# Radio Wave Propagation and WSN Deployment in Complex Utility Tunnel Environments +
## 2 Materials and Methods
### 3D Ray-Launching Technique  
The in-house implemented RL algorithm, based on MATLAB programming environment, was used to analyze radio wave propagation in the considered underground tunnel scenario. The main difference between RL and classical RT methods is that, in the RL technique, the principle is that rays are launched in a solid angle and the rays arriving at the receiver are considered the true path. However, in classical RT techniques, the image of the transmitter or of the receiver is calculated, to be used to find the reflected and refracted paths.  
The RL algorithm is based on geometrical optics (GO) and the geometrical theory of diffraction (GTD). To avoid the nonfield regions predicted by GO in the shadow areas, the diffracted rays are considered with the GTD and its uniform extension, called the uniform GTD (UTD). These diffracted rays are introduced to avoid the abrupt field changes and consider the proper field corrections. Electromagnetic phenomena such as reflection, refraction and diffraction are considered. The principle of the algorithm is that hundreds or thousands of rays are launched for a fixed position of the transmitter, which is an input parameter of the algorithm. The radiation pattern of the transmitter and receiver antennas can be introduced, with the aid of the elevation angle \(\theta\) and the azimuth angle \(\varphi\), considering the spherical coordinate system. Each ray has a different path in the considered scenario, and all the parameters related with its path are stored in a matrix. All the rays that achieve the receiver are considered in the calculation of the electromagnetic field at that point. The whole scenario is divided into a three-dimensional array of cuboids, with a different spatial resolution in the \(x\)-axis, \(y\)-axis and  
Figure 1: Schematic view of the structure of this work. WSN: wireless sensor network and 3D-RL: three-dimensional ray-launching.  
\(z\)-axis, depending on the specific characteristics and dimensions of the considered scenario. The basis is that, when a ray impacts an obstacle or a wall in the scenario under analysis, reflected and refracted rays are created, following [PERSON]'s law. When a ray hits an edge, a new family of diffracted rays are created, according to the UTD. The methodology is shown in Figure 2.  
As input parameters of the algorithm, the frequency of operation, number of multipath reflections and spatial and angular resolution are considered. In the simulations, the material properties of all the obstacles within the scenario are also considered, taking into account the conductivity and relative permittivity at the frequency range of operation of the system under analysis. The in-house implemented 3D-RL algorithm has already been validated in the literature for different complex scenarios for frequencies up to 6 GHz. Some scenarios that have been considered have been typical office scenarios [31; 32], sports environments [33], vehicular communications [34] or WSNs in smart cities [35]. The detailed description of the algorithm can be found in [36].