## 3 Experimental Setup  
The measurements were performed in the frequency domain, using a Keysight Streamline USB Vector Network Analyzer (VNA) model number P9371A, as can be seen in Figure 2. A VNA measures the scattering parameters, which describe the relationship between the different ports. A network analyzer is especially useful when the effect of the network in terms of amplitude and phase need to be described. During the experiment, the complex \(S_{21}\) parameter was measured, which represents the difference in amplitude and phase between port 1, the transmitter (Tx), and port 2, the receiver (Rx). The VNA is a portable device, allowing for use in the tunnel in order to receive results as accurate as possible. The VNA parameters are detailed in Table 3.  
Figure 1: Reflected rays not arriving simultaneously at the receiver. Figure 2: Network analyzer. The transmitting antenna was connected to Port 1, which was placed at the entrance to the tunnel without movement throughout the experiment. In contrast, the receiving antenna, which was connected to Port 2, was moved along the tunnel prior to each measurement. A broadband horn antenna as shown in Figure 3 was used at both ports, as detailed in Table 4. This was done so that as much power as possible will be in the direction of the transmission, in order to intensify the reflections from the tunnel walls. Although the antenna supports a wide spectrum of frequencies, the antenna gain varies according to the frequency. The gain and antenna factor were measured in an antenna test range, the results of which can be seen in Table 5.  
In order to eliminate the uneven frequency response of the antennas, a calibration operation was activated in the VNA prior to the experiment. Thus, the VNA takes into \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameters** & **Value** \\ \hline Manufacturer & Chendgu A-INFO \\ Model & JXTXLB-10180 \\ Frequency range & 1–18 GHz \\ Gain & 11 dBi Typical \\ Polarization & Linear \\ VSWR & 2.0:1 Typical \\ H-Plane 3 dB Beamwidth & 37\({}^{\circ}\)–71\({}^{\circ}\) \\ E-Plane 3 dB Beamwidth & 39.7\({}^{\circ}\)–70\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Wide-band Horn Antenna Parameters. Figure 3: Wide-band horn antenna. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameters** & **Value** \\ \hline Manufacturer & Keysight \\ Model & P9371A \\ Frequency range & 300 kHz to 6.5 GHz \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Vector network analyzer parameters. account the frequency response of the antenna in the calculation of the S21 so that the S21 only expresses the propagation. To ensure that the measurement process performs smoothly and gives us the ability to sample the effect of the tunnel many times along the tunnel, an autonomous measuring setup was designed as shown in Figure 4 which parameters are detailed in Table 6.  
In order to perform autonomous measuring, the VNA was controlled by a PC running Standard Commands for Programmable Instruments (SCPI) coding sent from the MATLAB environment. With the help of this, there was full control over the timing of the measurement and synchronization with the distance data. Additionally, this enabled the results to be stored on the PC for later processing. In order to accurately measure the distance between the antennas, a Laser Distance Measuring Sensor was used. The distance sensor was connected to the PC via RS232 serial data connection. These serial commands were likewise sent from the MATLAB environment. The laser was placed at the entrance of the tunnel, next to the transmitting antenna. Simultaneously, with each measurement that was performed by the network, a measurement was performed by the distance sensor. In this way, coordinated measurements were obtained. With the intention of measuring the S21, it is necessary that the receiving antenna will likewise be connected to the network analyzer. Since in the experiment the receiving antenna is on the other side of the tunnel, this phenomenon was accomplished using an optical fiber.