基于全局透射边界条件的宽角抛物方程电波预测模型

提出了一种新型的基于全局透射边界条件（non-local boundary condition,NLBC）的Greene近似宽角抛物方程（wide-angle parabolic equation,WAPE）电波预测模型,用于求解对流层远距离复杂环境中的电磁波传播特性.采用有限差分法（finite difference method,FDM）求解WAPE得到了三对角线性方程组,可以快速地求解整个空间的电场分布,也可以对不规则的地表环境进行精确建模.本文提出的WAPE模型解决了传统的PE离轴传播角度偏小的问题,将电波的最大传播仰角提升至约50°,同时大大减小了计算区域中上边界吸收层的设置尺寸,从而提高了PE的计算效率.实验证明,当伪微分算子的相位误差不超过0.002时,Tappert、Claerbout和Greene近似形式得到的最大传播角分别为20°、35°和45°.最后,通过与经典的光学双射线模型进行对比,证明本文提出的基于NLBC的Greene近似WAPE模型的可计算传播仰角更大,对上边界处反射电磁波有良好的吸收效果.因此,本文的模型适用于对流层远距离复杂环境中电磁波传播特性的精确预测.     

Microwave Biomedical Data Inversion Using the Finite-Difference Contrast Source Inversion Method

We present a contrast source inversion (CSI) technique which is based on a finite-difference (FD) solver for use in microwave biomedical imaging. The algorithm is capable of inverting complex-permittivity biomedical data sets without the explicit use of a forward solver at each iteration. The FD solver is based in the frequency domain, utilizes perfectly matched layer (PML) boundary conditions, and the stiffness matrix is solved via an LU decomposition and Gaussian elimination. An important feature of the FD-CSI algorithm is that the stiffness matrix associated with the FD solver depends only upon the background medium and frequency, and thus the LU decomposition is only performed once, before the iterative inversion process. Unlike the usual Integral Equation (IE) based inversion techniques, the FD-CSI algorithm is readily capable of utilizing an arbitrary background medium for the inversion process.      

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     

New full-vectorial numerically efficient propagation algorithmbased on the finite element method

A new full-vectorial beam propagation algorithm based on the versatile finite element method, in order to accurately characterize three-dimensional (3-D) optical guided-wave devices, is presented. The computationally efficient formulation is based on the two transverse components of the magnetic field without destroying the sparsity of the matrix equation. The robust perfectly matched layer (PML) boundary condition is incorporated into the formulation so as to effectively absorb the unwanted radiation out of the computational domain. The efficiency and precision of the proposed full-vectorial propagation approach is demonstrated through the analysis of single optical waveguide, directional couplers, and electrooptic modulator     

A Hybrid SIM-SEM Method for 3-D Electromagnetic Scattering Problems

A new method combining the spectral integral method and spectral element method (SIM-SEM) is proposed to simulate 3-D electromagnetic scattering from inhomogeneous objects. In this hybrid technique (a special case of the finite element boundary integral (FEM-BI) combination), the SEM with the mixed-order curl conforming vector Gauss-Lobatto-Legendre (GLL) basis functions are used to represent the interior electric field with high accuracy, while the SIM on a cuboid surface is used as an exact radiation boundary condition. The Toeplitz property of the SIM matrix is utilized to reduce the memory and CPU time costs in an iterative solver by using the fast Fourier transform algorithm. Unlike the traditional FEM-BI combination where the BI portion usually dominates the computational complexity, the computational costs are much lower in the SIM-SEM method. Numerical results verify the accuracy and capability of this method, confirming that the SIM-SEM method is a good alternative for solving scattering problems from inhomogeneous objects.      

A method of moments model for VHF propagation

Predictions of a numerical model for site specific very high frequency (VHF) propagation over irregular terrain are compared to experimental data and to other propagation models. The numerical model is based on an iterative version of the method of moments (MOM) known as the banded matrix flat surface iterative approach (BMFSIA) for either perfectly conducting or penetrable surfaces rough in one direction only. Due to the large size of the numerical problem (65000 to 130000 unknowns), a parallel implementation of the method is presented and applied in the simulations. Comparisons with measurement data show good agreement overall and also illustrate the sensitivity of the model to input terrain profiles. Comparisons with other propagation models show good agreement also in cases where these models are expected to be valid and further clarify the limitations of the approximations made in these methods     

A versatile wave propagation model for the VHF/UHF rangeconsidering three-dimensional terrain

A polarimetric wave propagation model for field strength forecasting and coverage prediction in the VHF/UHF frequency range is presented. The model uses a digital terrain data bank and considers multipath propagation. Based on the uniform geometrical theory of diffraction (UTD) and physical optics an approach is described for calculating the propagation effects in natural 3-D terrain, given by topological and morphographical data. The method for field strength forecasting is described and methods for the analysis of the predicted multipath signal are discussed. It is shown how the complex probability density function (PDF) for the receiver field strength and the field strength delay spectrum can be derived. Methods for further evaluation of the transmitting channel characteristics are discussed     

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。     

Analysis of low frequency scattering from penetrable scatterers

A method is presented for solving the surface integral equation using the method of moments (MoM) at very low frequencies, which finds applications in geoscience. The nature of the Helmholtz decomposition leads the authors to choose loop-tree basis functions to represent the surface current. Careful analysis of the frequency scaling property of each operator allows them to introduce a frequency normalization scheme to reduce the condition number of the MoM matrix. After frequency normalization, the MoM matrix can be solved using LU decomposition. The poor spectral properties of the matrix, however, makes it ill-suited for an iterative solver. A basis rearrangement is used to improve this property of the MoM matrix. The basis function rearrangement (BFR), which involves inverting the connection matrix, can be viewed as a pre-conditioner. The complexity of BFR is reduced to O(N), allowing this method to be combined with iterative solvers. Both rectilinear and curvilinear patches have been used in the simulations. The use of curvilinear patches reduces the number of unknowns significantly, thereby making the algorithm more efficient. This method is capable of solving Maxwell's equations from quasistatic to electrodynamic frequency range. This capability is of great importance in geophysical applications because the sizes of the simulated objects can range from a small fraction of a wavelength to several wavelengths     

Notes on semiempirical terrestrial wave propagation modeling for macrocellular environments - comparisons with measurements

Due to their low computational requirements, two-dimensional semiempirical wave propagation algorithms are still indispensable tools for terrestrial mobile communications and radio broadcasting coverage predictions in the very high and ultrahigh frequency bands. In this paper, we discuss various improvements of an algorithm based on digital terrain data. The algorithm combines the basic empirical propagation curves of Okumura et al. (1968) with terrain adaptive propagation curves derived from Fresnel zone clearance analyses of several terrain subsections. Also, a multiple knife-edge diffraction algorithm with approximate evaluation of the Kirchhoff diffraction integrals is applied when the line of sight is obstructed. Prediction quality is further improved by a robust algorithm for determination of effective transmitter antenna heights, and land usage along the terrain profile different from "open terrain" is considered by a multilevel Fresnel zone blockage evaluation. Prediction errors with standard deviations of about 6 to 7 dB were found for a great variety of measurements in flat and moderately undulating terrain. Transmitter stations with very high antennas (more than 200 m) caused larger standard deviations of the prediction errors. However, improvements of the predictions could be achieved in these cases by evaluating street orientations with respect to the direct path.     

电波传播抛物方程模型在航空通信中的应用

针对航空通信中电波传播损耗预测需要满足精确性、实时性及复杂环境适应性的要求,在分析电波传播损耗对航空通信系统作用范围的影响基础上,采用抛物方程模型研究了航空通信中电波在空间区域的传播特性。该模型利用分步傅里叶算法实现快速求解,采用边界平移法处理复杂地形边界,并通过非均匀网格技术提高空间任意一点的场强计算精度,从而改善了复杂环境下电波传播损耗预测的精确性和实时性。将该模型应用于真实地形环境下的航空通信仿真算例中,仿真结果表明：该模型能有效预测复杂环境下电波的传播损耗,评估在正常通信条件下飞行器的飞行范围、最大飞行距离以及最低飞行高度等性能。     

A fast solver for the Helmholtz equation on long, thin structures

We present a fast solver for the Helmholtz equation on long, thin structures. It operates on an integral equation formulation of the problem, in which the solution is represented as a superposition of fields generated by sources on the structure (usually on the boundary or boundaries of the structure). It uses a standard iterative solver for linear equations, in conjunction with a novel method for applying the forward matrix, whose computational complexity is O(N), where N is the number of points on which the integral equation is solved. The algorithm is suitable for structures in either two dimensions (2-D) or three dimensions. It does not depend in any great detail on the specifics of the Helmholtz equation, and, thus, is also suitable for similar equations. We demonstrate the algorithm by using it to simulate scattering in 2-D from dielectric structures, using an integral equation formulation constructed using a combination of single-layer and double-layer potentials, yielding a second-kind integral equation. Numerical results show the algorithm to be efficient and accurate.     

基于抛物方程的3.6 GHz典型应用场景传播特性分析

文中利用抛物方程(parabolic equation,PE)方法,从纵向剖面和区域覆盖两个维度,对3.6 GHz频点在都市、郊区、乡村三种典型场景下的传播特性进行分析,并将仿真结果与ITU-R P.1546方法仿真结果进行对比分析.分析结果表明:PE方法能够描述信号传输直射、绕射、反射波束,与各场景传播特点相匹配,具...     

A wide-band propagation model based on UTD for cellular mobileradio communications

The present wide-band propagation model based on uniform geometrical theory of diffraction (UTD) for cellular mobile radio communications includes two major contributions. First, a UTD-based narrow-band channel transfer function containing both the diffracted electric field and the reflection of diffracted electric fields is derived. Not only is it an important element of the wide-band modeling method, but it also leads to a total path-loss prediction model verified by comparisons with previously published theoretical and experimental results. In particular, the distance for horizontal placement on the street allows one to calculate the ray-path length difference (used in wide-band modeling) for the diffracted field and the reflection. Second, new refinements (including a number of explicit-form expressions to an existing method experimentally confirmed, simulating wide-band radiowave propagation for rural environments including terrain profiles) are added, making it applicable here. The method generates the time-domain path loss, wide-band path loss, and the relative power in the frequency domain. The time-domain path loss physically interprets and reasonably predicts the power delay profiles. The presence of this and similar power delay profiles, as well as the behavior of the relative power in the frequency domain, has been confirmed by existing wide-band propagation measurements. The value of the wide-band path loss is of the order of the total path loss at the carrier frequency     

Propagation and coverage prediction for cellular radio systems

The development of a computerized UHF signal propagation and coverage prediction system for Singapore is described. This system consists of a terrain database, a propagation prediction model, and a subsystem to plot coverage patterns. The predicted results were verified by field strength measurements. The comparison showed that the errors of the prediction for two UHF bands have a standard deviation of less than 10 dB     

Low-grazing angle scattering from rough surfaces in a duct formedby a linear-square refractive index profile

The problem of rough surface scattering and propagation over rough terrain in a ducting environment has been receiving considerable attention in the literature. One popular method of modeling this problem is the parabolic wave equation (PWE) method. An alternative method is the boundary integral equation (BIE) method. The implementation of the BIE in inhomogeneous media (ducting environments) is not straightforward, however, since the Green's function for such a medium is not usually known. In this paper, a closed-form approximation of the Green's function for a two-dimensional (2-D) ducting environment formed by a linear-square refractive index profile is derived using asymptotic techniques. This Green's function greatly facilitates the use of the BIE approach to study low-grazing angle (LGA) rough surface scattering and propagation over rough surfaces in the aforementioned ducting environment. This paper demonstrates how the BIE method can model the combined effects of surface roughness and medium inhomogeneity in a very rigorous fashion. Furthermore, it illustrates its capability of accurately predicting scattering in all directions including backscattering. The boundary integral equation of interest is solved via the method of ordered multiple interactions (MOMI), which eliminates the requirements of matrix storage and inversion and, hence, allows the application of the BIE method to very long rough surfaces     

A prediction model for multipath propagation of pulse signals at VHF and UHF over irregular terrain

A prediction model is presented that permits calculation of the probability of occurrence of distinct multipath propagation of pulse signals at VHF and UHF over irregular terrain. The model applies to terrain characterized by an irregular distribution of obstacles such as hills, buildings, trees, etc., so as to make it impractical to calculate the effect of multipath propagation by diffraction or bistatic-reflection theory. Statistical data on wave propagation over irregular terrain form the basis for the empirical model developed. Generally, the model predicts that 1) for constant transmitter-receiver separation, the amplitudes of the received echoes decrease with increasing echo delay, and 2) for constant echo delay, the occurrence of echo pulses increases as the transmitter-receiver distance increases. The results obtained from the model for rural, hilly terrain, and for a built-up metropolitan area are compared with available measured data.     

OFDM系统相位噪声的Huber ML抑制方法

OFDM系统对相位噪声(PHN)非常敏感,由其引起的子载波相位旋转和载波间干扰(ICI)会严重恶化系统性能。该文提出了一种新的OFDM接收机PHN估计和抑制方法,利用判决数据采用Huber ML估计方法对PHN引起的ICI分量进行迭代估计,将估计的ICI系数变换到时域来校正每个样点的相位误差,从而达到抑制PHN的目的。与传统的基于判决的估计方法相比,该方法对判决的错误传播具有鲁棒性,可进一步提高ICI抑制性能。对算法在AWGN和多径信道环境下的仿真结果表明所提方法对PHN引起的ICI有较好的抑制性能。     

Efficient computation of frequency-dependent parameters for on-chipinterconnects via two-dimensional FDTD and time signal predictiontechnique

An efficient two-dimensional finite difference time domain (2-D-FDTD) method combined with time signal prediction technique has been proposed for the frequency-dependent parameters computation of on-chip interconnects in high-speed integrated circuits (ICs). A graded mesh algorithm and lossy absorbing boundary condition are proposed and adopted in the 2-D FDTD analysis to reduce the number of spatial grid points in the simulation region. The introduction of time signal prediction technique to predict the future signal in the time domain or extract the parameters in the frequency domain of uniform transmission lines reduces the computation time drastically. With these, the substrate and conductor losses are both included in one analysis. This algorithm leads to a significant reduction in CPU time and storage requirements as compared with the conventional FDTD. The simulation results are in good agreement with the results obtained by other methods and measurements     

3-D FEM Modeling and Fabrication of Circular Photonic Crystal Microcavity

In this paper, we study an unconventional kind of quasi-three-dimensional (3-D) photonic crystal (PhC) with circular lattice pattern: it consists of air holes in a GaAs material $({rm n}=3.408)$ along circular concentric lines. This particular PhC geometry has peculiar behavior if compared with the traditional square and triangular lattices, but it is difficult to model by using conventional numerical approaches such as wave expansion method. The resonance and the radiation aspects are analyzed by the 3-D finite-element method (FEM). The model, based on a scattering matrix approach, considers the cavity resonance frequency and evaluates the input–output relationship by enclosing the photonic crystal slab (PhCS) in a black box in order to define the responses at different input–output ports. The scattering matrix method gives important information about the frequency responses of the passive 3-D crystal in the 3-D spatial domain. A high sensitivity of the scattering parameters to the variation of the geometrical imperfection is also observed. The model is completed by the quality factor (Q-factor) estimation. We fabricated the designed circular photonic crystal over a slab membrane waveguide embedding InAs/GaAs quantum dots emitting around 1.28 $mu{hbox{m}}$. Good agreement between numerical and experimental results was found, thus validating the 3-D FEM full-wave investigation.