## 3 Implementation and Results  
The setup configuration consists of two aligned multifrequency antennas (Huber + Shuner Sencity Rail Antenna 1399.17.0122 [33]) on a metallic plane as a test bed for a train rooftop, separated by a distance of 1 m inside of an anechoic chamber (see Figure 10). The considered services of the railway rooftop antenna are mainly those included in Table 1. The FSS structure is fabricated on an FR-4 substrate of 0.8 mm thickness using conventional, low-cost printed circuit techniques. The attenuation achieved is obtained from the transmission parameter (S21) when the FSS structure is interposed between the antennas at a distance of 50 cm from each one. The S\({}_{21}\) parameter is measured with a vector network analyzer (VNA, Keysight E5071A). First, the transmission coefficient between the antennas is saved (memory), then the FSS is placed between the antennas (data) and the VNA data/memory option is applied, which allows to obtain the attenuation in dB normalized to the transmission without the FSS structure. For the measurements, the VNA was calibrated from 300 kHz to 8.5 GHz with 1601 points to achieve a high resolution. It is important to highlight that we can obtain the scale factor (\(\alpha\) = 1.2) from the previous simulations to adjust the resonant frequency without the need to fabricate neither FSS\({}_{mc}\) nor FSS\({}_{mc}\), as the main outcome of the design workflow. Only FSS\({}_{scaled}\) should be fabricated. This is performed in two sizes: 3 \(\times\) 3 and 4 \(\times\) 4, for final tuning and bandwidth analysis. The fabricated 4 \(\times\) 4 prototype FSS\({}_{scaled}\) is presented in Figure 11, and Table 2 shows the unit cell dimensions, including the distance between the cells. The scale factor is applied only to the outer resonator in order to preserve the WiFi II band filtering as much as possible. Figure 10: Experimental setup for the FSS structure measurement in an anechoic chamber. Figure 12 compares the simulated transmission coefficient of FSS\({}_{mc}\) and the measured 3 \(\times\) 3 and 4 \(\times\) FSS\({}_{scaled}\) with a good agreement, particularly for the band for which the methodology was applied. The 4 \(\times\) 4 FSS\({}_{scaled}\) achieves a maximum attenuation of 25 dB at 2 GHz but does not fully cover the rest of the target bands (grey vertical bands). The 3 \(\times\) 3 FSS\({}_{scaled}\) covers all bands under 6 dB (dashed horizontal line). The 6 dB threshold level allows the reduction of half of the distance between antennas given by the Friis equation [34], with equal system performance. This is particularly helpful when space constraints are present in vehicular technology. Figure 11: FSS\({}_{scaled}\) prototype. \begin{table}
\begin{tabular}{c c} \hline
**4 \(\times\) 4 FSS\({}_{scaled}\)** & **Dimensions (mm)** \\ \hline \(L_{s}\) & 42 \\ \(h_{s}\) & 0.8 \\ \(w\) & 1.5 \\ \(L_{d}\) & 34.8 \\ \(L_{t}\) & 9.24 \\ \(L_{g}\) & 1.2 \\ \(L_{d}\) & 3.6 \\ \(s\) & 9.12 \\ \(d\) & 7.2 \\ \hline \end{tabular}
\end{table} 
Table 2: Unit cell dimensions of the FSS\({}_{scaled}\) prototype. Figure 12: Comparison of simulated FSS\({}_{mc}\) (unit cell boundary condition) and measured FSS\({}_{scaled}\). The study examined the inclination effect of the \(3\times 3\) FSS\({}_{scaled}\) design from theta (\(\theta\)) = 0\({}^{\circ}\) to 45\({}^{\circ}\) on the horizontal plane. The findings presented in Figure 13 illustrate how the angle at which the FSS array is inclined affects the maximum attenuation that can be achieved in response to an incoming wave. It is worth noting that, despite the angle, the bandwidth remains relatively consistent in both frequency bands, achieving a 6 dB attenuation level. However, a noticeable decrease in attenuation is observed, particularly in the second frequency band.