## 1 Introduction
In a nutshell, the overall status of the research work is presented in Table 1.  
As revealed in Table 1, the power allocation problem of hybrid FSO/RF systems in SAGIN with parallel FSO and RF relay links was rarely studied, especially considering the limited transmission power of the relay node. Only the authors of [9] have considered the problem of parallel FSO/RF transmissions in satellite-terrestrial integrated networks with power allocation. However, the system performance in [9] was only evaluated in terms of capacity outage probability (COP) with unacceptable computational complexity, and the differences in quality of service (QoS) among ground users were not considered. Additionally, to the best of our knowledge, the study on the weighted average bit-error rate (BER) performance of parallel FSO/RF links in which the FSO link and RF link transmit signals simultaneously is limited, and this is a very important link performance index. Furthermore, the energy efficiency optimization problem should be further considered, which is of great significance for improving the endurance of relay nodes and matching the energy efficiency of ground networks. Hence, the main contributions of this paper are summarized as follows:  
1. We have proposed a three-hop-based hybrid FSO/RF system in SAGIN, in which the parallel FSO/RF scheme is considered to serve users simultaneously. Specifically, considering the impacts of complex weather conditions and the limited transmission power of the HAP, we have further studied the power allocation problem between FSO and RF links. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Ref.** & **Weather** & **Parallel Links** & **Power Allocation** & **QoS** & **Metrics** & **Relay** \\ \hline [2] & No & No & No & No & OP, EC, BER & AF \\ [9] & Yes & Yes & Yes & No & COP & No \\ [13] & No & No & No & NO & OP, EC & DF \\ [16] & Yes & No & No & No & OP, SEP & DF \\ [17] & Yes & No & No & No & OP, EC, BER & AF \\ [20] & Yes & No & No & No & OP, SEP & No \\ [22] & Yes & No & No & No & OP, EC, SE & AF \\ [26] & Yes & No & Yes & No & OP, BER & AF \\ [27] & Yes & No & Yes & No & OP & No \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The Comparison of Some Related Hybrid FSO/RF Systems. 2. In order to better evaluate the average BER performance of parallel FSO/RF links, we have proposed a novel formula for the weighted average BER, which is calculated by using the weighted ergodic capacity of parallel FSO and RF links. 3. To maximize system energy efficiency, we have proposed an energy efficiency optimization model under the constraints of QoS among different users and obtained the optimum power allocation coefficient by using a numerical optimization technique. 4. Based on the proposed model, we have derived the closed-form expressions for system capacity outage probability, weighted average BER, and energy efficiency. Asymptotic capacity outage probability and diversity order at high SNR regions are provided to reveal more engineering insights. 5. The simulation results indicate that our proposed parallel FSO/RF scheme has superior capacity outage and energy efficiency performance compared to only the FSO and only the RF scheme, with acceptable performance loss in average BER. Furthermore, limited by the GS-satellite and satellite-HAP FSO links, performance saturation appears in the high SNR region. The remainder of this article is organized as follows. In Section 2, system and channel models are discussed in detail. The closed expressions for capacity outage probability, weighted average BER, and the energy efficiency optimization model are provided in Section 3. Section 4 shows the asymptotic analysis at high SNR regions, in which the diversity order and coding gain are also provided. The numerical and simulation results are given in Section 5. Finally, concluding remarks and future work are drawn in Section 6.