Wave Propagation In Tunnels Research Articles

Comparative analysis of finite‐difference and split‐step based parabolic equation methods for tunnel propagation modelling

AbstractRadio wave propagation modelling in railway environments is of fundamental importance in designing reliable train communication systems. Parabolic equation (PE) methods have been widely applied to the modelling of wave propagation in tunnels due to their high computational efficiency and fidelity. The finite‐difference parabolic equation (FDPE) and the split‐step parabolic equation (SSPE) methods are two commonly used approaches to solve PE numerically. However, the relevant literature is still missing a comprehensive study of their performance, including the selection of parameters such as discretisation steps and the tradeoffs involved in terms of their accuracy and efficiency, especially as current wireless systems shift to high frequencies. In this study, a systematic analysis of the error and computational complexity of the FDPE and SSPE methods for radio wave propagation modelling in tunnels is provided. Guidelines for the choice of their parameters are provided, and their performance is demonstrated through both numerical examples and experimental measurements in actual tunnel cases.

Generalisable convolutional neural network model for radio wave propagation in tunnels

AbstractPropagation models are essential for the prediction of received signal strength and the planning of wireless systems in a given environment. The vector parabolic equation (VPE) method has been widely applied to the modelling of radio wave propagation in tunnels. However, carrying out simulations for large‐scale environments is still computationally expensive. A convolutional neural network (CNN)‐based propagation model, which can provide high‐fidelity received signal strength prediction based on results from low‐cost VPE simulations, is proposed. A thorough study of the generalisability, including both interpolation and extrapolation capabilities, of the proposed CNN model is conducted. It is found that the proposed model can achieve significant computational savings while maintaining acceptable accuracy, and its performance is validated in both simulations and actual tunnel cases.

Efficient physics‐based recurrent neural network model for radio wave propagation in tunnels at 2.4 GHz

AbstractThe vector parabolic equation (VPE) method has been widely applied to the modelling of radio wave propagation in tunnel environments. However, dense spatial discretizations are generally required for VPE simulations to achieve acceptable accuracy. This results in high computational costs for large‐size tunnels and high‐frequency wireless systems. This letter presents an efficient physics‐based recurrent neural network (RNN) model for modeling radio wave propagation in tunnels. The proposed RNN‐based model can leverage coarse‐mesh VPE to generate high‐fidelity received signal strength and achieve significant computational savings. The validity of the proposed approach is demonstrated against fine‐mesh VPE simulations in various tunnel cases.

Scaled Modeling and Measurement for Studying Radio Wave Propagation in Tunnels

The subject of radio wave propagation in tunnels has gathered attention in recent years, mainly regarding the fading phenomena caused by internal reflections. Several methods have been suggested to describe the propagation inside a tunnel. This work is based on the ray tracing approach, which is useful for structures where the dimensions are orders of magnitude larger than the transmission wavelength. Using image theory, we utilized a multi-ray model to reveal non-dimensional parameters, enabling measurements in down-scaled experiments. We present the results of field experiments in a small concrete pedestrian tunnel with smooth walls for radio frequencies (RF) of 1, 2.4, and 10 GHz, as well as in a down-scaled model, for which millimeter waves (MMWs) were used, to demonstrate the roles of the frequency, polarization, tunnel dimensions, and dielectric properties on the wave propagation. The ray tracing method correlated well with the experimental results measured in the tunnel as well as in a scale model.

Efficient solution of Noye–Hayman implicit finite‐difference method for modelling wave propagation in tunnels

Parabolic equation models discretised with the finite-difference method have been a research topic for a long time. Through the simulation of electromagnetic wave propagation characteristics in typical scenarios, it is pointed out that the fast algorithm needs to be developed for the solution of two-level Noye–Hayman (NH2) implicit method to meet the accuracy and computational requirements of electromagnetic wave propagation problems in three-dimensional environments. In this Letter, hierarchical skeletonisation is used for an efficient inversion of three-dimensional parabolic equation discretised by the NH2 implicit method which is the modification of conventional Crank–Nicolson (CN) method. Numerical results show that the NH2 implicit method is more accurate than the CN method at no additional cost for a given numerical example.

Statistical Modeling of Electromagnetic Wave Propagation in Tunnels With Rough Walls Using the Vector Parabolic Equation Method

The vector parabolic equation (VPE) method is a very efficient methodology for high-fidelity modeling of electromagnetic wave propagation. While the VPE has been widely applied to model wave propagation in tunnel environments, most of the work involves only smooth surface walls and leaves out of consideration scenarios with rough surfaces. Although it is often disregarded, surface roughness, as an additional source of path loss, is very important in the accurate modeling of tunnel propagation. This paper presents a rigorous approach to incorporate surface roughness into VPE-based models. To that end, the rough surface is first parameterized using a Karhunen–Loeve expansion and then embedded into the VPE. The proposed approach can be applied to realistic tunnel geometries with arbitrary cross sections and curvature variations. Validations are provided by comparisons with experimental data in various practical tunnel cases.

A Hybrid Ray and Graph Model for Simulating Vehicle-to-Vehicle Channels in Tunnels

Wave propagation in tunnels for vehicle-to-vehicle (V2V) communications scenarios is characterized by multiple diffuse reflections on tunnel surfaces as well as specular reflections on other objects inside the tunnel, leading to a nonstationary fading process. Such a fading process is difficult to model by ray tracing (RT), requiring a prohibitively high computational complexity due to the large number of diffuse reflections. In this paper, we propose two new ideas for modeling diffuse reflections in nonstationary scenarios: 1) We partition the nonstationary fading process into multiple stationarity regions with a given extent in time and frequency for which approximate wide-sense stationarity can be assumed; 2) we propose a hybrid model, tightly interlinking RT with a propagation graph, such that vertices for the propagation graph are obtained from interaction points calculated by RT for each stationarity region. We compare our hybrid model with measurement data in terms of the time-variant power-delay and the Doppler-power spectral-density as well as the root-mean square delay- and Doppler-spread. This analysis shows, that our hybrid model is the first numerical simulation model that is able to model diffuse reflections inside a tunnel with correct nonstationary (i.e., time-variant) temporal correlation for a nonstationary V2V communication link.

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.

Complete Propagation Model in Tunnels

The wave propagation in tunnels does not only depend on the carrier frequency and properties of the tunnel, but also differs along with the distance between transmitter (Tx) and receiver (Rx). This letter presents a complete structure and model for propagation in tunnels. Compared to existing models, the complete model unifies different academic viewpoints, reveals all possible propagation mechanisms, and localizes all the dividing points between every two adjacent propagation mechanism zones. When the user is close to the Tx, the propagation is dominated by the free-space mechanism, then the multimode mechanism is established. Afterwards, when the high-order modes have been largely attenuated, the fundamental-mode guided propagation is dominant. Finally, when the user is extremely far away, the waveguide effect vanishes because of attenuation of reflected rays. Measurements and simulations validate the model. This complete structure and model can be essential to establish a comprehensive understanding of the propagation in tunnels and can be applied for network planning and interference analysis of advanced communication systems.

An ADI-PE Approach for Modeling Radio Transmission Loss in Tunnels

Alternate direction implicit (ADI) method is used to study radio wave propagation in tunnels using the parabolic equation (PE). We formulate the ADI technique for use in tunnels with rectangular, circular and arched cross sections and with lossy walls. The electrical parameters of the lossy walls are characterized by an equivalent surface impedance. A vector PE is also formulated for use in tunnels with lossy walls. It is shown that the ADI is more computationally efficient than the Crank Nicolson method. However, boundary conditions become more difficult to model. The boundary conditions of the ADI intermediate planes are given the same boundary conditions as the physical plane and the overall accuracy is reduced. Also, when implementing the ADI in tunnels with circular cross sections the order at which the line by line decomposition occurs becomes important. To validate the ADI-PE, we show simulation results for tunnel test cases with known analytical solutions. Furthermore, the ADI-PE is used to simulate real tunnels in order to compare with experimental data. It is shown that the PE models the electric fields most accurately in real tunnels at large distances, where the lower order modes dominate.

Numerical Analysis of Effect of Water on Explosive Wave Propagation in Tunnels and Surrounding Rock

Abstract Based on the application of practical engineering, propagation processes of explosive waves in rock with water well and tunnel are simulated by ANSYS/LS-DYNA software. The evolution of damage in rock is presented. The effect of water on the damage of the concrete slab in a tunnel is compared with damage inflicted without water. The numerical simulation illustrates that water plays an important role in the evolution of damage of the concrete slab in a mine tunnel. In the presence of water in the rock the concrete slab is damaged more severely than without water in rock. The effect of water location in the rock is also considered. It is found that the concrete slab in the tunnel shows various degrees of damage as a function of the different locations of water. Attenuation laws of stress waves over time-space in rock with water are also obtained. Numerical results indicate that, under blast loading, there are three zones in the rock: a crushed zone nearby the explosive charge, a damaged zone and an elastic zone. The conclusions of numerical analysis may provide references for blasting designs and structure protection.

Wave propagation in tunnels in a MIMO context—a theoretical and experimental study

MIMO (Multiple-Input Multiple-Output) techniques, based on multiple antennas at both the transmitting and receiving sites, use multipath propagation to transform the overall channel into numerous independent virtual channels. However, when the link is made in a long tunnel, the number of reflecting objects between, or near, the transmitter and the receiver is often quite low. In addition, due to the large transverse dimensions of the tunnel compared to the wavelength, the tunnel acts like a lossy oversized waveguide. In such situations, the concept of spatial diversity must be replaced by the concept of modal diversity. This article uses theoretical and experimental results to show the conditions in which MIMO techniques allow the ergodic capacity of the channel to be increased. To cite this article: M. Lienard et al., C. R. Physique 7 (2006).

Modeling radio wave propagation in tunnels with a vectorial parabolic equation

To study radio wave propagation in tunnels, we present a vectorial parabolic equation (PE) taking into account the cross-section shape, wall impedances, slowly varying curvature, and torsion of the tunnel axis. For rectangular cross section, two polarizations are decoupled and two families of adiabatic modes can be found explicitly, giving a generalization of the known results for a uniform tunnel. In the general case, a boundary value problem arises to be solved by using finite-difference/finite-element (FD/FE) techniques. Numerical examples demonstrate the computational efficiency of the proposed method.

SBR image approach for radio wave propagation in tunnels with and without traffic

We propose a deterministic approach to model the radio propagation channels in tunnels with and without traffic. This technique applies the modified shooting and bouncing ray (SBR) method to find equivalent sources (images) in each launched ray tube and sums the receiving complex amplitude contributed by all images coherently. In addition, the vector effective antenna height (VEH) is introduced to consider the polarization-coupling effect resulting from the shape of the tunnels. We verify this approach by comparing the numerical results in two canonical examples where closed-form solutions exist. The good agreement indicates that our method can provide a good approximation of high-frequency radio propagation inside tunnels where reflection is dominant. We show that the propagation loss in tunnels can vary considerably according to the tunnel shapes and the traffic inside them. From the results we also find a "focusing" effect, which makes the power received in an arched tunnel higher than that in a rectangular tunnel. Besides, the deep fading that appears in a rectangular tunnel is absent in an arched tunnel. The major effect of the traffic is observed to be the fast fading due to the reflection/obstruction of vehicles. Additional considerations, such as time delay, wall roughness, and wedge diffraction of radio wave propagation in tunnels are left for future studies.

Finite‐volume/time‐domain analysis of electromagnetic wave propagation in two‐dimensional tunnels with fundamental junctions

AbstractThe problem of electromagnetic wave propagation in tunnels with branches and bends, such as those that would be found in an underground shopping center, has been analyzed with the finite‐volume/time‐domain (FV‐TD) method. The FVTD method is based on difference equations discretized by a volume integration of Maxwell's equations for arbitrarily small polygonal cells. In this method, the medium constants within the infinitesimal cell are constant and their values differ from cell to cell. Therefore, this method can easily handle the boundary value problem with an arbitrary shape that contains inhomogeneous media. In homogeneous media, the FVTD method and the finite‐difference/time‐domain (FDTD) method are equivalent in the Descartes coordinate system. In one application of the FVTD method, numerical calculations were made for tunnel structures that are typically difficult to analyze. To prove the usefulness of the FVTD method, a microwave simulation experiment was done. The numerical and experimental values were shown to agree well.

Theoretical and experimental approach of the propagation of high frequency waves in road tunnels

Characterization of high frequency electromagnetic wave propagation in tunnels has important applications in the field of mobile communication. In long tunnels, the amplitude of the electric field radiated by a retransmitting antenna can be easily calculated from ray theory. However, for short tunnels, one of the most critical points is either the radiation towards free space of a mobile station emitting in the tunnel or, on the contrary, the penetration of an external wave inside the tunnel. This coupling between the inside and the outside is treated through the uniform theory of diffraction. By comparing theoretical and experimental results, it is shown that this theory leads to adequate prediction of the field variation and allows the authors to point out the influence of parameters, such as the position of the mobile in the tunnel and the influence of the angle of incidence, on the entrance plane of an incoming external wave.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

EM propagation in tunnels

Various aspects of electromagnetic wave propagation in tunnels and of radio communication in such media are reviewed. A quantitative description is given for propagation in empty tunnels and in tunnels containing axial conductors or leaky feeders. The limitations of such simplified approaches are stressed. Quantitative studies of these phenomena are then reviewed. Engineering considerations are briefly mentioned. Attention is drawn to mode conversion techniques and to the multimode operation of systems. It is concluded that the theoretical aspects of EM wave propagation in tunnels are currently well understood, although work remains to be done on wideband and microwave communication systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>