## 4 Propagation and Challenges of the Wireless Communication
We can compute the breaking point according to the equation:  
\[BP=\frac{D^{2}}{\lambda}\,[\text{m}] \tag{4}\]  
\[(D:\text{ Diameter of the tube}/\text{tunnel.})\]  
In Figure 4, we can see an example of measurements at two different frequencies on subway round tunnel of 4 m diameter at 2.5/5.7 and 24 GHz [28], and, in Table 5, we have the results of BP and path loss for different frequencies. In this case, the tunnel walls are made of concrete with a dielectric constant of \(\epsilon_{r}=5\) and low conductivity (\(\sigma=10^{-3}\)). We can see that BP distance becomes larger as frequencies increase and path losses decrease also with frequency. Thus, the use of high frequencies is better for propagation in confined environments like tunnels. In metal vacuum tubes, we expect even lower losses due to the permittivity and conductivity of the walls. In Figure 5, we can see two simulation made with a propagation simulator [29] for a steel tube of 4 m diameter, straight 1000 m length with a capsule in the middle and curved 3000 m. The frequency of the site antenna 2.5 GHz with a transmit power of 0 dBm and the parameters of the simulation are given in Table 5. In this case, we can see that the losses from the BP (133 m) to the capsule (500 m) the received power changes from \(-60\) dBm to \(-75\) dBm so that losses are 4 dB/100 m, similar to that in subway tunnels. In addition, 23 dBm power at 2.5 GHz could have a cell. \begin{table}
\begin{tabular}{l l l l l l} \hline
**Object** & **Material** & **Relative Permeability** & **Conductivity** & **Length** & **Diameter** \\ \hline
**Tube** & Steel & \(\sim\)100 & \(0.2\times 10^{7}\) S/m & 1000 m & 4 m \\
**Capsule** & Carbon Fiber & 1 & \(10^{6}\) S/m [8] & 33 m & 3 m \\ \hline \end{tabular}
\end{table} 
Table 4: Parameters of the simulation. Figure 4: Measurements of Path Losses (PL) at 2.5, 5.7, and 24 GHz, round subway tunnel \(D\) = 4 m diameter. \begin{table}
\begin{tabular}{l l l l} \hline
**Frequency** & **BP** & **Path Loss (L\({}_{mm}\))** & **PATH LOSS (L\({}_{11}\))** \\
**[GHz]** & **[m]** & **before BP [dB/100 m]** & **after BP [dB/100 m]** \\ \hline
2.5 & 133 & 21.0 & 5.3 \\
5.7 & 304 & 10.5 & 4.1 \\
24 & 1280 & 6.3 & 3.9 \\ \hline \end{tabular}
\end{table} 
Table 5: Calculation of BP and path losses for different frequencies in concrete tunnel of 4 m diameter. In the straight tunnel, we can see the path losses from the BP (133 m) to the capsule (500 m), the received power changes from \(-60\) dBm to \(-75\) dBm so that losses are 4 dB/100 m, similar to that in subway tunnels. In addition, 23 dBm power at 2.5 GHz could have a cell. In the curved tunnel, we can see that there is a high attenuation (50 dB) of the signal due to the shadowing effect of the capsule, so that, on a real network, there must be a strong overlap of the coverage of two neighborhood antennas. With this results of path loss, a system like 802.11 xx with a radius of up to 2.5 km and a 5G system working in mmW band (28/34 GHz) with 50 dBm Isotropic Radiated Power could reach a 3.5 km cell radius, minimizing the need of handovers and allowing a good overlap of cell radius. **Handover:** is necessary to maintain the connection active while moving from one cell to another. Due to the ultra-high velocity, there is a very short time to perform the handover as this is one of the key points of the communications system, and it must be minimized. The handover times of current HSR using the GSM-R system are on the order of 300 ms and requires six seconds of signal overlap of two cells. These requirements limit a \"hard\" handover to a top speed of 400 km/h, and this is absolutely unacceptable for Hyperloop capsules. Therefore, it is necessary to use soft handovers and having the capsule continuously linked to two neighboring cells will have a moderate overlap.