# Radio Wave Propagation and WSN Deployment in Complex Utility Tunnel Environments +
## 3 Radio Channel Analysis
### Simulation Results  
Once the calibration and verification of the 3D-RL algorithm for this singular scenario was achieved, the input optimal parameters, in terms of angular resolution and number of reflections, were applied in the simulations of the underground utility scenario. Large and small-scale radio wave propagation analyses were performed with the aid of simulations in order to provide a general signal propagation understanding within this complex and singular environment. The tunnel cross-sections have an important impact on the signal attenuation in this type of environment, as it is stated in [38]. In this sense, typical tunnel cross-sections can be classified in rectangular or circular shapes, where the tunnel width and height need to be considered when calculating the radio signal attenuation. Nevertheless, it has been shown in the literature [39; 40] that cross-section dimensions within tunnels (i.e., different heights and widths of the tunnels) have a higher impact on the signal attenuation than distinct shapes, such as rectangular or circular. Therefore, the methodology, signal propagation analysis and WSN deployment presented in this work could potentially also be applied to cylinder tunnels, as long as tunnel cross-sections are of similar dimensions than the ones presented in this work. In fact, the cylindrical shape of the tunnel will generate slightly lower multipath propagation within the environment, as the number of reflections and diffractions within the surface of the tunnel will be lower. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Case 1** & **Case 2** & **Case 3** & **Case 4** & **Case 5** & **Case 6** \\ \hline Mean Error (dB) & 2.95 & 1.34 & 2.74 & 5.24 & 5.24 & 1.06 \\ Standard Deviation (dB) & 16.14 & 5.90 & 16.56 & 14.29 & 14.29 & 6.14 \\ Computational Time (s) & 52,664 & 78,459 & 4852 & 883 & 1656 & 265,320 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison between different simulation cases. Figure 5: Comparison of different cases of simulation and measurement results for the service tunnel section under analysis. Large scale propagation analysis was performed by means of the RF power distribution for the whole volume of the scenario. For that purpose, the transmitter antenna was placed at the beginning of the tunnel model, at a height of 2 m (represented by a red triangle in Figure 6). The same simulation parameters as in the experimental measurements were considered for the operational frequency and the transmitted power: 868 MHz and \(-\)10 dBm, respectively, emulating a ZigBee or LoRaWAN system at this specific frequency. Figure 6 shows the obtained RF power distribution estimations for the XY bidimensional plane at a height of 2 m (the same height as the transmitter antenna). It can be seen, the variability of received power along the distance, showing some spatial points with lower received power in the final part of the tunnel. The service trays on the sides of the tunnel generated a nonhomogeneous variation of the signal distribution levels along the tunnel distance. To gain insight into the multipath behavior of the considered scenario, due to the rough surfaces of the walls and the service trays located in the tunnel, the power delay profile (PDP) is shown in Figure 7 for a specific point of the scenario, showing the high multipath trajectories within a time span of 200 and 2500 ns. The high multipath propagation within the environment can lead to signal fading in some spatial locations, which can lead to areas with a lack of coverage within the tunnel if the network design is not adequately performed. In addition, another parameter that can grossly quantify the multipath channel is the root mean square delay spread (RMS DS), referred also as \(\sigma_{\tau}\), which shows the effects of dispersion and is determined from the PDP.