## 4 Propagation and Challenges of the Wireless Communication  
The special characteristics of the Hyperloop tube and ultra-high-speed capsule impose numerous challenges on the design and evaluation of the capsule to ground wireless communication systems [8]. Nevertheless, the high mobility and fully enclosed vacuum tube wall also provide a continuous environment, with some similarities to railway tunnels that can be exploited to facilitate system designs and to improve system performance. The key challenges for the design of capsules wireless communication are listed as follows:  
* Propagation: fully guided in a metal tube with high conductivity. * Doppler shift--extremely high Doppler shift especially at microwave frequencies can cause significant variation of the received signal. * Handover--high speeds make it difficult and virtually impossible with current technology and network design. MAC layer of the wireless communication system needs to be modified. * Delay Spread: can be very variable due to the all-metal steel and carbon fiber structure. Must be carefully characterized. Figure 3: Communication network. * Penetration losses: are high although design or access and emergency doors and other connections of the tube can reduce it. * MIMO capabilities are very limited as happens in HSR environments. Propagation characteristics in the tube: the knowledge of the wireless channel that has a close relationship with propagation scenarios is the fundamental basis. The environment is similar to traditional railway tunnel scenarios [24] with the difference that the Hyperloop is operating inside a fully enclosed metal tube wall resulting in a special propagation environment for wireless signal that has a guided propagation with a high pass response with potential low losses at high frequencies. From the aspect of guided propagation, the concept of \"modal propagation\" can be used to analyze the propagation characterization of radio waves in the tube [25]. Based on this theory, the high-order mode gradually decays and disappears as the distance between transmitter and receiver increases only leaving the low-order mode. Thus, we have two propagation zones and a breakpoint [26] (BP) that can be computed to distinguish both zones. At lower frequencies, attenuations are higher in the region close to the antenna where multimodal propagation is dominant. Losses become lower when we pass the BP, and there is only propagation of the dominant mode. The attenuation losses of the different modes (\(\alpha_{mn}\)) can be computed with the following equation for modal analysis [27]:  
\[\alpha_{mn}=\frac{2}{a}\cdot\left(\frac{mc}{2 af}\right)^{2}\cdot\text{Re} \left[\frac{1}{\sqrt{\epsilon-1}}\right]+\frac{2}{b}\cdot\left(\frac{nc}{2 bf} \right)^{2}\cdot\text{Re}\left[\frac{\epsilon}{\sqrt{\epsilon-1}}\right]\,[ \text{Np}/\text{m}] \tag{1}\]  
where \(f\) is the frequency, and \(a/b\) (width/height) are the dimensions of the free area inside the tube that can be approximated as \(a=b=D\) (4 m for Hyperloop). Then, \"\(m\)\" and \"\(n\)\" are the index of the mode and \"\(e\)\" is the complex permittivity of the tube walls defined as :  
\[\epsilon=\epsilon_{r}-i\sigma\lambda k \tag{2}\]  
where \(\epsilon_{r}\) is the real permitivity, \(\lambda\) is the wavelength, \(\sigma\) is the conductivity of the walls (S/m), \(c\) is the speed of light in vacuum and \(k=\frac{n_{0}c}{2\pi}\approx 60.0\)\(\Omega\) is a newly introduced constant (\(\mu_{0}\): Vacuum permeability). Then, using steel on the walls with high conductivity (Table 4), we can compute propagation losses as:  
\[L_{nm}=8.68\cdot\alpha_{mn}\,[\text{dB}/\text{m}] \tag{3}\]  
Thus, for high frequencies and large tube diameter, we have hundreds of modes \((m,n)\) propagating with high losses on the region close to the antenna. As attenuation increases with the order of the model \((m+n)\), far from the antenna, we have only low order mode (1,1) propagation with low losses. These two regions can be distinguished as defining a \"BreakPoint\" [24].