**1. Introduction**

Railway, roadway and mine tunnels, buildings, and warehouses are some examples of confined environments, in which electromagnetic wave propagation has to be investigated

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for communication channel characterization. In this paper, we shall focus on tunnel environments. The prediction and characterization of the radio-wave propagation is needed to optimize the system performances.

Confined environments are complex real-life electromagnetic (EM) problems. Several techniques and methods are used to study the radio-wave propagation or to design antennas to achieve some good performance. Experimental techniques, analytical methods (exact solutions), numerical methods (approximate solutions), asymptotic methods (approximate high-frequency expansions of Maxwell's equations), and approximate techniques (approximate solutions applicable for certain types of electromagnetic problems) are among the most commonly used techniques in confined structures. Experiments might be expensive and time consuming. Analytical and approximate techniques are limited to some structures. In turn, asymptotic methods are mostly used to study the wave propagation in tunnels. However, in many cases, the antennas employed to provide the communication in these systems are strongly affected by its surrounding environment, affecting the performance of the system. Thus, near-field considerations have to be accounted for, which cannot be considered by these techniques. Finally, the practical utilization of numerical full-wave methods has been hampered by their large computational time compared to asymptotic methods.

With the increasing development of computers, appropriate new models and simplifications are being developed. The formulation of an efficient modal approach stemming from the fact that tunnels can be modeled by an over-sized waveguide and the *a priori* knowledge of the fields in the axial direction is presented. It allows one to have a better physical insight into wave propagation in confined environments, as well as dealing with electrically large structures like tunnels. The mode parameter determination is carried out by a full-wave time-domain method, namely, the transmission-line matrix (TLM) method.

The calculation volume has to be limited in full-wave volumic methods, and we are interested only in the fields inside the tunnel. Thus, the electromagnetic modeling of the tunnel walls, which can be lossy dielectric, is addressed. Lastly, by assimilating a confined environment to a lossy dielectric waveguides of arbitrary cross section, the mode extraction of these structures is presented. To the best of the authors' knowledge, no such model has been reported.

The chapter is structured as follows: In the first section, an overview of the principal techniques for the description of the EM wave propagation in above structures is briefly presented. In the second section, the formulation of the modal approach is described in detail. In the following section, the implementation for a simple canonical case is shown. Lastly, the numerical analysis of multimodal waveguides representative of confined environments is illustrated in a realistic rectangular tunnel. Finally, discussions and conclusions are developed at the end of the chapter.
