Discretized Gabor-based beam algorithm for time-harmonic radiation from two-dimensional truncated planar aperture distributions .II. Asymptotics and numerical tests

For pt.I see ibid., vol.50, no.12, p.1751-59 (2002). In this second part of the two-part sequence dealing with Gabor-based Gaussian beam (GB) representations for the excitation of time-harmonic three-dimensional (3-D) vector electromagnetic fields excited by two-dimensional (2-D) arbitrarily polarized truncated planar aperture distributions (set in a discretized [configuration (space)]-[spectrum (wavenumber)] phase space), we employ high-frequency asymptotic approximations to reduce the formal solutions developed in part I to efficient algorithms for implementation. The resulting explicit expressions for the 3-D GB propagators are applied to the species of narrow-waisted GBs, which possess ray-like features without the failures of ray fields in ray-optical transition regions. The potential utility of such GBs in the synthesis of wave interactions with complex environments has been discussed previously. The narrow-waisted GB algorithms for the aperture and radiated near-to-far zone fields are calibrated for robustness, accuracy and efficiency by comparison with numerically generated reference solutions in a series of tests involving coordinate-separable rectangular aperture distributions with cosine amplitude tapers.     

Two-dimensional pulsed propagation from extended planar aperture field distributions through a planar dielectric layer via quasi-ray Gaussian beams

A previously developed Gabor-based quasi-ray narrow-waisted (NW) Gaussian beam (GB) algorithm for time-harmonic propagation of aperture-excited two-dimensional (2-D) electromagnetic fields through a planar dielectric layer is extended here to the time domain (TD) to deal with short-pulse excitation. The dielectric layer is assumed to be nondispersive; however, slight Ohmic losses can be accommodated. The frequency domain (FD) algorithm is based on a self-consistent discretization of the aperture field distribution in terms of basis NW-GBs in conjunction with an efficient quasireal ray tracing scheme for tracking the individual basis beams. The TD results are obtained by analytic Fourier inversion from the FD in terms of pulsed beam wavepackets, following a procedure similar to that utilized by Galdi et al. (see IEEE Trans. Antennas Propagat., vol.49, p.1322-32, Sept. 2001) in connection with free-space aperture radiation. The proposed algorithm is validated and calibrated against a rigorous numerical reference solution via an extensive series of numerical experiments. A priori accuracy assessments in terms of critical nondimensional estimators, and computational costs, are also given attention.     

Quasi-ray Gaussian beam algorithm for short-pulse two-dimensional scattering by moderately rough dielectric interfaces

We consider short-pulse (SP) time-domain (TD) two-dimensional (2-D) scattering by moderately rough interfaces, which separate free space from a slightly lossy dielectric half-space, and are excited by one-dimensional (1-D) SP-TD aperture field distributions. This study extends to the SP-TD in our previous investigation of time-harmonic high frequency 2-D scattering of Gabor-based quasi-ray Gaussian beam fields excited by 1-D aperture field distributions in the presence of moderately rough dielectric interfaces (Galdi et al.). The proposed approach is based on the Kirchhoff physical optics (PO) approximation in conjunction with the Gabor-based quasi-ray narrow-waisted Gaussian pulsed-beam (PB) discretization (Galdi et al.), which is applied to the SP-induced equivalent magnetic surface currents on the interface that establish the TD reflected/transmitted fields. We show that, for well-collimated truncated SP incident fields, the PO-PB synthesis of the reflected/transmitted fields yields an approximate explicit physically appealing, numerically efficient asymptotic algorithm, with well-defined domains of validity based on the problem parameters. An extensive series of numerical experiments verifies the accuracy of our method by comparison with a rigorously-based numerical reference solution, and assesses its computational utility. The algorithm is intended for use as a rapid forward solver in SP-TD inverse scattering and imaging scenarios in the presence of moderately rough dielectric interfaces.     

Discretized Gabor-based beam algorithm for time-harmonic radiation from two-dimensional truncated planar aperture distributions .I. Formulation and solution

In this first part of a two-paper sequence, we develop a Gabor-based Gaussian beam (GB) method for the representation of three-dimensional (3-D) time-harmonic vector electromagnetic fields excited by two-dimensional (2-D) truncated arbitrarily polarized planar aperture field distributions. The biorthogonal Gabor basis is tied to a lattice in the discretized four-dimensional (4-D) [configuration (space)]-[spectrum (wavenumber)] phase space which spans the 2-D aperture plane. This study generalizes previous investigations of the simpler corresponding procedure for 2-D fields excited by one-dimensional (1-D) apertures. By subsequent specialization, in the 1-D aperture case, to narrow-waisted 2-D ray-like GBs, we have shown that tracking such beams through interactions with complex environments and recombining them to synthesize the total 2-D field produces robust, efficient and accurate algorithms that are useful for a variety of forward and inverse scattering scenarios. Extension to the time domain via narrow-waisted pulsed GBs has likewise been considered. These potential applications have motivated the extension here to general 3-D EM fields excited by time-harmonic 2-D truncated apertures. The presentation relates each step in the analytic development to a corresponding step in the 1-D aperture case, thereby highlighting the complications (in the parameterizing phase space) associated with the 2-D aperture problem. The outcome is the formal exact solution of the problem under consideration.     

Narrow-waisted Gaussian beams for aperture-generated scattering from planar conducting surfaces with complex coatings described by higher order impedance boundary conditions

In this paper, we use higher order impedance boundary conditions (HOIBCs) for studying high frequency asymptotic two-dimensional (2-D) scattering of truncated aperture-generated electromagnetic fields from planar conducting surfaces coated by multiple layers of homogeneous bi-anisotropic media. The reflected field syntheses are carried out via asymptotic reduction of rigorous plane-wave spectral integrals, which are subsequently discretized and transformed to the spatial domain through use of a Gabor-based narrow-waisted (NW) Gaussian beam (GB) algorithm. In this discretized algorithm, the GB propagators are approximated by previously explored standard and modified (uniform) complex-source-point paraxial asymptotic techniques. Example applications are restricted to zeroth and second order IBCs for single- and multilayer complex coatings, with emphasis on the adaptation of the NW-GBs to the HOIBC launch conditions in the presence of localizing (e.g., focused and/or abruptly truncated) illumination. The results confirm that the previously established utility of the NW-GB algorithm with respect to accuracy and computational feasibility continues to hold for this fairly general combination of environmental complexity and strongly inhomogeneous (localizing) illumination.     

Narrow-waisted Gaussian beam discretization for short-pulseradiation from one-dimensional large apertures

We develop a Gabor-based Gaussian beam (GB) algorithm for representing two-dimensional (2-D) radiation from finite aperture distributions with short-pulse excitation in the time domain (TD). The work extends previous results using 2-D frequency-domain (FD) narrow-waisted Gaussian beams. The FD algorithm evolves from the rigorous Kirchhoff integration over the aperture distribution, which is then parameterized via the discrete Gabor basis and evaluated asymptotically for high frequencies to furnish the GB propagators to the observer. The TD results are obtained by Fourier inversion from the FD and yield pulsed beams (PB). We describe the resulting TD algorithm for several aperture distributions, ranging from simple linearly phased (linear delay) to arbitrary time delay profiles; the latter accommodate the important case of focusing TD aperture fields. For modulated pulses with Gaussian envelopes, we compute accurate closed form analytic solutions, which have been calibrated against numerical reference data. Our results confirm that the previously established utility of the Gabor-based narrow-waisted FD-GB algorithm for radiation from distributed apertures remains intact in the TD     

Short-pulse three-dimensional scattering from moderately rough surfaces: a comparison between narrow-waisted Gaussian beam algorithms and FDTD

In this paper, with reference to short-pulse three-dimensional scattering from moderately rough surfaces, we present a comparison between Gabor-based narrow-waisted Gaussian beam (NW-GB) and finite-difference time-domain (FDTD) algorithms. NW-GB algorithms have recently emerged as an attractive alternative to traditional (ray-optical) high-frequency/short-pulse approximate methods, whereas FDTD algorithms are well-established full-wave tools for electromagnetic wave propagation and scattering. After presentation of relevant background material, results are presented and discussed for realistic parameter configurations, involving dispersive soils and moderately rough surface profiles, of interest in pulsed ground penetrating radar applications. Results indicate a generally satisfying agreement between the two methods, which tends to improve for slightly dispersive soils. Computational aspects are also compared.     

复空间定位法——一种分析复波束散射的有效方法

本文提出了的复空间定位法，可对目标散射的复射线轨迹进行了复空间定位，并可用于分析目标对频域复源波束与对时域复源脉冲波束产生的空散射场，这种方法不仅与成熟的复空间追踪法具有相同的精度，而且能将后者三维空间的四维未知量的求解降低到二维，将二维空间的二维未知量的求解降低到一维，还解决了复射线近轴近似理论遇到的困难，因而一种行之有效的分析方法，作为实例，本文用复空间定位法分析计算了导体板，凸导体球与凹导体     

Time-domain radiation from large two-dimensional apertures via narrow-waisted Gaussian beams

This paper deals with the short-pulse radiation of three-dimensional (3-D) vector electromagnetic fields from arbitrarily polarized large two-dimensional (2-D) truncated aperture distributions, which are parameterized in terms of narrow-waisted ray-like pulsed Gaussian basis beams centered on a discretized Gabor lattice in a four-dimensional (4-D) configuration-spectrum phase space. The study extends our previous Gabor-based investigation of time-domain (TD) short-pulse radiation of 2-D fields from 1-D large truncated apertures with nonphased, linearly phased (delayed) and nonlinearly phased focusing aperture field profiles . We begin with, and summarize, a Gabor-based frequency domain (FD) formulation of the 2-D aperture problem which has been presented and tested elsewhere, but we include additional numerical examples for validation and quality assessment. As done by Galdi, Felsen and Castanon (see ibid., vol 49, p. 1322-32, Sept. 2001) we access the time domain by Fourier inversion from the FD, starting from the initial 3-D space-time Kirchhoff formulation (whose numerical integration furnishes reference solutions), and then passing on to Gabor-parameterized field representations in terms of pulsed beam (PB) wavepackets which are launched by linearly and nonlinearly phase-delayed focusing aperture distributions. Example calculations and comparisons with numerically generated reference data serve to calibrate the Gabor-PB algorithms and assess their domains of validity.     

Gaussian beam analysis of propagation from an extended planeaperture distribution through dielectric layers. I. Plane layer

High-frequency propagation of electromagnetic wavefields from an extended planar aperture distribution through a complicated environment is addressed. Geometric optical ray tracing provides a versatile approximate approach to the class of problems, but it fails in transition regions surrounding shadow boundaries and caustics. The uniformity required there can be established by field tracking with Gaussian beams. The basic theory is summarized and applied to the two-dimensional test problem of transmission of radiation from a finite one-dimensional plane aperture through a planar dielectric layer. For a truncated uniform or focused aperture illumination, tracking the edge or caustic transition regions through the layer when it is located within the Fresnel zone of the aperture poses a problem of substantial complexity. It is shown that narrow-waisted beams, which can be propagated in their far zone as complex ray fields, reconstruct the correct transmitted field in these cases, as established independently by numerical evaluation of an exact spectral integral     

各向异性介质中的一种地震走时CT方法的实现

本文以弱各向异性准P波速度表达式建立地震波传播走时与弹性系数的线性关系，基于惠更斯原理计算准P波射线传播；由数据残差项与模型正则项来形成目标函数，并以共轭梯度求其I2范数解；从而实现了各向异性介质中地震波射线迭代层折反演方法，并应用于数值计算和实测资料处理中，效果良好．     

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 novel propagation modeling for microcellular communications inurban environments

A novel method for microcellular communications to predict propagation characteristics is presented in this paper. It takes into account multiple reflections among walls, ground, vehicles, as well as the transmission/reflection due to groups of trees. Although these are three-dimensional (3-D) problems, we can combine two-dimensional (2-D) ray tracing and simple 3-D geometric considerations to solve them in a very efficient way. We have investigated the propagation loss versus size, number, and locations of vehicles and groups of trees on a safe island. Our results show that the radio wave propagation exhibits severe fast fading, attenuation, and blockage due to reflection, transmission, and shadowing, respectively     

Moderately rough surface underground imaging via short-pulse quasi-ray Gaussian beams

An adaptive framework is presented for ultra-wideband ground penetrating radar imaging of shallow-buried low-contrast dielectric objects in the presence of a moderately rough air-soil interface. The proposed approach works with sparse data and relies on recently developed Gabor-based narrow-waisted quasi-ray Gaussian beam algorithms as fast forward scattering predictive models. First, a nonlinear inverse scattering problem is solved to estimate the unknown coarse-scale roughness profile. This sets the stage for adaptive compensation of clutter-induced distortion in the underground imaging problem, which is linearized via Born approximation and subsequently solved via various pixel-based and object-based techniques. Numerical simulations are presented to assess accuracy, robustness and computational efficiency for various calibrated ranges of problem parameters. The proposed approach has potential applications to antipersonnel land mine remediation.     

A 3‐D Propagation Model Considering Building Transmission Loss for Indoor Wireless Communications

In the development of a new wireless communications system, a versatile and accurate radio channel for indoor communications is needed. In particular, the investigation of radio transmission into buildings is very important. In this letter, we present an improved three‐dimensional electromagnetic wave propagation prediction model for indoor wireless communications that takes into consideration building penetration loss. A ray tracing technique based on an image method is also employed in this study. Three‐dimensional models can predict any complex indoor environment composed of arbitrarily shaped walls. A speed‐up algorithm, which is a modified deterministic ray tube method, is also introduced for efficient prediction and computation.     

基于高斯光束与射线追踪的短波波场计算算法

短波通信中几何光学理论难以计算焦散波场的传播问题,提出一种基于高斯光束的短波传播计算算法.首先,采用高斯光束法将产生高频波场的波源分解为若干个高斯光束;然后,通过射线追踪法与拉格朗日公式计算每个高斯光束,通过沿光束中心射线的ODE(常微分方程)计算曲率与光束宽度等定量;最终,采用泰勒展开式决定中心射线附近光束的贡献度,将接收点附近的高斯光束进行加权求和,获得接收端的波场.实验结果表明,本算法可有效地计算焦散的短波传播,并且与几何光学法的误差极为接近.     

非平行分层等离子体鞘套电波传播的复射线方法

基于损耗媒质的复Snell定律提出采用复射线方法研究电磁波在非均匀且非平行分层的等离子体媒质中的传播特性.该方法考虑非均匀平面电磁波的复射线(包括等幅度面的传播射线和等相位面的传播射线), 追踪电磁波复射线在每层媒质中的传播路径以及它们透过媒质分界面时的折射射线, 同时根据复射线的传播方向计算电磁波在每层媒质中的传播衰减, 数值累计整个传播过程中的传播衰减即可获得电磁波穿过等离子体鞘套的总衰减.由钝锥体仿真流场数据简化出非平行分层几何模型并采用复射线方法进行计算分析.计算结果表明:飞行器头部至尾部的传播衰减相差巨大且呈现迅速减小趋势, 非平行分层非均匀等离子体媒质存在某特定入射角, 能使传播衰减达到最小值.     

The 3-D multidomain pseudospectral time-domain algorithm for inhomogeneous conductive media

A three-dimensional (3-D) multidomain pseudospectral time-domain (PSTD) method with a strongly well-posed perfectly matched layer (PML) is developed as an accurate and flexible tool for the simulation of electromagnetic wave propagation and scattering in inhomogeneous and conductive media. This approach allows for an accurate treatment of curved geometries by multidomain decomposition and curvilinear coordinate transformation. Numerical experiments show the results agree excellently with analytical solutions and results of other well-known algorithms, and demonstrate a remarkable improvement in accuracy and efficiency over the FDTD method. The 3-D multidomain PSTD algorithm is then applied to calculate radar cross sections (RCS).     

室外微蜂窝小区3.5GHz 电波传播特性仿真和分析

射线跟踪方法是研究室外微蜂窝小区电波传播的有效方法。基于入射及反弹射线法/ 镜像法对室外微小区环境中3. 5GHz 电波传播的路径损耗进行了仿真和分析,仿真结果与文献所给的结果一致性良好,验证了该 方法的正确性。提出了一种新型的射线管判收方法,可有效判断到达接收机的所有射线管。分析了仿真中得到的接收功率、均方根时延扩展、波达方向等传播参数,并比较了视距传播(LOS)和非视距传播(NLOS)的传播特性,这些分析结果可为3. 5GHz 频段无线通信系统的覆盖提供相应的理论依据。     

A hybrid technique based on combining ray tracing and FDTD methodsfor site-specific modeling of indoor radio wave propagation

The paper presents a hybrid technique based on combining ray tracing and finite-difference time-domain (FDTD) methods for site-specific modeling of indoor radio wave propagation. Ray tracing is used to analyze the wide area and FDTD is used to study areas close to complex discontinuities where ray-based solutions are not sufficiently accurate. The hybrid technique ensures improved accuracy and practicality in terms of computational resources at the same time since FDTD is only applied to a small portion of the entire modeling environment. Examples of applying the method for studying indoor structures and penetration of wave from outdoor to indoor are given at 2.4 GHz. Numerical results are compared with known exact solutions or results of the full wave analysis or traditional ray model to demonstrate the accuracy, efficiency, and robustness of the novel method. Numerical results are also compared with reported measurement results for waves at 1.29 GHz penetrating an external wall with metal-framed windows. Cumulative distributions of field envelope obtained from the hybrid method show close resemblance to the Rayleigh distribution, which conforms to the reported measurement results