Xingqi Zhang

A High-Accuracy ADI Scheme for the Vector Parabolic Equation Applied to the Modeling of Wave Propagation in Tunnels

The vector parabolic equation has been widely used to model radio wave propagation in tunnels. For its numerical solution, the Crank-Nicolson as well as the Alternating Direction Implicit (ADI) methods have been employed, with the latter being significantly faster than the former. This letter focuses on a modified ADI method, namely a Mitchell-Fairweather scheme. Applied to the vector parabolic equation, this scheme significantly improves the accuracy of the original ADI formulation while retaining its computational efficiency. The relative advantages of the Mitchell-Fairweather scheme are demonstrated in a case study involving an actual tunnel geometry.

A Hybrid Ray-Tracing/Vector Parabolic Equation Method for Propagation Modeling in Train Communication Channels

In recent years, various techniques have been applied to modeling radio-wave propagation in railway networks, each one presenting its own advantages and limitations. This paper presents a hybrid channel modeling technique, which combines two of these methods, the ray-tracing (RT) and vector parabolic equation (VPE) methods, to enable the modeling of realistic railway scenarios including stations and long guideways within a unified simulation framework. The general-purpose RT method is applied to analyze propagation in complex areas, whereas the VPE method is reserved for long and uniform tunnel as well as open-air sections. By using the advantages of VPE to compensate for the limitations of RT and vice versa, this hybrid model ensures improved accuracy and computational savings. Numerical results are validated with experimental measurements in various railway scenarios, including an actual deployment site of communication-based train control (CBTC) systems.

Error Analysis and Comparative Study of Numerical Methods for the Parabolic Equation Applied to Tunnel Propagation Modeling

Parabolic equation (PE) methods have been widely applied to the modeling of wireless propagation in tunnel environments. However, the relevant literature does not include concrete guidelines for the choice of the parameters of these methods and the tradeoffs involved. This paper provides a comprehensive analysis of the two sources of error that arise when PE methods are employed for the modeling of radio-wave propagation scenarios: the well-known numerical dispersion error stemming from the finite-difference solvers for PE and the approximation error stemming from the use of PE for the solution of wave propagation problems that are subject to Maxwells equations. The analysis is performed for four methods, three of which have been already used in PE-based propagation studies, namely, the Crank-Nicolson (CN) scheme, the alternative-direction-implicit (ADI) method, and its locally one-dimensional (LOD-ADI) version. The fourth method is the Mitchell-Fairweather (MF)-ADI scheme that has been recently shown to be a promising alternative technique for tunnel propagation modeling. The proposed method leads to robust criteria for the choice of spatial discretization in realistic propagation scenarios, as shown via numerical examples.

Efficient propagation modeling in railway environments using a hybrid vector parabolic equation/ray-tracing method

This paper presents a hybrid channel modeling technique, which combines the ray-tracing (RT) and vector parabolic equation (VPE) methods using advantages of VPE to compensate for the limitations of RT and vice versa. The proposed method enables the modeling of realistic railway scenarios including stations and long guideway tunnels within a unified simulation framework. Results are validated with measured data from an actual deployment site of communication-based train control systems.

Calibration of a 3-D ray-tracing model in railway environments

A three-dimensional ray-tracing model is calibrated using measured data from railway environments. First, the input geometry is extracted by systematically adding incremental details that result in significant deviations in the simulated received power. Then, sensitivity analysis is performed to ascertain optimal values for the uncertain input parameters. The input parameters obtained by this procedure lead to a good agreement between the simulated and measured data, highlighting the importance of the calibration process.

Modeling and optimization of coverage in London Underground Subway Tunnels

A semiautomatic model extraction procedure is used together with an image-based ray tracer to study the radio coverage in London Underground Subway Tunnels. The simulated received signal strength is compared with that obtained via measurements. The prospects of optimizing the location of access points to improve the coverage in the tunnel is also investigated.

A Gaussian beam approach for embedding antennas into vector parabolic equation based propagation models

Vector parabolic equation (VPE) offers a very efficient methodology for high fidelity modeling of wave propagation in complex environments. While the propagation environment can be discretized and represented in detail, the representation of radiating sources (such as transmitting antennas) requires the calculation, analytical if possible or numerical via another method such as ray-tracing, of the fields that the sources generate on the initial plane of the VPE model. These initial conditions are necessary for subsequently applying VPE. Addressing this significant limitation of VPE methods, we introduce a technique that allows one to directly embed antennas into a VPE mesh, via a Gaussian beam approximation of their radiated fields. Hence, the initial conditions for VPE are generated for practical antenna patterns, without invoking other techniques and with no compromise on the inherent efficiency of VPE. Comparisons of numerical results to experimental data demonstrate the validity and usefulness of the technique.

A hybrid vector parabolic equation/ray-tracing propagation modeling technique for rail transportation systems

The deployment of modern communication-based train control (CBTC) systems along a guideway requires a careful study of the radio-wave propagation characteristics of the corresponding wireless channel. Carrying out this study via experimental means can be both expensive and time consuming, considering that current rail transportation networks extend over tens to hundreds of kilometers. Hence, research on numerical techniques that can assist and accelerate, though not replace, the experimental survey of a guideway as a communication channel, is as timely as ever, notwithstanding the large volume of pre-existing work on the subject.

Spatially-filtered FDTD subgridding for ground penetrating radar numerical modeling

Subgridding schemes are often implemented in the standard finite-difference time-domain (FDTD) method especially when fine geometric features and/or media with a high relative permittivity need to be modeled. In this paper, we propose an FDTD subgridding scheme which employs spatial filtering, to numerically model ground penetrating radar (GPR), using time steps well beyond the FDTD stability limit. To demonstrate the accuracy and efficiency of the proposed approach, comparisons of its numerical modeling results with the standard FDTD method and a previously proposed subgridding scheme are provided.

A Gaussian Beam Approximation Approach for Embedding Antennas Into Vector Parabolic Equation-Based Wireless Channel Propagation Models

Vector parabolic equation (VPE) methods have been widely applied to the modeling of radio-wave propagation in tunnel environments, offering high computational efficiency and fidelity. While the propagation environment can be discretized and represented in detail, the representation of radiating sources (such as transmitting antennas) requires the calculation, analytical if possible or numerical via another method such as ray-tracing (RT), of the fields that the sources generate on the initial plane of the VPE model. These initial conditions are necessary for subsequently applying VPE. However, the solutions offered so far compromise either the accuracy or the efficiency of VPE. For example, generating the initial conditions for VPE through RT adds significant computational overhead to the typically fast VPE solver. To address this significant limitation of VPE methods, we introduce a technique that allows one to directly embed antennas into a VPE mesh, via a Gaussian beam approximation of their radiated fields. Hence, the initial conditions for VPE are generated for practical antenna patterns, without invoking other techniques and with no compromise on the inherent efficiency of VPE. Concrete guidelines on how to choose parameters for Gaussian beams are provided. Numerical results are compared to experimental measurements in various tunnel scenarios, demonstrating the validity and usefulness of the technique.