# Scaled Modeling and Measurement for Studying Radio Wave Propagation in Tunnels
## 5 Scale Model Experiments in the SHF and the MMWs Regime  
As field experiments in an underground tunnel often prove to be difficult, an experiment in a miniaturized environment in which physical properties are maintained is preferable. Scaling models have previously been shown to be useful for radio wave propagation in tunnels [5; 6; 13]. In our case, we used a subscale 1/10 th tunnel model, as summarized in Table 2.  
Figure 5: Normalized results of the field experiments and simulation as a function of distance in a rectangular tunnel for different frequencies of (**a**) UHF 1 GHz, (**b**) UHF 2.4 GHz, and (**c**) SHF 10 GHz. The system for the scaled experiments was based on the schematics presented in Figure 4b. For the W-band experiment at a frequency of 94 GHz, the transmitter \(T_{x}\) consisted of a signal generator outputting a CW signal at a constant power of 17 dBm. The CW signal was fed to a standard W-band (75-110 GHz) horn antenna (QUINSTAR QGH-WPRR00), with cross-section of 25 \(\times\) 20 mm\({}^{2}\) and gain of 24 dB. The receiving system \(R_{x}\) had a detector with an RF gain of 10 dB and a receiving antenna is the same as the transmitting one. For the X-band experiment at a frequency of 10 GHz, we used a homemade horn antenna with cross-section of 45 \(\times\) 25 mm\({}^{2}\) and 10.8 dBi gain, at the transmitter. The receiving homemade horn antenna was of 15.7 dBi gain (cross-section of 55 \(\times\) 50 mm\({}^{2}\)). It was connected to the power detector sensor. The antenna data are summarized in Table 3.  
For both W-band and X-band measurements, the antennas were attached to the same adjustable stands. The transmitter antenna remains stationary, while the receiving one was moved along a rail installed inside the scaled tunnel model, as shown in Figure 6b. The signal generator and the receiving system were both located outside of the tunnel model. The horn antennas collect all rays arriving at their aperture, and the power measured is a result of a coherent summation of all contributing rays. Knowing the antenna aperture, the corresponding gain is considered in the multi-ray simulation. A sub-scale tunnel-like model was built. The scale model is presented in Figure 6. It represents a 1/10 th down-scaled version of the real pedestrian tunnel and was constructed using 4.8 m plates made of Formica, with straight, smooth walls, and a rectangular shape with height \(H=0.2\) m and width \(W=0.1\) m. The sub-scaled ratio was chosen to fit the experimental setup in a lab environment, and the frequency was up-scaled corresponding with the dimensions of the tunnel by the same ratio. Although the electromagnetic properties of the real tunnel were not scaled exactly in the lab model, the impact of this mismatching proved to be negligible. The transmitting and receiving antennas were placed at the center of the down-scaled tunnel cross-section. The measurements started at the respective far field at a distance between the antennas from 0.4 m up to 4.5 m. The receiving antenna was moved in steps of 2 cm while carefully maintaining the antennas position relative to the walls. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Band** & **UHF** & **SHF** & **SHF** & **W-Band** \\  & **Real Tunnel** & **Scaling for 1 GHz** & **Real Tunnel** & **Scaling for 10 GHz** \\ \hline Frequency (GHz) & \(1\) & \(10\) & \(10\) & \(94\) \\ Wavelength (cm) & \(\lambda=29.98\) & \(\lambda/S=2.998\) & \(\lambda=2.998\) & \(\lambda/S=3.19\) \\ Width (m) & \(W=1\) & \(W/S=0.1\) & \(W=1\) & \(W/S=0.1\) \\ Height (m) & \(H=1.85\) & \(H/S\approx 0.2\) & \(H=1.85\) & \(H/S\approx 0.2\) \\ Antenna Aperture & \(\Theta_{v}\cong 70^{o}\) & \(\Theta_{v}\cong 30^{o}\) & \(\Theta_{v}\cong 70^{o}\) & \(\Theta_{v}\cong 30^{o}\) \\ (deg) & \(\Theta_{h}\cong 30^{o}\) & \(\Theta_{h}\cong 8^{o}\) & \(\Theta_{h}\cong 30^{o}\) & \(\Theta_{h}\cong 8^{o}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the real tunnel and its subscale model.