Propagation without wave equation toward an urban area model

Propagation in random media is a topic of great interest, whose application fields include, among others, the so-called last mile problem as well as the modeling of dense urban area radio communication channels. A simple scenario for this issue is considered, with an optical-ray propagation across a medium of disordered lossless scatterers. The propagation medium behaves like a percolating lattice and the goal is to characterize statistically the propagation depth in the medium as a function of the density g of scatterers and of &thetas;-the ray incidence angle. To the best of our knowledge, this approach is totally new. The problem is mathematically formulated as a random walk and the solutions are based on the theory of the martingale random processes. The obtained (approximate) analytical formulas have been validated by means of numerical simulations, demonstrating the applicability of the proposed model for a wide range of the global parameters q and &thetas;. We believe that our results may constitute a promising first step toward the solution of more complicated propagation models and a wide class of communication problems     

Quasi-ray Gaussian beam algorithm for time-harmonic two-dimensionalscattering by moderately rough interfaces

Gabor-based Gaussian beam (GB) algorithms, in conjunction with the complex source point (CSP) method for generating beam-like wave objects, have found application in a variety of high-frequency wave propagation and diffraction scenarios. Of special interest for efficient numerical implementation is the noncollimated narrow-waisted species of GB, which reduces the computationally intensive complex ray tracing for collimated GB propagation and scattering to quasi-real ray tracing, without the failure of strictly real ray field algorithms in caustic and other transition regions. The Gabor-based narrow-waisted CSP-GB method has been applied previously to two-dimensional (2-D) propagation from extended nonfocused and focused aperture distributions through arbitrarily curved 2-D layered environments. In this 2-D study the method is applied to aperture-excited field scattering from, and transmission through, a moderately rough interface between two dielectric media. It is shown that the algorithm produces accurate and computationally efficient solutions for this complex propagation environment, over a range of calibrated combinations of the problem parameters. One of the potential uses of the algorithm is as an efficient forward solver for inverse problems concerned with profile and object reconstruction     

Signal processing in a nonperiodically time-varying magnetoelastic medium

Wave propagation in a nonperiodically time-varying medium provides a means for realizing in simple physical structures a variety of signal-processing operations, such as frequency translation and coding, variable delay recall, gating, time-scale stretching or shrinking, and time reversal. The use of low-velocity modes, such as acoustic, spin, or magnetoelastic waves in solids, reduces the length of the propagation structure required to less than an inch. A general review is given of the principles of wave propagation in a spatially uniform medium with nonperiodic time variation. Both abrupt and gradual time variations are discussed. Illustrations are given for the cases of spin-wave and magnetoelastic-wave propagation and signal processing operations in these media are explained. Consideration is given to the problem of spin-wave propagation in a time-and space-varying magnetic field of the form encountered in experiments; and it is shown that a simple separated variable solution exists. For the more difficult problem of magnetoelastic propagation with both space and time variations, an approximate space-time ray theory is described. Experimental results for pulsed-field processing of spin and magnetoelastic waves are given and related to the theory.     

Relations entre distribution stationnaire et distribution aux instants d’arrivée pour des files d’attente usuelles

In queueing theory, three probability distributions naturally arise: arriving customer’s distribution, departing customer’s distribution and stationary queue length distribution. The aim of this paper is to generalize the PASTA property by using a martingale formulation, so to obtain easily relations between these probability distributions. This approach is applied to queues arising when modelling networks based upon the asynchronous transfer mode, namely those composed of a Markov jump process, an Erlang process or a renewal process whose interarrivai time has a Cox distribution.     

Reverse-time Markov processes (Corresp.)

The problem of representing a Markov process as a reverse-time Markov process is discussed. Diffusions and finite-state Markov processes are two important classes of Markov processes for which this problem has been considered. A gap in a paper of Castanon is pointed out which discusses diffusions; reverse-time finite and discrete-state Markov processes are then considered using martingale methods.     

Maximum likelihood coordinate registration for over-the-horizonradar

Over-the-horizon radar exploits the refractive and multipath nature of high-frequency propagation through the ionosphere to achieve wide-area surveillance. The coordinate registration process converts the group delays and azimuths (i.e., slant coordinates) from a set of multipath target returns to an estimate of its location (i.e., ground coordinates). This is performed by associating the target returns with ray modes determined using a computational electromagnetic propagation model. Not surprisingly, errors in the estimates of down-range ionosphere parameters can seriously degrade the accuracy of the target location estimate. The coordinate registration method presented is designed to achieve improved accuracy by employing a statistical model for uncertainties in the ionosphere. Modeling down-range ionospheric parameters as random variables with known statistics facilitates maximum likelihood (ML) target location estimation, which is more robust to errors in the measured ionospheric conditions. The statistics of down-range ionospheric parameters can be determined using current and historical soundings of the ionosphere. ML target localization consists of determining the most likely target ground coordinates over an ensemble of ionospheric conditions consistent with the data. For greater computational efficiency, the likelihood function is approximated by a hidden Markov model (HMM) for the probability of a sequence of observed slant coordinates given a hypothesized target location. The parameters of the HMM are determined via Monte Carlo execution of a ray tracing propagation model for random realizations of the ionosphere. A simulation study performed using a random ionospheric model derived from ionogram measurements made at Wallops Island suggests that the ML method can potentially achieve average absolute miss distances as much as five times better than a conventional coordinate registration technique     

Ray-optical modeling of simulcast radio propagation channels in tunnels

Simulcast radio propagation channel characteristics inside tunnels are considered in this paper. Based on the image theory of ray optics, a simulcast radio propagation channel in a rectangular tunnel is exactly formulated. As only the field components of horizontal and vertical polarization are of interest in real implementation, the exact formulation is approximated to facilitate the numerical computation. The calculated simulcast radio propagation channels are comparable fairly to measurements at 900 MHz and 2.0 GHz. The validated ray-optical modeling approach is then applied to simulate simulcast radio propagation channel characteristics at 900 MHz and 2.0 GHz to gain deeper insight and better understanding of this type of channels in tunnels. Results show that large fluctuations occur in the capture regions of the distributed antennas for both 900 MHz and 2.0 GHz. The fluctuations in the simulcast regions are larger at 2.0 GHz than at 900 MHz. The root-mean-squared (rms) delay spread is greater in the simulcast regions than in the capture regions of the distributed antennas. This larger delay spread is mainly due to the delay introduced by the transmission medium. Large values of the rms delay spread can be avoided by a careful design of the distance between the distributed antennas.     

Alternative methods for ray propagation in absorptive media

The determination of a set of Hamilton equations for ray tracing in absorbing media is still an open problem. Recently Suchy proposed another alternative, based on the Connor-Felsen criterion of real propagation vectors. It is shown here that the same criterion can be applied in a different form, leading to yet another alternative. The present method, similarly to a previous one, preserves the analytic properties of the complex ray tracing formalism, and adds to it an appropriate constraint.     

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.     

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     

On the Entropy Rate of Hidden Markov Processes Observed Through Arbitrary Memoryless Channels

This paper studies the entropy rate of hidden Markov processes (HMPs) which are generated by observing a discrete-time binary homogeneous Markov chain through an arbitrary memoryless channel. A fixed-point functional equation is derived for the stationary distribution of an input symbol conditioned on all past observations. While the existence of a solution to the fixed-point functional equation is guaranteed by martingale theory, its uniqueness follows from the fact that the solution is the fixed point of a contraction mapping. The entropy or differential entropy rate of the HMP can then be obtained through computing the average entropy of each input symbol conditioned on past observations. In absence of an analytical solution to the fixed-point functional equation, a numerical method is proposed in which the fixed-point functional equation is first converted to a discrete linear system using uniform quantization and then solved efficiently. The accuracy of the computed entropy rate is shown to be proportional to the quantization interval. Unlike many other numerical methods, this numerical solution is not based on averaging over a sample path of the HMP.      

分析凋落波场传播的三维复射线理论

将二维复射线理论推广到三维空间，讨论无界均匀媒质中三维复射线场的基本特点，以及它在曲界面上的反射特性和在分层媒质中的传播特性。由于采用了复射线近轴近似和集合复射线技术，使分析过程显著简化。本文给出的这种理论分析方法可应用于激光射束在光学系统中的传播，雷达波束在天线罩中的传播，以及目标散射特性分析等。     

随机射线方法分析飞机尾流的电磁散射特性

使用渗流网格建模飞机尾流区域内的湍流介质,在此基础上使用随机射线方法从概率论的角度分析和研究电磁波在飞机尾流这种非均匀湍流介质内后向散射的平均行为.通过数学推导得到后向散射的平均接收功率和RCS的解析表达式,以及用于数值计算的积分表达式.对模型参数的取值范围进行了讨论和分析,给出了典型的飞机尾流介质物理参数条件下的雷达散射截面.     

Frequency-dependent FDTD methods using Z transforms

The frequency-dependent finite-difference time-domain method (FD) ²TD method has been shown to be capable of correctly calculating electromagnetic propagation through media whose dielectric properties are frequency dependent. However, as researchers search for more elaborate applications, the formulation of the (FD)²TD methods becomes more complex. In this work, the mathematics of the (FD) ²TD method is developed using Z transform theory. This has the advantages of presenting a clearer formulation, and allowing researchers to draw on the literature of systems analysis and signal processing disciplines     

Variational propagation constant expressions for lossyinhomogeneous anisotropic waveguides

Based on reciprocal relationships for the adjoint operator, we derive a variational formulation for the propagation constant satisfying the divergence-free condition in lossy inhomogeneous anisotropic waveguides whose media tensors have all nine components. In addition, with some advantages over previous representations, two variational formulations have been derived for waveguides with the transverse part of the media tensors decoupled from the longitudinal part. However, to obtain a variational formulation for a general lossy reciprocal problem the waveguide must be bi-directional. Each of the variational expressions results in a standard generalized eigenvalue equation with the propagation constant appearing explicitly as the desired eigenvalue. The stationarity of the formulations is shown. It is also shown that for a general lossy nonreciprocal problem the variational functional exists only if the original and adjoint waveguide are mutually bi-directional     

UTD propagation model in an urban street scene for microcellularcommunications

A three-dimensional propagation model for microcellular communications in an urban street scene is presented. The model is based on the uniform theory of diffraction (UTD) and takes into account multiple wall-to-wall, wall-to-ground, and ground-to-wall reflections, the diffraction from corners of buildings, and subsequent reflections from such diffracted signals. The ray geometry is made extremely complex by the presence of ground reflections and the many combinations of sequences of reflections or diffractions from walls, edges, and ground. At each reflection or diffraction point, the local ray-fixed coordinate system or edge-fixed coordinate system is used together with appropriate dyadic reflection or diffraction coefficient matrices. The theoretical results for the signal path loss along the streets are compared with measurements done in New York and Tokyo for various values of the propagation parameters. Agreement with these measurements indicates that the UTD formulation is a good model for such urban communication applications     

Performance of a wireless access protocol on correlatedRayleigh-fading channels with capture

The throughput performance of a wireless media access protocol taking into account the effect of correlated channel fading, capture, and propagation delay is analyzed. For efficient access on the uplink (mobile-to-base-station link), the protocol makes use of the uplink channel status information which is conveyed to the mobiles through a busy/idle flag broadcast on the downlink (base-station-to-mobile link). A first-order Markov model is used to describe the correlation in the packet success/failure process on a Rayleigh-fading channel. The analytical results obtained through the first-order Markov approximation of the channel are compared to those obtained from an independent and identically distributed (i.i.d.) channel model. The Markovian-fading channel model is shown to provide better performance results than the i.i.d. channel model. Simulations show that a first-order Markov approximation of the Rayleigh-fading process is quite accurate. An enhanced version of the access protocol to take advantage of the memory in the fading channel behavior is proposed and analyzed. The effect of retransmission of erroneous data packets and propagation delay on the throughput is also analyzed. It is shown that the access protocol with an error detect (ED) feature is efficient in slow fading (e.g., pedestrian user speeds), whereas a retransmission protocol is more efficient in fast fading (e.g., vehicular user speeds)     

Wave packets, group velocities, and rays in lossy media revisited

A study prompted by discussions of the group velocity concept in absorptive media and the correctness of Maxwell's equation is presented. A simple model for a wave packet train is obtained by beating two waves with adjacent frequencies and wavenumbers. By extending frequencies and propagation vectors into the complex domain, it is shown that a consistent definition of real group velocity in absorptive media can be stated. Numerical examples are displayed, and theoretical and experimental aspects are briefly discussed. An extension of Hamilton's ray equations for absorptive media is given. This formalism is used for numerical ray tracing in an absorptive ionosphere. The arguments show that a physically meaningful definition of the group velocity in absorptive media is consistent with the Fermat principle and the special relativistic limitation on the speed of light