## 2 Dielectric Properties and Channel Modeling
### Channel Models  
In our analysis of rainy weather conditions, we consider the presence of rainwater adhering to bare skin, forming a uniform and planar water layer. When the power is focused onto a small area of the skin, both the skin and water layers can be treated as uniform and planar. The water layer introduces power losses, including reflection and absorption losses, on the MMW/sub-THz waves. We estimate the total power loss resulting from these effects by the equation  
\[A_{water}\ (\text{dB})=10\log T_{tr} \tag{3}\]  
with \(T_{tr}\) being the total transmissivity through the water layer, which can be derived by using a multi-layer model [36]. As shown in Figure 1b, a three-layer structure (air-water-skin) is presented and can be estimated by the Fresnel principle simply, which has been confirmed in reference [36], when each layer is considered to be uniform. An expression for the total transmissivity from air into the skin can be expressed by the equation [37]  
\[T_{tr}=\frac{(1+\rho_{12})(1+\rho_{23})e^{-jk_{2}\delta\cos\theta_{2}}}{1+\rho _{12}\rho_{23}e^{-j2k_{2}\delta\cos\theta_{2}}}, \tag{4}\]  
where \(\rho_{12}\) and \(\rho_{23}\) are the reflection coefficients of the air-water interface and the water-skin interface, respectively. Parameter \(k_{2}\) is the wave number in the water layer, \(\delta\) is the thickness of the water layer, and \(\theta_{2}\) is the refraction angle in the water layer corresponding to the incident angle \(\theta_{1}\), as shown in Figure 1b. The exponential term represents the propagation factor in the water layer between its top boundary (air-water interface) and bottom boundary (water-skin interface) along the angle \(\theta_{2}\). Here, we neglect the scattering loss due to random wrinkles of the skin surface with a maximum depth of 0.3 mm [36], which is much smaller than the wavelength of the MMW/sub-THz waves. Thus, the total transmissivity relates to the reflection by the air-water interface and the water-skin interface, and also to the absorption by the water layer. Figure 1c shows a calculation of total transmissivity through the water layer with different incident angles. It increases first and then starts to decrease for frequencies above 100 GHz. By comparing it with the evolution curve of transmissivity in Figure 1a, we can attribute the difference between both trends to the absorption loss by the water layer. To further confirm this, we calculate the total transmissivity through a water layer with different thicknesses and plot it in Figure 1d. The total transmissivity increases with respect to frequency when the water layer is thinner than 0.2 mm, and follows an opposite trend when the thickness (\(\delta\)) is larger than 0.2 mm, due to the higher absorption loss by the increased water layer thickness. In clear weather, the gaseous composition of the atmosphere, mostly water vapor, strongly affects the propagation of MMW/sub-THz waves. The gaseous attenuation is commonly described as the summation of spectral absorption lines of water vapor and oxygen, and a water vapor continuum component. A line-by-line calculation is provided by the ITU recommendation sector (ITU-R) [38] based on the physical model MPM93 [39]. This method is proven to be valid at frequencies up to 500 GHz [40]. The results shown in Figure 2 indicate the ability to reduce the influence of atmospheric attenuation by setting the incident frequencies away from the water vapor absorption resonances. It should also be noted that higher terahertz frequencies are not preferred due to the large gaseous attenuation, especially when the relative humidity (RH) is higher than 60% in rainy weather. The attenuation due to falling rain can generally be predicted by using the Mie scattering theory. This is reasonable because the ordinary size of raindrop particles is in the range from mm to cm [41], which is comparable to the MMW/sub-THz wavelength. The scattering characteristics can be described by the absorption and scattering coefficients.