## 6 Simulations and Results
### Evaluation of a Single Terminal
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Alt.of GEO Sat. & 35,786 km \\ Gain of Sat. \(G_{3}\) & 48.2 dB \\ Lon.\(\uppsi_{s}\) and Lat. \(\upphi_{s}\) of GEO Sat. & (143\({}^{\circ}\)31\({}^{\prime}\) E, 0\({}^{\prime}\) N) \\ Lon. Vector \(\uppsi_{H}\) of HAP & (118\({}^{\circ}\)08\({}^{\prime}\) E, 118\({}^{\circ}\)38\({}^{\prime}\) E, 118\({}^{\circ}\)41\({}^{\prime}\) E, 118\({}^{\circ}\)23\({}^{\prime}\) E) \\ Lat. Vector \(\upphi_{H}\) of HAP & (39\({}^{\circ}\)50\({}^{\prime}\) N, 39\({}^{\circ}\)51\({}^{\prime}\) N, 39\({}^{\circ}\)55\({}^{\prime}\) N, 40\({}^{\circ}\)02\({}^{\prime}\) N) \\ Alt. of HAP & 22 km \\ Lon. \(\uppsi_{c}\) and Lat. \(\upphi_{c}\) of city & (118\({}^{\circ}\)31\({}^{\prime}\) E, 39\({}^{\circ}\)56\({}^{\prime}\) N) \\ Alt. of city & 200 m \\ Lon. \(\uppsi_{T}\) and Lat. \(\upphi_{T}\) of terminal & (118\({}^{\circ}\)22\({}^{\prime}\) E, 39\({}^{\circ}\)41\({}^{\prime}\) N) \\ Power required for terminal reception & 150 mW \\ Power required for HAP reception & 150 mW \\ Data rate \(R_{b}\) & 1.544 Mbps \\ Carrier frequency of \(HAP\leftrightarrow Sat.\) link & 48 GHz \\ Carrier frequency of \(T_{i}\leftrightarrow HAP\), \(T_{i}\leftrightarrow Sat.\) links & 3.4 GHz \\ Gain of \(HAP\leftrightarrow Sat.\) antennas \(G_{s,2}\) & 42.3 dB \\ Gain of terminal antenna \(G_{1}\) & 23.7 dB \\ Gain of \(HAP\to T_{i}\) antennas \(G_{r,2}\) & 29.1 dB \\ Vector of path loss exponents \(\mathbf{n}\) & \((2.2,2.9,2)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters used in the simulations and their values. Figure 3 shows the energy consumption for the direct path, relay paths and adaptive path selection at the source level. The energy consumption at the source level is defined as the overall energy consumption at the terminal end. In Figure 3, the term adaptive algorithm denotes that the terminal selects the path based on the proposed adaptive energy-efficient path selection algorithm. We can observe that the energy consumption of the \(i\)-th terminal for the \(T_{i}\to HAP_{1}\to Sat\). path, \(T_{i}\to HAP_{2}\to Sat\). path, \(T_{i}\to HAP_{3}\to Sat\). path, \(T_{i}\to HAP_{4}\to Sat\). path and adaptive algorithm path is \(78.99\%\), \(73.62\%\), \(69.19\%\), \(69.98\%\) and \(84.36\%\) lower than that for the \(T_{i}\to Sat\). path. Therefore, the relay path can significantly reduce the terminal energy consumption compared to the direct link, and the terminal energy consumption of the path using the adaptive algorithm is the lowest. From Figure 3, it can be further observed that the terminal energy consumption to process the broadcast LSAs is a little increased (the upper red sub-bars in Figure 3), although the adaptive algorithm is employed. This is due to the proposed LSA concept, which estimates the link state information by broadcasting LSAs in the HAP end and satellite end rather than sensing it at the terminal end. The terminal only receives a tiny quantity of the LSA packets, which can significantly reduce the energy consumption. This is especially applicable for slow flat Rician fading channels. Figure 4 depicts the total energy consumption for the direct link, relay links and adaptive path selection at the system level, where the total energy consumption at the system level is the sum of the energy consumption at both the terminals and the HAPs, and the energy consumption of the satellite is not included. For the T-S direct path, the energy consumption at the system level is equal to that at the source level. However, for the T-H-S relay path, the energy consumption at the system level consists of the energy consumption by the terminals and the energy consumption by the HAPs. From Figure 4, it can be observed that the energy consumption at the system level for the adaptive algorithm path is \(43.34\%,19.54\%,2.25\%,13.81\%\mathrm{\;and\;}22.44\%\) lower than that for the \(T_{i}\to Sat\). path, \(T_{i}\to HAP_{1}\to Sat\). path, \(T_{i}\to HAP_{2}\to Sat\). path, \(T_{i}\to HAP_{3}\to Sat\).