## 1 Introduction
In the case of low-frequency wireless systems such as 5 GHz (Wi-Fi and low band of 5G), modelling of the behaviour of electromagnetic waves in different environments such as rain, snow, sand, and forests shows a substantial impact on the transmissibility of electromagnetic waves, which is observed to cause scattering [36; 39], while more recent studies show that 5G is particularly vulnerable to rain scattering [40; 41] for ultra-high frequencies (20.2, 39.4, 73.0, and 83.0 GHz). Although different models have been developed to study the impact of precipitation on wireless telecommunications [42; 43], the results are insufficient in a field with a rapidly evolving technology as seen currently. Thus, the core part of this work is to identify the effects of precipitation in the form of rain in the main transmission rate band for the emerging 5G technology. In this work, we seek to provide a quantitative solution to this problem by employing a computational simulation of these phenomena based on [PERSON]'s electromagnetic theory [44], considering an appropriate treatment of the constitutive relations that allow us to simulate the hydrometeoric phenomena, which are time-dependent. Among the different numerical algorithms used for the solution of hyperbolic partial differential equations, such as [PERSON]'s equations, the Finite Difference Time Domain (FDTD) method, based on the application of [PERSON]'s step cell [45], stands out for its ease of implementation as well as for the reliability of its results. Regarding 5G modelling and simulation, the FDTD method has recently been applied. For instance, [PERSON] [46] developed an effective FDTD method in order to be able to simulate stochastic electromagnetic fields in the frequency band of 5G, while [PERSON] et al. [47] combined the FDTD and the Finite Element Method (FEM) to design a MIMO antenna for 5G in the context of cellular phones. Moreover, a large amount of concern has arisen regarding the impact of 5G on human health, which has been studied with (mostly parallel) FDTD methods. [PERSON] and [PERSON] [48] reported the effects of the 2.6 GHzMid-Band of 5G on different human head exposures, while [PERSON] et al. [49] studied the shadowing generated by the human body for 5G indoor propagation. Moreover, [PERSON] et al. [50], estimated the propagation loss generated by the human body in 5G frequencies. This research tackles the problem of electromagnetic wave propagation in two different frequencies in the presence of hydrometeors, in particular rainfall, by developing a numerical algorithm based on the second-order of precision in the space and time FDTD, with Convolutional Perfectly Matched Layer (CPML)-type absorbing boundary conditions [51], to solve [PERSON]'s equations considering constitutive relations for linear, isotropic, and inhomogeneous time-dependent media. To simulate rain, a parallel version of the Ziggurat algorithm was used to generate pseudo-random numbers. In this way, the effects of rain on electromagnetic wave propagation were studied for both sources at 5 GHz and 25 GHz. Furthermore, the generated code was accelerated at a high level by introducing directives in the serial code, which allow its parallelisation. In this case, the FDTD algorithm was accelerated with OpenACC directives (in GPU), while the Ziggurat problem was accelerated through OpenMP. The main motivation of this work is to provide a numerical study of the impact of sweet water rainfall on the propagation of the 5 and 25 GHz bands of 5G technology for 5G developers to be aware of the associated drawbacks, and to be able to provide a more robust and extensive infrastructure. This paper is structured as follows: Section 2 presents the development of [PERSON]'s equations for the time-dependent constitutive relations and their development in finite differences, the implementation of the CPML boundary condition, the development of the case studies, and the designed computational performance tests.