## 5 Conclusions  
In this work, a formulation for [PERSON]'s equations in two dimensions for the TE mode is developed, considering constitutive relations for linear, inhomogeneous, and isotropic time-dependent propagation media, in their electrical, magnetic, and conducting properties. This formulation is numerically solved by means of a conventional second-order in space and time FDTD method, coupled to Convolutional PML-type absorbing boundary conditions. Two sinusoidal sources were studied: \(f_{0}=5\) GHz (corresponding to Wi-Fi in its 802.11n standard as well as the lowest 5G band) as well as \(f_{0}=25\) GHz (5G), for a rectangular domain of 10 m \(\times\) 3 m, both in free space (air) and in the presence of rain. The \begin{table}
\begin{tabular}{c c c} \hline \hline
**Scenario** & **5 GHz** & **25 GHz** \\ \hline
**Free Space** & 137.2 Mb & 11.2 Gb \\
**Rainfall** & 141.5 Mb & 11.5 Gb \\ \hline \hline \end{tabular}
\end{table} 
Table 6: NVRAM use for the propagation scenarios herein studied. Figure 19: Comparison between the computing time (s) obtained for each scenario (free and rain) under the three computing platforms, for the 5 GHz experiments. Figure 20: Comparison between the computing time (s) obtained for each scenario (free and rain) under the three computing platforms, for the 25 GHz experiments. rain was simulated by means of a highly efficient pseudo-random numbering generator based on the parallel Ziggurat algorithm. Despite the precipitations being idealised by considering completely vertical rainfall and by testing only one rain intensity, the main result of proving the intense absorption of 25 GHz waves by precipitation holds. Moreover, more realistic rainfall simulations can be straightforwardly performed by adding an angle for precipitation to simulate wind, as well as further values of the \(M\) parameter to test different rain intensities. Furthermore, although we present the results of electromagnetic propagation considering raindrops with sweet water properties, the developed model is suitable for studying the interaction of electromagnetic waves with other hydrometeors. Simulations performed on \(f_{0}=5\) GHz propagation reveal that in the presence of rain, the droplets act as scatterers of the electromagnetic field, generating quasi-stationary states (electromagnetic noise), hindering the propagation and absorption of the waves by the CPML boundary for extended periods after the rain stops. This effect occurs because the droplet size is smaller than the propagated wavelength. In the case of \(f_{0}=25\) GHz propagation, on the other hand, the propagated wavelength is of the same order of magnitude as the characteristic length of droplets, causing a strong attenuation phenomenon and yielding complete absorption. This result is essential for the implementation of 5G infrastructure in its more promissory operating band in the following years, according to 5G standards, as such vulnerabilities in this emerging technology must be addressed by developers and manufacturers through protection and backup measures in the presence of hydrometeors, allowing for higher service integrity and operability. Conceptualisation, G.A.Y.-C. and J.J.H.-G; methodology, G.A.Y.-C., [PERSON]-G., and C.C.-C.; software, [PERSON]-C. and C.C.-C.; validation, [PERSON]-G. and C.C.-C.; formal analysis, [PERSON]-C., [PERSON]-G., and C.C.-C.; investigation, [PERSON]-C. and J.J.H.-G; resources, [PERSON]-G. and C.C.-C.; data curation, [PERSON]-G. and C.C.-C.; writing--original draft preparation, [PERSON]-C., [PERSON]-G. and C.C.-C.; writing--review and editing, [PERSON]-G. and [PERSON]-C.; visualisation, C.C.-C.; supervision, M.A.E.-A. ; project administration, [PERSON] and M.A.E.-[PERSON]; funding acquisition, [PERSON]-C., [PERSON]-[PERSON], [PERSON]-C., and M.A.E.-A. All authors have read and agreed to the published version of the manuscript. This research was funded by Secretaria de Investigacion y Posgrado, Instituto Politecnico Nacional grant numbers 20231067, 20230476, 20230593, 20230035, EDI and PIFI.