# A Clutter Loss Model for Satellite Communication Systems
## 6 Model Results  
As it is not possible to test the model against the few measurements available in the literature (as mentioned in Section 5.1, this is due to the lack of measurements with directive antenna receivers), the predictions of the analytical model, described in Section 5.2, are compared to the simulation results. Melbourne and London, considered in Report ITU-R P.2402, present different planimetric characteristics, both in terms of building height and distance. The clutter loss calculation methodology presented in Sections 2, 3 and 4.1 is applied by simulating \(10^{5}\) rays with TE polarization and \(10^{5}\) rays with TM polarization, at 6 GHz. Asphalt is considered to model the ground, while, as for buildings, the probability of concrete/brick and glass walls is assumed to be equal to 90% and 10%, respectively. The results achieved with a uniform random horizontal incidence angle between \(0^{\circ}\) and \(60^{\circ}\) are presented in Figures 11 and 12, respectively, for London and Melbourne, with the height of the base station uniformly distributed between 4 and 6 m. A horizontal incident angle between \(0^{\circ}\) and \(60^{\circ}\) has been chosen according to the steering capabilities of the transmitting antenna. In fact, in a three sectoral antenna, the allowed horizontal steering directions are between \(-60^{\circ}\) and \(+60^{\circ}\). Therefore, transmitted rays can impact on a building in front of the antenna with an incident angle between \(0^{\circ}\) and \(60^{\circ}\). Figures 13 and 14 present the results obtained by fixing the base station height at 18 m in London and Melbourne. In each figure, the statistics from the Monte Carlo simulation presented in Section 5.1 are compared to the analytical model illustrated in Section 5.2, as well as the results obtained by simulations of Report ITU-R P.2402. \begin{table}
\begin{tabular}{c c} \hline \hline
**Coefficient** & **Value** \\ \hline \(b_{1}\) & 0.0029 \\ \(b_{2}\) & \(-0.0355\) \\ \(b_{3}\) & \(-0.1310\) \\ \(b_{4}\) & \(-0.7389\) \\ \(b_{5}\) & \(-0.000026176\) \\ \(b_{6}\) & \(-0.00033019\) \\ \(b_{7}\) & \(-0.0033\) \\ \(b_{8}\) & \(0.0852\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coefficients of the expression approximating the clutter loss statistics for \(H_{\rm S}\) = 4–6 m. \begin{table}
\begin{tabular}{c c} \hline \hline
**Coefficient** & **Value** \\ \hline \(c_{1}\) & 0.0003623 \\ \(c_{2}\) & \(-3.0036\) \\ \(c_{3}\) & \(-0.000010054\) \\ \(c_{4}\) & \(-0.0007.1147\) \\ \(c_{5}\) & \(-0.0020\) \\ \(c_{6}\) & \(0.0534\) \\ \(c_{7}\) & \(-0.0000348\) \\ \(c_{8}\) & \(0.001177\) \\ \(c_{9}\) & \(-0.003921\) \\ \(c_{10}\) & \(-0.0002\) \\ \(c_{11}\) & \(0.0068\) \\ \(c_{12}\) & \(-0.0070\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Coefficients of the expression approximating the clutter loss statistics for \(H_{\rm S}\) = 18 m.  
Figure 11: Clutter loss cumulative distributions: comparison between the proposed model and the ITU-R P.2402 model, for elevation angles of 15, 40 and 70 degrees in London (base station height uniformly distributed between 4 and 6 m). Figure 12: Clutter loss cumulative distributions: comparison between the proposed model and the ITU-R P.2402 model, for elevation angles of 15, 40 and 70 degrees in Melbourne (base station height uniformly distributed between 4 and 6 m). Figure 13: Clutter loss cumulative distributions: comparison between the proposed model and the ITU-R P.2402 model, for elevation angles of 15, 40 and 70 degrees in London (base station height fixed at 18 m). Figures 11-14 show that the statistics from the proposed Monte Carlo simulation provide similar or larger clutter loss values if compared to the results obtained by the report ITU R P.2402 model, for elevation angles of +15\({}^{\circ}\) and +40\({}^{\circ}\). The proposed Monte Carlo simulation yields lower values than the ITU-R approach in the low probability range, for the 70\({}^{\circ}\) elevation angle.