# 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  
In this section, we simulate the energy efficiency of different transmission schemes. The relevant simulation parameters are set as: \(h_{l}=1,\overline{\gamma}_{i}=1\) and \(\sigma_{n}^{2}=1\). The energy efficiency of different IR-HARQ transmission schemes with various values of \(\epsilon_{0}\) is shown in Figure 6 with \(K=5\) and \(R=2\). As shown in Figure 6, the energy efficiency of the proposed IR-HARQ-VPA scheme is much higher than that of the IR-HARQ-EP scheme. The higher the reliability that is required, the greater the energy efficiency improvement provided by the IRHARQ-VPA scheme. When \(L=3\), \(\epsilon_{0}=10^{-6}\), the energy efficiency of IR-HARQ-VPA scheme is 63.6% higher than that of the IR-HARQ-EP scheme. When the outage probability \(\epsilon_{0}=0.1\), the energy efficiency of two schemes is almost the same as the exact value obtained by the MNI method. The results of the proposed NI-FFT method under different rates \(R\) are shown in Figure  
same. This is mainly because the transmission power required by the two schemes is small under this condition and the advantage of power allocation will become smaller. Figure 7 shows the energy efficiency of two schemes under different transmission rates with \(K=2\) and \(\epsilon=10^{-3}\). With the increase in the rate \(R\), the energy efficiency of both schemes will decrease. The energy efficiency of the IR-HARQ-VPA scheme is 44.4% higher than that of the IR-HARQ-EP scheme when \(R=1\) and \(L=2\). When \(L=4\), the optimized power sequence \((P_{1},P_{2},P_{3},P_{4})\) of the IR-HARQ-VPA scheme is shown in Figure 8 in detail. As it can be seen, the power sequence is not monotonic. The power value of the last IR-HARQ round is much greater than that of each previous round. This may be due to using small power in previous rounds to improve energy efficiency and using large power in the last round to ensure the transmission reliability under the condition that the previous decoding fails. Figure 6: The energy efficiency of IR-HARQ-EP and IR-HARQ-VPA schemes with \(K=5\) and \(R=2\) under different values of \(\epsilon_{0}\). Figure 7: The energy efficiency of IR-HARQ-EP and IR-HARQ-VPA schemes with \(K=2\) and \(\epsilon=10^{-3}\) under different values of \(R\). The energy efficiency of both schemes increases with the increase in the transmission rounds \(L\) as shown in Figure 9. This is mainly due to the increase in diversity gain caused by the increase in transmission rounds. As analyzed in Section 3.2, the complexity of the proposed scheme is \(\mathcal{O}(U\cdot Q\cdot L\cdot M\cdot\log 2(M))\), which increases with the increase in \(L\). The energy efficiency increases with the increase in \(L\), as shown in Figure 9. In addition, the value of \(L\) will also affect the transmission delay; when the value of \(L\) is too large, the transmission delay will increase. Therefore, the value of \(L\) should be properly selected to achieve a trade-off between energy efficiency, complexity, and transmission delay. When \(\epsilon_{0}=10^{-5}\) and \(L=3\), the energy efficiency of the IR-HARQ-VPA scheme is 2.6 times than that of the IR-HARQ-EP scheme. In Figure 10, the energy efficiency of the proposed IR-HARQ-VPA scheme is higher than that of the IR-HARQ-EP scheme under different values of \(K\). Especially when the channel condition is very poor with \(K=1\), the energy efficiency of the IR-HARQ-VPA scheme is 37.1% higher than that of the IR-HARQ-EP scheme. Figure 8: The value of \(P_{i}\left(1\leq i\leq L\right)\) to be used in different IR-HARQ rounds for the IR-HARQ-VPA scheme \(\left(K=2,\epsilon_{0}=10^{-3},L=4\right)\). Figure 9: The energy efficiency of IR-HARQ-EP and IR-HARQ-VPA schemes under different values of \(L(R=2,K=0)\). In [24], a variable-power allocation for the IR-HARQ scheme was studied for the Rayleigh fading case \((K=0)\).