## 3 Results
### Auditorium
Figure 11: RMS delay at the auditorium, at both considered bands, moving the receiver along the central corridor: (**a**) Received by antenna 2; (**b**) by antenna 3; (**c**) by antenna 4. Taking a closer look at Table 1, it shows that the most restrictive antenna (the one with the larger value of RMS delay) is antenna \"3\", which is the one at the front. Hence the system must be designed to take that value into account. Again, the lower delay spread at 60 GHz, when compared to 40 GHz, is obvious in Table 1.  
The second computed parameter is the coherence bandwidth. At 40 GHz, the results are very similar for all three antennas, as can be seen in Figure 8.0 For the signal received by antenna \"2\" and \"4\" similar behavior is observed: A level of about 800 MHz for \(\alpha\) = 0.5 until the antennas are moved 100 cm on the rail. The reason for this large coherence bandwidth is that at short distances the main contribution is the direct one, while the ground reflection is attenuated by the antenna pattern (as seen in Figure 9). As the distance increases, the ground reflected component is received through the center of the main lobe of the antenna pattern, and the coherence bandwidth decreases drastically. Comparing those results with the ones obtained by antenna \"3\", the level of the coherence bandwidth in the latter is smaller and the decay is produced at a closer distance to the transmitter. \begin{table}
\begin{tabular}{c c c c} \hline
**Band** & **Received by Antenna “2”** & **Received by Antenna “3”** & **Received by Antenna “4”** \\ \hline
40 GHz & 7.46 & 8.64 & 5.43 \\
60 GHz & 1.51 & 2.73 & 1.83 \\ \hline \end{tabular}
\end{table} 
Table 1: RMS delay spread stays below this value (ns) 99% of the time, in the auditorium. Figure 12: _Cont._  
When looking at the results for 60 GHz in Figure 13, one can observe the increase in the mean level of the coherence bandwidth for all correlation levels. This can be explained by the reduced number of echoes, compared to the 40 GHz frequency campaign. Figure 12: Coherence bandwidth as a function of the receiver position on the rail at 40 GHz received by (**a**) antenna 2; (**b**) by antenna 3; (**c**) by antenna 4. As with the RMS delay, the percentage of the time the coherence bandwidth is above a desired threshold and is a useful metric for the design of communication systems. Here, the results for the 99 th percentile can be seen in Table 2.  
Figure 13: _Cont._  
We can observe that for a coherence level of 0.9, 60 GHz clearly outperforms 40 GHz. For lower correlation levels, that behavior is not that clear. In addition, for both frequency bands, the worst scenarios are given when receiving through antenna \"3\". Comparing the coherence bandwidth and the RMS delay spread values, it is clear that there is an inverse relation. The more replicas of the signal received, the larger the RMS delay spread and the lower the coherence bandwidth become. The mathematical relation is given by [PERSON]'s limit [14; 15] in Equation (5). \[Bc\geq\frac{\cos^{-1}\alpha}{2\pi\tau_{rms}} \tag{5}\]  
where \(Bc\) is the coherence bandwidth for a correlation level \(\alpha\) and \(\tau_{rms}\) is the RMS delay spread. Figure 14 illustrates both theoretical lower limits for the coherence bandwidth with different correlations and the results obtained by analyzing the available data and plotting them as a function of RMS delay at 60 GHz. \begin{table}
\begin{tabular}{c c c c c} \hline
**Band** & **Correlation Level** & **Received by Antenna “2”** & **Received by Antenna “3”** & **Received by Antenna “4”** \\ \hline \multirow{3}{*}{40 GHz} & 0.5 & 204 & 199 & 217 \\  & 0.7 & 132 & 132 & 144 \\  & 0.9 & 30 & 24 & 36 \\ \hline \multirow{3}{*}{60 GHz} & 0.5 & 222 & 186 & 192 \\  & 0.7 & 168 & 138 & 144 \\ \cline{1-1}  & 0.9 & 96 & 78 & 78 \\ \hline \end{tabular}
\end{table} 
Table 2: The 99 th percentile of coherence bandwidth (MHz), in the auditorium.