A higher order FDTD method for EM propagation in a collisionlesscold plasma

A fourth-order in time and space, finite-difference time-domain (FDTD) scheme is presented for radio-wave propagation in a lossless cold plasma. As with previously reported fourth-order schemes, the methodology is founded on the principle that correction derivatives (i.e., three derivatives in time) can be converted into vector spatial derivatives. From the error analysis and phase-velocity data, it is argued that this approach will significantly minimize the dispersion errors while still maintaining minimal memory requirements. This claim is also supported by data obtained from FDTD simulations. Using a one-dimensional plasma slab problem as the test case, we show that the bandwidth and dynamic range associated with this fourth-order scheme are significantly improved with respect to its second-order counterpart. The impact of other error mechanisms, namely material boundary-related errors, is also discussed     

A higher order FDTD method in Integral formulation

We present a fourth-order (4, 4) finite-difference time-domain (FDTD)-like algorithm based on the integral form of Maxwell's equations. The algorithm, which is called the integro-difference time-domain (IDTD) method, achieves its fourth-order accuracy in space and time by taking into account the spatial and temporal variations of electromagnetic fields within each computational cell. In the algorithm, the electromagnetic fields within each cell are represented by space and time integrals (or integral averages) of the fields, i.e., the electric and magnetic fluxes (D,B) are represented by the surface-integral average, and the electric and magnetic fields (E,H) by the line and time integral average. In order to relate the integral average fields in the staggered update equations, we have obtained constitutive relations for these fields. It is shown that the IDTD update equations combined with the constitutive relations are fourth-order accurate both in space and time. The fourth-order correction terms are represented by the modified coefficients in the update equations; the numerical structure remains the same as the conventional second-order update equations and more importantly does not require the storage of field variables at the previous time steps to obtain the fourth-order accuracy in time. Furthermore, the Courant-Friedrichs-Lewy (CFL) stability criteria of this fourth-order algorithm turns out to be identical to the stability limits of conventional second-order FDTD scheme based on differential formulation.     

碰撞等离子体的高阶FDTD算法

给出了电磁波在均匀、碰撞等离子体中传播的四阶时间和四阶空间FDTD算法.该算法比Yee氏FDTD算法每一个网格每一维增加一个存储单元,与常规的二阶等离子体FDTD算法相同.由于采用四阶时间和四阶空间近似,因此该算法能有效地减小数字色散误差,其频带宽度比二阶算法的频带宽度更宽.为了验证该高阶算法的正确性,对均匀、碰撞等离子体平板的电磁波反射系数进行了计算,并与解析结果、二阶FDTD计算结果进行了比较,证明了该算法的高效和精确.     

Fringe wave diffraction coefficients for higher order discontinuities

We consider the diffraction of waves by objects with higher order discontinuities. The geometric theory of diffraction (gtd) diffracted field for this type of discontinuities have strong divergence near normal incidence. We substract from this diffracted field, the field radiated by the Luneberg-Kline currents to get the fringe diffracted field; and show that this field is finite. The formulae can be used to improve the accuracy of physical theory of diffraction (ptd) for smooth objects without edges. Explicit formulas are given for the discontinuity up to order 5. We present a numerical application for the discontinuity in the curvature. All computations are done by using Maple symbolic computation system.     

A ray-tracing method for modeling indoor wave propagation andpenetration

A ray-tracing method for waves inside buildings is presented. Ray tubes are used to model the wave propagation and penetration and all the significantly reflected and transmitted ray tubes from interfaces are included. Also, the cross sections of the ray tubes at the field points are evaluated to find the spreading factors of the waves and then the geometrical optics (GO) contributions at the locations of the receiving antenna. A program has been developed according to this ray-tracing technique that can be applied to simulate waves transmitted through and reflected from electrically large complex 2D and 3D bodies. To verify this ray-tracing program, 2D moment method (MM) solutions for wave propagating in a two-room structure and also through a stair-shaped wall above a lossy ground are used to compare with those obtained from the ray tracing. Besides, comparisons of field measurements and ray-tracing simulations at 900 and 1800 MHz performed in a corridor on different floors and inside a staircase are shown. The effective complex dielectric constants of the buildings determined from a free-space method are employed in the simulations and a vector network analyzer is used for the field measurements. Good agreements are obtained. In addition, measured results for waves penetrating an exterior wall with metal-framed windows at 1290 MHz are employed to test the ray-tracing solutions, which indicate that scattering from the metal frames may be significant for field points near the windows. This ray-tracing program can be applied to evaluate the channel characteristics for the indoor wireless communications     

A special higher order finite-element method for scattering by deepcavities

A special higher order finite-element method is presented for the analysis of electromagnetic scattering from a large, deep, and arbitrarily shaped open cavity. This method exploits the unique features of the finite-element equations and, more importantly, the unique features of the problem of scattering by a large and deep cavity. It is designed in such a manner that it uses minimal memory, which is proportional to the maximum cross section of the cavity and independent of the depth of the cavity, and its computation time increases only linearly with the depth of the cavity. Furthermore, it computes the scattered fields for all angles of incidence without requiring significant additional time. The technique is implemented with higher order tetrahedral and mixed-order prism elements, both having curved sides to allow for accurate modeling of arbitrary geometries. Numerical results show that higher order elements yield a remarkably more accurate and efficient solution for scattering by three-dimensional (3-D) cavities. Of the two kinds of element, the mixed-order prism is optimal for the proposed special solver     

一种基于高阶累积量的复杂调制样式识别方法

针对卫星数字化视频广播第二代标准（Digital Video Broadcasting-Satellite-Second Generation,DVB-S2）中多进制幅度移相键控（Multiple Amplitude and Phase-Shift Keying,MAPSK）和多进制正交幅度调制（Multiple Quadrature Amplitude Modulation,MQAM）信号的调制识别,提出了基于高阶累积量的识别方法。首先对16QAM、32QAM、16APSK、32APSK信号的高阶累积量及其特征进行分析,进而利用其高阶累积量的不同提取用于信号分类的特征参量进行调制识别。给出了算法的详细流程,并对算法进行了仿真分析,结果表明,当样本数越多时,算法信噪比适应能力越好,而与相位偏差无关;在信号样点数为2 048点且信噪比为10 dB时,算法可实现96%的正确识别率,完全满足实际系统对信号分类的需要。     

自适应交叉近似压缩的高阶矩量法的并行实现

高阶矩量法在计算电磁学中的应用越来越广泛, 为了进一步提高其计算规模, 引入并行的自适应交叉近似压缩算法(Adaptive Cross Approximation algorithm, ACA).该算法首先采用非均匀有理B样条建模(Non-Uniform Rational B-Splines, NURBS)的方法进行面片分组; 然后利用矩量法中远区阻抗矩阵的低秩特性进行ACA压缩; 最后采用稀疏近似逆预条件(Sparse Pattern Approximate Inverse preconditioning, SPAI)的共轭梯度法(Conjugate Gradient method, CG)快速求解矩阵方程.该算法中的ACA压缩过程和迭代求解过程都特别适合并行计算.数值实验表明, 对于电大尺寸问题, ACA压缩后的矩阵占用的内存远远低于原矩阵, 而预条件的共轭梯度法可以很快收敛.此外该算法在大规模并行时的效率较高.     

A general method for FDTD modeling of wave propagation in arbitraryfrequency-dispersive media

A general formulation is presented for finite-difference time-domain (FDTD) modeling of wave propagation in arbitrary frequency-dispersive media. Two algorithmic approaches are outlined for incorporating dispersion into the FDTD time-stepping equations. The first employs a frequency-dependent complex permittivity (denoted Form-1), and the second employs a frequency-dependent complex conductivity (denoted Form-2). A Pade representation is used in Z-transform space to represent the frequency-dependent permittivity (Form-1) or conductivity (Form-2). This is a generalization over several previous methods employing either Debye, Lorentz, or Drude models. The coefficients of the Pade model may be obtained through an optimization process, leading directly to a finite-difference representation of the dispersion relation, without introducing discretization error. Stability criteria for the dispersive FDTD algorithms are given. We show that several previously developed dispersive FDTD algorithms can be cast as special cases of our more general framework. Simulation results are presented for a one-dimensional (1-D) air/muscle example considered previously in the literature and a three-dimensional (3-D) radiation problem in dispersive, lossy soil using measured soil data     

A novel implementation of multilevel fast multipole algorithm for higher order Galerkin's method

A new approach is proposed to reduce the memory requirements of the multilevel fast multipole algorithm (MLFMA) when applied to the higher order Galerkin's method. This approach represents higher order basis functions by a set of point sources such that a matrix-vector multiply is equivalent to calculating the fields at a number of points from given current sources at these points. The MLFMA is then applied to calculate the point-to-point interactions. This permits the use of more levels in MLFMA than applying MLFMA to basis-to-basis interactions directly and, thus, reduces the memory requirements significantly.     

A generalized higher order finite-difference time-domain method and its application in guided-wave problems

In this paper, a (2M,4) scheme of the finite-difference time-domain (FDTD) method is proposed, in which the time differential is of the fourth order and the spatial differential using the discrete singular convolution is of order 2M. Compared with the standard FDTD and the scheme of (4, 4), the scheme of (2M, 4) has much higher accuracy. By choosing a suitable M/spl ges/2, the (2M, 4) scheme can arrive at the highest accuracy. In addition, an improved approximation of the symplectic integrator propagator is presented for the time differential. On the one hand, it can directly simulate unlimited conducting structures without the air layer between the perfectly matched layer and inner structure; on the other hand, it needs only a quarter of the memory space required by the Runge-Kutta time scheme and requires one third of the meshes in every direction of the standard FDTD method. By choosing suitable meshes and bandwidth M, our scheme not only retains higher accuracy but also saves memory space and CPU time. Numerical examples are provided to show the high accuracy and effectiveness of the proposed scheme.     

部分森林覆盖山区电波传播特性预测的快速算法

为提高部分森林覆盖山区电波传播特性预测的时效性,提出了一种基于宽角抛物方程(PE)的快速预测算法。采用PE通过分步傅里叶变换(SSFT)求解;在SSFT步进迭代过程中,根据传播路径上森林的等效介电常数、地形的起伏情况,动态选择PE的水平步长。通过对部分森林覆盖的不规则地形条件下的电波传播特性进行仿真,探讨了该方法的可行性和有效性。结果表明：相比于均匀大步长算法,该方法更准确;而相比于均匀小步长算法,该方法能够保证抛物方程的计算精确度,同时极大地提高计算效率。     

HIGHER ORDER ITERATIVE APPROXIMATION OF EM WAVE PROPAGATION IN A MULTILAYER NONLINEAR SLAB

Based on the nonlinear dispersive relation for fundamental frequency, reflection and transmission from a multilayer nonlinear slab is discussed when a plane wave is obliquely incident on it. The higher order iterative approximations of reflectivity and transmittivity are derived. Some calculations are made on a single-layer slab and a two-periodic multilayer slab, which is composed of two different nonlinear dielectric plates. It was concluded by some discussions about the influences of nonlinearity to EM wave propagation.     

电波传播的抛物方程近似分析法

文中提出了一种电波传播模式分析方法. 通过对PJ (Paulus-Jeske)波导进行参数估计,实现蒸发波导的完备性建模;采用抛物方程法分析气象环境中的二维电波传播路径损耗分布,利用最大值池化降低数据量,并采用自适应聚类分析实现电波传播模式分析,进而建立海杂波衰减规律与电波传播模式之间的映射,统计条件概率. 结果表明,蒸发波导环境下海杂波衰减与电波传播模式之间具有相关性,分析结果能够展示蒸发波导中的电波传播模式,并且能够为海杂波反演大气波导提供先验条件概率分析.     

Equations for wave propagation in a stratified compressible electron?ion magnetoplasma

This letter deals with the propagation of coupled electromagnetic, electron-acoustic and ion-acoustic waves in a horizontally stratified horizontally magnetised compressible electron?ion plasma. Propagation transverse to the magneto-static field is considered, and some first-order coupled-wave equations are derived.     

Numerical dispersion of higher order nodal elements in thefinite-element method

The discretization inherent in the finite-element method results in numerical dispersion. This dispersion is investigated for a time-harmonic plane wave propagating through an infinite, two-dimensional, finite-element mesh composed of uniform quadrilateral and triangular elements. The effects on the dispersion due to the propagation direction of the wave, the order of the elements, the node density, and the mesh geometry are studied. Results are given which can serve as a guide in selecting the appropriate element order, node density, and mesh geometry when applying the finite-element method     

A nonparametric phase estimation method for SIMO systems based onsecond-order and higher order statistics

We present a nonparametric phase estimation algorithm for linear single-input multiple-output (SIMO) channels. Given an unknown stationary input signal with known statistics, our approach is to obtain the joint minimum mean square phase estimation based on the polyspectra and the cross-spectra of the SIMO channel outputs. By utilizing both higher order and second-order statistics of the channel outputs, our approach is shown to be more accurate and reliable than methods based on higher order statistics alone. It can be applied to SIMO channels with common zeros     

On a method computing transient wave propagation in ionospheric regions

A consequence of an exoatmospheric nuclear burst is an electromagnetic pulse (EMP) radiated from it. In a region far enough away from the burst, where nonlinear effects can be ignored, the EMP can be represented by a large-amplitude narrow-time-width plane-wave pulse. If the ionosphere intervenes the origin and destination of the EMP, frequency dispersion can cause significant changes in the original pulse upon reception. A method of computing these dispersive effects of transient wave propagation is summarized. The method described is different from the standard transform techniques and provides physical insight into the transient wave process. The method, although exact, can be used in approximating the early-time transient response of an ionospheric region by a simple integration with only explicit knowledge of the electron density, electron collision frequency, and electron gyrofrequency required. As an illustration of the method, it is applied to a simple example and contrasted with the corresponding transform solution.