## 4 Discussion
### Propagation Results
#### 4.1.2 Propagation in the Presence of Rain  
For the 5 GHz experiment, the snapshots in Figure 7 show the wave scattering effect produced by the rain, which can be better appreciated in the zoom presented in Figure 16. In the snapshot at \(n=6000\), it can be observed that the source is switched off, and the wavefronts are absorbed by the CPML in step \(n=8000\), while the rain continues on the right side of the computational domain. It is very interesting to note the presence of residual energy at \(n=50{,}000\) within the domain, which is not completely absorbed by the boundary conditions generated by the scattering caused by the rain interacting with the wavefronts. The latter can be corroborated by analysing the electromagnetic energy flux in the entire domain (see Figure 8).  
The scattering effect is associated with the wavelength \(\lambda=0.0599584916\) m, and the simulated droplets, in this case, are of the order of 0.012-0.024 m, so they essentially act as electromagnetic field scattering particles in the short wavelength limit [44].  
For the 25 GHz propagation experiment under the presence of rainfall, which is the core experiment of this work, Figure 13 shows how the wavefront reaches the region where the rain occurs, specifically, at snapshot \(n=50{,}000\), where its interaction with the raindrops can be observed, proving a strong absorption process. This effect can be better appreciated in the zoom made of such a snapshot, which can be observed in Figure 17. At the same time, perfectly formed wavefronts arrive at the left boundary (see Figure 13d); a visual inspectionof the right side of the domain where rain is present reveals that the vast majority of the wave has been absorbed (Figure 17). Only small, extremely thin wave beams (which have not interacted with random drops) remain, propagating towards the right boundary of the domain.  
Later, in the snapshot at \(n=70\),000, the wave source has been switched off, and the last wavefronts can be observed to be spreading within the domain (Figure 13c). Finally, for the snapshot at \(n=80\),000, all the wavefronts have been absorbed by the CPML, leaving no remaining energy in the domain (see Figure 13d). In fact, the energy flow in the whole domain can be observed in Figure 14, where it can be appreciated that the energy cannot remain constant when propagation is turned on due to the interactions between the electric field and the water droplets, generating a continuous process of energy absorption. Subsequently, when the source is switched off, the energy is rapidly absorbed by the CPML boundaries, confirming that there is no residual electromagnetic field in the domain, as can be witnessed in the domain viewers shown in Figure 15. \(E_{z}\) remains zero throughout the simulation, proving the CPML absorption.  
Analysing the results concerning the 25 GHz propagation in the presence of rain, it can be concluded that the simulated rain generates strong absorption processes of the electromagnetic waves in question. In this particular case, the characteristic length of the droplets (see Table 5) coincides with the propagated wavelength. In this way, the droplets essentially act as obstacles. These results are consistent with those reported in the scientific literature, where it has been reported that electromagnetic waves with frequencies higher than 10 GHz suffer strong attenuation in the presence of precipitation such as rain and snow [35; 36].  
Finally, it should be stated that the CPML boundary condition becomes fully effective when simulating the absorption of the energy flow for both propagation scenarios, free space and with rain, considering the found set of optimised CPML parameters. To extend this set of optimum CPML parameters to propagation frequencies farther than 25 GHz would require further numerical experiments.  
Figure 16: Zoom of the right section for the Wi-Fi rain scenario, from the snapshot at time iteration \(n=6000\) (see Figure 7b).  
Figure 17: Zoom of the right section for the 5G rain scenario.