# Reliable and Energy-Efficient LEO Satellite Communication with IR-HARQ via Power Allocation
## 4 Algorithm Implementation and Simulation Results
### Simulation Results of the Energy Efficiency of Different Transmission Schemes
The authors used the approximation method to calculate the outage probability, and then used KKT conditions to solve the optimization problems. We call this method VPA-Approximation. Figure 11 shows that our proposed VPA-GA method has the higher energy efficiency. This is mainly because the VPA-Approximation method has a large approximation error and affects the optimal power allocation. The energy efficiency of the VPA-GA method is 15.4%, 26.6% higher than that of the VPA-Approximation method when \(\epsilon_{0}=10^{-3}\), \(\epsilon_{0}=10^{-2}\). Figure 12 shows the optimization process of the VPA-GA method. The energy efficiency quickly converges to the optimal value, which also verifies the effectiveness of the proposed algorithm. Figure 11: The comparison between the VPA-GA method and VPA-Asymptotic method under \(K=0\). Figure 10: The energy efficiency of IR-HARQ-EP and IR-HARQ-VPA schemes under different Rician factors \(K\). In addition, we apply the proposed IR-HARQ-VPA scheme to the LEO satellite communication system. For rainy weather, the impact on the \(C/N\) is shown in Figure 2. We assume the satellite can predict the large-scale fading information based on the satellite trajectory and the weather forecast. The Rician fading is used to model the small-scale fading. To adjust the power of different IR-HARQ rounds is equivalent to adjusting the received \(C/N\) in each round. Therefore, the value of \(C/N\) in Figure 2 is the maximum value of \(P_{i}\) in (9) under the condition that \(h_{l}=1\), \(\overline{\tau}_{i}=1\) and \(\sigma_{n}^{2}=1\). In order to shorten the simulation time, we exploit the symmetry of the satellite orbit and only simulate half the time of the LEO satellite communication window. Figure 13 shows the reliability of different transmission schemes in half of the communication window. When \(\epsilon=10^{-5}\), the scheme without HARQ cannot satisfy the requirements of reliability during the whole communication window. As the channel condition is poor at low elevation angles, both the IR-HARQ-EP and the IR-HARQ-VPA schemes cannot satisfy the requirements of reliability in the early stages of the LEO satellite entering the communication window. It can also be seen from Figure 13 that when the energy efficiency reaches the maximum, the outage probability satisfies \(e_{L}=\epsilon_{0}\). Figure 14 shows the energy efficiency of different transmission schemes in half of the communication window. The maximum transmission power is assumed to be \(P_{max}=300\) W. The scheme without HARQ has the smallest energy efficiency as the scheme has no diversity gain. The energy efficiency of all schemes will become higher as the channel state becomes  
Figure 12: Energy efficiency optimization process based on a genetic algorithm. Figure 7:0 The outage probability of different transmission schemes for half of the communication window. better, especially the IR-HARQ-EP and the IR-HARQ-VPA schemes. The proposed IR-HARQ-VPA scheme achieves more than twice the energy efficiency of the IR-HARQ-EP scheme during most of the communication window.