## 2 Atmospheric mmW Propagation in the Presence of Water Suspension  
An electromagnetic radiation that transmitted in atmospheric medium is affected by the macroscopic dielectric properties of the air as customary in homogeneous medium. The effect is expressed in various factors, refraction, absorption and dispersion. In RF links, these effects are expressed mainly in millimeter and sub-millimeter (terahertz) waves, for which the wavelength is still higher than the size of the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Frequency Band** & **Advantages** & **Disadvantages** \\ \hline
28 GHz & Suffers the least path loss; Low oxygen absorption and rain attenuation. & Lightly licensed; The bandwidth is relatively small. \\
38 GHz & Relatively less attenuation caused by oxygen absorption and rain. & Less research and applications done. \\
60 GHz & Unlicensed bands; Large bandwidth to achieve multi-gigabit rate. & Peak point of oxygen absorption; Relatively large rain attenuation. \\
73 GHz & Small effects of atmospheric absorption. & Large rain attenuation; \\  & & Large path loss due to high frequency point. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Millimeter wave band for 5G communications. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Frequency** & **Reference** & **Vapor Concentration** & **Measured** & **Comments** \\
**[GHz]** & & **[g/m3]** & **Attenuation [dB/km]** & **Comments** \\ \hline
72.56 & [12] & 0.2 & 0.6 \\
210 & [13] & 0.03 & 0.4 \\
240 & [14] & 3 & 37 \\
320 & [15] & 30 & 79.8 & Artificial fog was created by a thermal fog machine \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of measured fog attenuation in millimeter wavelengths with previous researches. water particles suspended in the air [16]. Signal attenuation during rainy conditions is well recognized by commercially available millimeter wave cloud radars (MMCR) and by Bistatic Radar System for Atmospheric Studies (BASTA) [18; 19; 20; 21]. When the wavelength is becoming comparable to or smaller than the water particles in the air, as in the visible and the Infrared radiation, the discontinuity of dielectric constant at a water/air interface leads to interferences within a single droplet and therefore breaks the assumption of homogeneous dielectric medium [22]. The Maxwell equations with this discontinuity boundary condition are analytically solvable by assuming that the water droplet is spherical and homogeneous and is well described in the framework of Mie scattering theory [23]. While full description of Mie theory is beyond the scope of this paper, we note here a relevant property for consideration later that is the size parameter \(x\equiv\pi D/\lambda\), where \(D\) is the droplet diameter and \(\lambda\) is the radiation wavelength under taken. This non-dimensional property is used to decide the scattering regime, whether it is a Rayleigh scattering in the case of mmW (\(x\ll 1\)) or Mie scattering when visible light is used (\(x<1\)). For the latter, we applied in our Mie model a water refractive index of \(n(635\ nm)=1.331+j1.5\cdot 10^{-8}\), whose imaginary part could actually be neglected. In the following, for reader's convenience, we review the propagation model employed along the study for analyzing the effects of the medium on the amplitude and phase of the millimeter wave signal. The notations and abbreviations used here are summarized in Appendix A. It is based on the characterization of the refractive index \(n(f)\) of the atmospheric medium in mmW frequencies. We follow [PERSON]'s Millimeter-wave Propagation Model (MPM), in which the refractive index is expressed as [24; 25]:  
\[n(f)=1+[N_{0}+N^{\prime}(f)-jN^{\prime\prime}(f)]\cdot 10^{-6} \tag{1}\]  
\(N_{0}\) is a real constant, nondispersive term, while \(N^{\prime}(f)\) and \(N^{\prime\prime}(f)\) are the frequency dependent, real and imaginary terms, respectively.