# Millimeter Wave Attenuation Due to Wind and Heavy Rain in a Tropical Region
## 3 Theory and Algorithms  
### FWS Link Budget  
Based on the E-band FWS experiment setup in this work, the signal-to-noise ratio should be affected by antenna gains, free-space loss, gaseous loss, rain attenuation and attenuation via wind effect, given using  
\[ \begin{array}{ll}\mathrm{SNR(dB)=}P_{tx}&+G_{t}+G_{r}\\ &-A_{free}-A_{gas}-A_{rain}-A_{wind}-N_{thermal}-N_{system}-M,\end{array}  \tag{1}\]  
Figure 3: Schematic illustration of the antennas/sensors setup and block diagram of connections. where \(P_{tx}\) is the transmit power (dBm), \(G_{t}\) and \(G_{r}\) are the gains (dBi) of the transmitter and receiver antennas, respectively, \(A_{free}\) is the free space attenuation (dB), \(A_{gas}\) is the gaseous attenuation (dB), \(A_{rain}\) is the rain-induced attenuation (dB), \(A_{wind}\) is the wind-induced attenuation (dB), \(N_{thermal}\) is the thermal noise level (dB), \(N_{system}\) is the system noise figure (dB) and \(M\) is the link margin (dB). The first three parameters, the transmit power (\(P_{tx}\)), the transmitter antenna gain (\(G_{t}\)) and the receiver antenna gain (\(G_{r}\)), are constant, given via the user setting and the datasheet as shown in Table 1. The antenna gains of the 30 cm antennas at both sites are \(G_{t}=G_{r}=43\) dB [28]. The next parameter, the free space attenuation, is determined by the frequency and path length:  
\[A_{free}=20\log_{10}\left(\frac{4\pi fr_{0}}{c}\right), \tag{2}\]  
where \(f\) is the carrier frequency (Hz), \(r_{0}\) is the path length (m) and \(c\) is the speed of light (m/s). At a frequency of \(f=74.625\) GHz and distance of \(r_{0}=150\) m, then \(A_{free}=113.4\) dB. The fourth parameter, gaseous attenuation, is calculated using ITU-R P.676 recommendation [29], as follows:  
\[A_{gas}=(\gamma_{o}+\gamma_{w})r_{0}=0.1820f\left(N_{\rm Oxygen}^{\prime\prime }(f)+N_{\rm Water\ vapour}^{\prime\prime}(f)\right)\cdot r_{0}, \tag{3}\]  
where \(\gamma_{o}\) and \(\gamma_{w}\) are the specific attenuations (dB/km) due to dry air and water vapor, respectively, \(f\) is the frequency (GHz) and \(r_{0}\) is the link distance (km). The imaginary parts of the frequency-dependent complex refractivities, \(N_{\rm Oxygen}^{\prime\prime}(f)\) and \(N_{\rm water\ vapour}^{\prime\prime}(f)\), are calculated using  
\[N_{\rm Oxygen}^{\prime\prime}(f)=\sum_{i}S_{io}F_{io}+N_{D}^{\prime\prime}(f), \tag{4}\]  
\[N_{\rm water\ vapour}^{\prime\prime}(f)=\sum_{i}S_{iw}F_{iw}, \tag{5}\]  
where \(S_{io}\), and \(S_{iw}\) are the strengths of the \(i\)th oxygen and water vapor lines, respectively, and \(F_{io}\) and \(F_{iw}\) are the oxygen and water vapor line shape factors, respectively. \(N_{D}^{\prime\prime}\) is the dry continuum due to pressure-induced nitrogen absorption and the Debye spectrum. The oxygen and water vapor line strengths are given using  
\[S_{io}=a_{1}\times 10^{-7}\cdot p_{\rm dry\ air}(300/T)^{3}\exp[a_{2}(1-300/T)], \tag{6}\]  
\[S_{iw}=b_{1}\times 10^{-1}\cdot p_{\rm water\ vapour}(300/T)^{3.5}\exp[b_{2}(1-300/T )], \tag{7}\]  
where \(p_{\rm dry\ air}\) is the dry air pressure (hPa), \(p_{\rm water\ vapour}\) is the water vapor partial pressure (hPa) and \(T\) is the temperature. The parameters \(a_{1}\), \(a_{2}\), \(b_{1}\) and \(b_{2}\) are given in [29] for all dry air and water vapor absorption lines between 50 GHz to 1780 GHz, which must be summed in Equations (4) and (5). The water vapor partial pressure can be estimated using the ITU-R P.835-6 recommendation [30] at a given altitude using  
\[p_{\rm water\ vapour}(h)=\frac{\rho(h)T}{216.7}=\frac{\rho_{0}\exp(-h/h_{0})\ T}{216.7}, \tag{8}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Values** & **Calculation Method/Reference** \\ \hline Transmit power \((P_{tx})\) & \(-5\) dBm & User setting \\ \hline Antenna gains \((G_{t},G_{r})\) & 43 dB & Datasheet \\ \hline Free-space loss (\(A_{free}\)) & 113.4 dB & at \(f=74.625\) GHz and \(r_{0}=150\) m \\ \hline Gaseous loss \((A_{gas})\) & 0.899–1.087 dB & ITU-R P.676 [29] \\ \hline \hline \end{tabular}
\end{table}