## 4 Results and Discussions  
Received powers have been calculated for 11 different sets of transmit and receive beam elevation angles for both links, taking N as 11. The common volumes formed by antenna beams with successive elevation angles are overlapping for both links. The transmit and receive beam elevation angles for different sets and height ranges of corresponding common volumes are given in Table 2. The difference in elevation between the lowest and highest beams is 1.75 degrees for the Ahmedabad link and 2.1 degrees for the Guwahati link, while the difference in height between the lowest and highest common volumes is 3082.7 m for the Ahmedabad link and 2719.7 m for the Guwahati link. Hence, the propagation characteristics of the tropospheric region over approximately 3 kms vertical extent were examined to determine the beam pointing dynamics of both links. The received power was calculated for each of the 11 sets of the beam elevation angles, for morning as well as evening times (0530 and 1730 IST), using IMD data from the Ahmedabad observatory for the year 2006 and from the Guwahati observatory for the year 2019. The maximum power, amongst the powers received for different elevation angles, has been determined for both times on each of these days.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Ahmedabad Link**} & \multicolumn{3}{c}{**Guwahati Link**} \\ \hline \multirow{3}{*}{**Beam Set**} & \multicolumn{2}{c}{**Beam Elevation Angle**} & \multicolumn{2}{c}{**Height Range**} & \multicolumn{2}{c}{**Beam Elevation Angle**} & \multicolumn{2}{c}{**Height Range**} \\  & \multicolumn{2}{c}{**Height Range (meters)**} & \multicolumn{2}{c}{**Beam Elevation Angle**} & \multicolumn{2}{c}{**(meters)**} \\ \cline{2-7}  & \multicolumn{2}{c}{**Transmit Beam**} & \multicolumn{2}{c}{**Receive Beam**} & \multicolumn{2}{c}{**Transmit Beam**} & \multicolumn{2}{c}{**Receive Beam**} & \\  & \multicolumn{2}{c}{**(rad)**} & \multicolumn{2}{c}{**(rad)**} & \multicolumn{2}{c}{**(rad)**} & \\ \hline
1 & \(5.8\times 10^{-3}\) & \(6.8\times 10^{-3}\) & 249.3–1790.0 & \(4.0\times 10^{-3}\) & \(5.8\times 10^{-3}\) & 323.8–1217.8 \\ \hline
2 & \(8.9\times 10^{-3}\) & \(9.8\times 10^{-3}\) & 404.4–1943.8 & \(7.7\times 10^{-3}\) & \(9.5\times 10^{-3}\) & 495.7–1399.7 \\ \hline
3 & \(11.9\times 10^{-3}\) & \(12.9\times 10^{-3}\) & 558.8–2097.8 & \(11.4\times 10^{-3}\) & \(13.2\times 10^{-3}\) & 674.4–1581.9 \\ \hline
4 & \(15.0\times 10^{-3}\) & \(15.9\times 10^{-3}\) & 712.8–2251.8 & \(15.0\times 10^{-3}\) & \(16.8\times 10^{-3}\) & 854.9–1764.2 \\ \hline
5 & \(18.0\times 10^{-3}\) & \(19.0\times 10^{-3}\) & 866.8–2406.0 & \(18.7\times 10^{-3}\) & \(20.5\times 10^{-3}\) & 1036.1–1946.6 \\ \hline
6 & \(21.1\times 10^{-3}\) & \(22.0\times 10^{-3}\) & 1020.6–2506.1 & \(22.4\times 10^{-3}\) & \(24.2\times 10^{-3}\) & 1217.8–2129.1 \\ \hline
7 & \(24.1\times 10^{-3}\) & \(25.1\times 10^{-3}\) & 1174.5–2714.3 & \(26.0\times 10^{-3}\) & \(27.8\times 10^{-3}\) & 1399.7–2311.7 \\ \hline
8 & \(27.2\times 10^{-3}\) & \(28.1\times 10^{-3}\) & 1328.3–2868.6 & \(29.7\times 10^{-3}\) & \(31.5\times 10^{-3}\) & 1581.9–2494.5 \\ \hline
9 & \(30.2\times 10^{-3}\) & \(31.2\times 10^{-3}\) & 1482.2–3023.0 & \(33.4\times 10^{-3}\) & \(35.2\times 10^{-3}\) & 1764.2–2677.4 \\ \hline
10 & \(33.3\times 10^{-3}\) & \(34.2\times 10^{-3}\) & 1636.0–3177.4 & \(37.0\times 10^{-3}\) & \(38.8\times 10^{-3}\) & 1946.6–2860.4 \\ \hline
11 & \(36.3\times 10^{-3}\) & \(37.3\times 10^{-3}\) & 1790.0–3332.0 & \(40.7\times 10^{-3}\) & \(42.5\times 10^{-3}\) & 2129.1–3043.5 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Beam elevation angles and common volume height ranges for the Ahmedabad link.