## 2 Concepts and Theory
### Tropospheric Scattering
#### 2.3.2 Transmission Loss  
In order to employ the troposcatter phenomenon for over-the-horizon communication, it is crucial to establish a suitable troposcatter propagation model that can accurately predict  
Figure 1: Reflection and scattering concept diagram of tropospheric scattering. \(\varepsilon_{r1}\) and \(\varepsilon_{r2}\) is the dielectric constant of different air mass, and \(\overline{\varepsilon_{r2}}\) is the mean of the dielectric constant. Differences in the refractive index of a single air mass from its surroundings can lead to the reflective surface. And the average refractive index of multiple air masses can also result in reflective surfaces due to differences in refractive index with other air masses. transmission loss. Since the 1980s, the ITU-R has collected measurement data worldwide and provided recommendations for standardized troposcatter loss prediction methods [13]. In this section, we briefly summarize the ITU-R's recommendations, and for more detail, readers can refer to the ITU-R's website ([[https://www.itu.int/rec/R-REC-P/en](https://www.itu.int/rec/R-REC-P/en)]([https://www.itu.int/rec/R-REC-P/en](https://www.itu.int/rec/R-REC-P/en)), accessed on 29 July 2023). In recommendation ITU-R P.617, the average annual transmission loss is written as [29]  
\[L_{617}=M+30\text{log}f+10\text{log}d+30\text{log}\theta_{0}+L_{N} \tag{8}\]  
where  
\[L_{N}=20\text{log}(5+\gamma H)+4.34\gamma h_{0} \tag{9}\]  
\[L_{\text{coup}}=0.07\text{exp}[0.055(G_{\text{t}}+G_{\text{r}})] \tag{10}\]  
\[\theta_{0}=10^{3}d/ka_{\text{e}}+\theta_{\text{t}}+\theta_{\text{r}} \tag{11}\]  
where \(\theta_{\text{t}}\) and \(\theta_{\text{r}}\) are the transmitter and receiver horizon angles, respectively, and  
\[H=\theta_{0}d/4 \tag{12}\]  
\[h_{0}=\theta_{0}{}^{2}ka_{\text{e}}/8 \tag{13}\]  
with the remaining parameters listed in Table 1.  
In Equation (8), \(Y_{617}(q)\) is a conversion factor for non-exceedance percentages, \(q\), other than 50% from  
\[Y_{617}(q)=C_{617}(q)Y_{617}(90) \tag{14}\]  
where \(Y_{617}(90)\) is the conversion factor for \(q=90\%\), and in most regions of China, \(Y_{617}(90)\) is  
\[Y_{617}(90)=-2.2-\left[8.1-2.3\times 10^{-4}\cdot\min(f,4000)\right]\cdot \text{exp}(-0.137h_{0}) \tag{15}\]  
The coefficient \(C_{617}(q)\) denotes the non-exceedance percentage of time. According to the ITU-R recommendations, the values of \(C_{617}(q)\) are 50 and 91.82 for \(q\) values of 50 and 99, respectively. The ITU-R continuously updates the current internationally agreed, general-purpose, wide-range, terrestrial propagation model that is known as ITU-R P.2001 [30]. The propagation model is used to predict terrestrial propagation loss due to both signal enhancements and fading over the time range 0% to 100% of an average year. It covers the frequency range from 30 MHz to 50 GHz and distances from 3 km to 1000 km. The prediction of troposcatter transmission loss is described as follows:  
\[L_{617}=M+30\text{log}f+10\text{log}d+30\text{log}\theta_{0}+L_{N} \tag{8}\]0 \begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Quantity** \\ \hline \(M\) (dB) & Meteorological parameters \\ \(\gamma\) (km\({}^{-1}\)) & Atmospheric structure parameters \\ \(f\) (MHz) & Frequency \\ \(G_{\text{t}}\) (dB) & Transmitting antenna gain \\ \(G_{\text{r}}\) (dB) & Receiving antenna gain \\ \(d\) (km) & Path length \\ \(a_{\text{e}}\) (km) & Radius of the Earth (6370 km) \\ \(k\) & Effective Earth radius factor for median refractivity conditions \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Principal parameters. where  
\[L_{\text{freq}}=25\text{log}\bigg{(}\frac{f}{1000}\bigg{)}-2.5\bigg{[}\text{log} \bigg{(}\frac{f}{2000}\bigg{)}\bigg{]}^{2} \tag{17}\]  
\[L_{\text{dist}}=\max[10\text{log}\,d+30\text{log}\,\theta_{0}+L_{\text{N}}, \tag{18}\]  
\[20\text{log}\,d+0.573\theta_{0}+20] \tag{19}\]  
\[Y_{2001}(q)=C_{2001}(q)Y_{2001}(90) \tag{20}\]  
Although \(Y_{2001}(90)\) is the same as \(Y_{617}(90)\) as in Equation (15), \(C_{2001}(q)\) is given by:  
\[C_{2001}(q)=\left\{