法和Floquet定理提出了一种分析无限平面金属栅周期结构电磁散射问题的新方法。数值结果与谱域法结果和实验结果一致,但本文方法具有数学模型简单,计算量小等优点。     

Millimeter Wave Scattering of 2-D Frequency Selective Surface by Efficient Method of Lines with Preconditioned CG Technique

In this paper, both banded and symmetric successive overrelaxation (SSOR) preconditioned conjugate gradient (PCG) techniques are combined with method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. The electromagnetic wave scattering of 2-D frequency-selective surface is used as the examples to describe its implementation, whose analysis usually needs fast algorithms because of electrically large dimension. For arbitrary incident wave, helmholtz equation and boundary condition are used to calculate the impedance matrix and then to obtain reduced current-voltage linear matrix equation in spatial domain. Both banded and effective symmetric successive overrelaxation preconditioned conjugate gradient iterative method are chosen to solve this matrix equation. Our numerical results show that PCG methods can converge to accurate solution in much fewer iteration steps for analysis of the electromagnetic wave scattering from 2-D frequency-selective surface.     

Application of Robust Incomplete Cholesky Factorizations Preconditioned CG Algorithms for FEM Analysis of Millimeter Wave Filters

The Incomplete Cholesky factorizations preconditioning scheme is applied to the conjugate gradient (CG) method for solving a large system of linear equations resulting from finite element method (FEM) analysis of millimeter wave filters. As is well known, the convergence of CG method deteriorates with increasing EM wave number and in millimeter wave band the eigen-values of A are more and more scattered between both the right and the left half-plane. The efficient implementation of this preconditioned CG (PCG) algorithm is described in details for Complex coefficient matrix. With incomplete factorization preconditioning scheme in the conjugate gradient algorithm, this PCG approach can reach convergence in 20 times CPU time shorter than CG for several typical millimeter wave structures.     

Application of Preconditioned GMRES Algorithm for Analysis of Millimeter Wave Ferrite Sphere Circulators

The generalized minimal residual (GMRES) iterative method is applied to solve such sparse large non-symmetric system of linear equations resulting from the use of edge-based finite element method. In order to speed up the convergence of GMRES, the symmetric successive overrelaxation (SSOR) preconditioning scheme is applied for the analysis of millimeter wave ferrite circulator. Consequently, this preconditioned GMRES (PGMRES) approach can reach convergence ten times faster than GMRES. The reflection and insertion losses of millimeter wave waveguide circulator are compared with those obtained from literature.     

Application of Preconditioned GMRES Algorithm for Analysis of Millimeter Wave Ferrite Sphere Circulators

The generalized minimal residual (GMRES) iterative method is applied to solve such sparse large non-symmetric system of linear equations resulting from the use of edge-based finite element method. In order to speed up the convergence of GMRES, the symmetric successive overrelaxation (SSOR) preconditioning scheme is applied for the analysis of millimeter wave ferrite circulator. Consequently, this preconditioned GMRES (PGMRES) approach can reach convergence 19 times faster than GMRES. The isolation and insertion losses of millimeter wave waveguide circulator are compared with those obtained from literature.     

An Efficient MAINV Preconditioned COCG Method for FEM Analysis of Millimeter Wave Filters

The modified AINV (MAINV) sparse approximate inverse preconditioner is applied to the conjugate orthogonal conjugate gradient (COCG) iterative method for solving a large systems of linear equations resulting from the use of edge finite element method (FEM). The proposed preconditioner is derived from basic AINV process by adding pivots compensation strategy to avoid the potential breakdowns. Numerical experiments on several typical millimeter wave structrues demonstrate the effectiveness of the MAINV-COCG method, in comparison with other conventional methods.     

Currents Induced by a Plane Wave on an Infinite Wire above a Flat Earth

A general formula for the currents induced in an infinitely long perfectly conducting wire above a finitely conducting ground plane is derived. The effects produced by multiple scattering from e the ground are discussed and are shown to be significant.     

均匀圆球对平面波的散射

本文给出均匀圆球对平面波散射的详细推导，散射场系数与散射角函数的递推公式，散射场与各种截面的计算步骤，特例与应用实例。它全面，完整，实用地论述了Ｍｉｅ理论。     

On Multiple Scattering of Radiation by an Infinite Grating of Dielectric Circular Cylinders at Oblique Incidence

A rigorous analytical representation for the multiple scattering coefficients of the fields radiated by an infinite grating of dielectric circular cylinders excited by an obliquely incident plane electromagnetic wave is derived in terms of the “well-known scattering coefficients of an isolated dielectric cylinder at oblique incidence” and “Schlömilch series”. In addition, a generalized sum-integral grating equation is acquired for the multiple scattered amplitude of a cylinder at oblique incidence in the grating in terms of the scattering coefficients of the insulating dielectric circular cylinder at oblique incidence.     

一种用于毫米波雷达目标的成象与识别算法

针对宽带高距离分辨率全极化雷达工作的体制背景,分析和研究了在该体制下,雷达目标散射信号模型、高分辨率谱估计成象算法以及在此基础上相应雷达二维图象的特征提取与目标识别,构造了一种由雷达成象、特征提取以及目标识别组成的先进自动雷达目标图象识别系统,最后,归纳了雷达目标散射特性与识别的关系。     

A Spectral Multigrid Method Combined With MLFMM for Solving Electromagnetic Wave Scattering Problems

A new spectral multigrid method (SMG) combined with the multilevel fast multipole method (MLFMM) is proposed for solving electromagnetic wave scattering problems. The MLFMM is used to speed up the matrix-vector product operations and the SMG is employed to accelerate the convergence rate of the Krylov iteration. Unlike traditional algebraic multigrid methods (AMG), the spectral multigrid method is an algebraic two-grid cycle built on a preconditioned Krylov iterative method that is used as the smoother, and the grid transfer operators are defined using the spectral information of the preconditioned matrix. Numerical experiments indicate that this class of multigrid method is very effective with the MLFMM and can reduce both the iteration number and the overall simulation time significantly.     

一种实用的毫米波大规模MIMO混合预编码算法

数字模拟混合预编码可以用较少的射频逼近全数字预编码的性能,可以用来解决毫米波大规模MIMO系统中由于射频链路过多造成的硬件损耗和校准问题。为解决传统混合预编码结构难以实现的缺点,该文的混合预编码研究基于一种简单的固定子连接结构。推导了系统可达速率最大,模拟预编码矩阵应满足的条件,从而将混合预编码矩阵设计问题转化为优化问题。采用鸟群算法(BSA)解决此优化问题,求得最优的预编码矩阵。针对模拟移相器分辨率有限的情况,提出一种直接量化的解决方案和一种基于改进的离散BSA的解决方案。仿真结果表明,所提算法能够基于简单结构实现较好的性能;移相器分辨率有限情况下,所提的两种解决方案都是有效的,且基于离散BSA的方案在分辨率较低时性能更优。     

Analytic Analysis of Transient Scattering From a Finite Second-Order Surface Illuminated by an Incident Plane Wave

A closed-form analytic solution based on a time-domain (TD) physical optics (PO) approximation is developed for the scattering from a finite second-order surface when illuminated by a transient impulsive plane wave. This TD-PO solution can be applied via a convolution to derive the early time transient fields scattered from the same scatterer that is illuminated by a realistic astigmatic finite-energy pulse. The closed form TD-PO solution is obtained by inverting the corresponding frequency-domain PO solution into TD. This solution can be expressed in terms of reflection and diffraction components of the scattering mechanisms as in other conventional high-frequency asymptotic solutions. Numerical examples are presented to demonstrate its physical phenomenon of the scattering mechanisms.     

The Optical Design of Relay Optics for Heterodyne Millimeter Wave Focal Plane Arrays

Since the use of focal plane arrays on millimeter and sub-millimeter telescopes has become more and more important during the last years, it has also become evident the need of optimized auxiliary optics that would efficiently couple the telescope to the receiver over large fields of view (i.e., ?5-10 beams). In this work we systematically analyze several relay optics configurations for heterodyne focal plane arrays, all based on the “Gaussian beam telescope” concept. Because in examining the image performance of auxiliary optics design at millimeter wavelengths one cannot follow the usual image quality criteria, we analyze the designs using both the Strehl ratio and the coupling efficiency to evaluate the quality of the off-axis wave-fronts and the loss in the power coupling with the horn. Coupling efficiency and Strehl ratio cannot be included in the optimization procedures of commercial optical modelling packages and we thus describe how to optimize the design using a customized algorithm. We show that the minimization of the appropriate error function can reduce the anamorphism of the exit pupil and reduce the loss in the horn coupling.     

Application of SSOR Preconditioning Technique to Method of Lines for Millimeter Wave Scattering

In this paper, symmetric successive overrelaxation (SSOR) preconditioned CG technique are introduced into method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. Millimeter wave scattering by an infinite plane metallic grating is used as the examples to describe its implementation, whose analysis usually needs fast algorithms because of electrically large dimension. For arbitrary incident wave, Helmholz equation and boundary condition are used to calculate the impedance matrix and then to obtain reduced current-voltage linear matrix equation in spatial domain. An effective symmetric successive overrelaxation preconditioned conjugate gradient iterative method, SSOR-PCG, is chosen to solve this matrix equation. With SSOR as the preconditioner as well as its efficient implementing in CG algorithm, PCG method can converge to accurate solution in much fewer iteration steps.     

Studies on Fast Algorithm for the Scattering of a Large Array of Waveguide-Fed Wide-Slot Antennas in Millimeter Wave Region

We present an effective numerical technique to characterize the scattering of wide-slot antennas fed by waveguides with arbitrary terminations in terms of the method of moment (MoM) and the mixed potential integral equation (MPIE). In particular, the precorrected-fast Fourier transform (P-FFT) eliminates the need to generate and store the usual square impedance matrix andthus leads to speed up the matrix-vector multiplication in the resultant system. This property makes the Rao-Wilton-Glisson (RWG) functions to be useful in simulating electrically large-scale problems. In addition, the scattering from the finite ground surfaces is accounted for in the total scattered field by using the method of equivalent edge currents. The numerical results are presented and compared with both the traditional method of moment results obtained using the entire-domain basis functions and the experimental results, to demonstrate the proposed method to be a good candidate for study on the scattering of arbitrary wide-slot large array.     

面向毫米波应用的一种改进的常数模盲均衡算法

本文面向毫米波零中频架构，针对毫米波系统信道时变性、环境敏感性，以及零中频载波同步性能等问题，对现有的盲均衡算法进行了理论分析，并对 CMA、MCMA 两种具备工程化意义的算法进行了仿真实验分析。结合毫米波大容量数据高速处理需求，给出了可硬件实现的并行处理方法。最后，针对 CMA 算法收敛后剩余误差较大的问题进行了改进，结合泄漏算法和高阶累积量思想提出了一种修正的 CMA 算法，在与传统 CMA 算法收敛速度相当的条件下降低了系统的码间干扰。