## 2 Principles
According to the probability density function of the channel gain above, 200 turbulence coefficients of different turbulence intensities are generated at each specific distance, which can be regarded as different turbulence experienced in 200 time slots at the certain distance and turbulence intensity. Figure 4 illustrates the magnitude and distribution of these turbulence coefficients. In FSO/RF systems, the RF link changes very slowly, and the coherence time is \(10^{2}\)-\(10^{3}\) times larger than that of the FSO link. For this reason, we can assume the RF link as quasi-static, and its channel remains unchanged during all the time slots [21]. Moreover, during all our simulations and experiments, we maintained the performance of the RF link better even than FSO performance at its best, and the devices of the RF link are all ideal. Consequently, we assumed that the channel gain of the RF link remains 1 during all the transmission and retransmission time slots, i.e., \(G_{RF,j}\equiv 1\), which is illustrated in Figure 5. As for the FSO link, different channel coefficient and channel gains are experienced due to the influence of atmospheric turbulence. Every FEC frame contains \(8\times 10^{4}\) symbols and lasts for 8 \(\upmu\)s at the rate of 10 Gbaud/s. Thus, each transmission and retransmission time slot of the FSO link is \(10^{3}\) times larger than the turbulence variation period which is millisecond order [19]. For this reason, we can assume that during each FSO transmission time slot, the channel remains unchanged. While in each retransmission round, different channel realizations are experienced, as is shown in Figure 5.  
Figure 4: The magnitude and distribution of turbulence coefficients in 200 time slots at the certain distance and turbulence intensity. In this paper, we considered HARQ with chase combining (cc-HARQ), which uses maximum ratio combining (MRC) to store previously failed packets so that they can be combined with subsequent packets. The mutual information accumulated by FSO link after \(M_{FSO}\) cc-HARQ rounds is given by [22]  
\[I_{FSO}^{\text{CC}}=log_{2}\Bigg{(}1+\sum\limits_{k=1}^{M_{FSO}}P_{FSO}G_{FSO} \Bigg{)} \tag{4}\]  
where we denote the signal-to-noise ratio (SNR) of the receiving end of the \(FSO\) link as \(P_{FSO}\), and \(P_{FSO}G_{FSO}\) represents the SNR at the receiving end of the \(FSO\) link under the influence of turbulence. Similarly, considering that the RF channel model gain equals to 1, the accumulated mutual information of RF link after \(M_{RF}\) HARQ rounds is  
\[I_{RF}^{\text{CC}} =log_{2}\Bigg{(}1+\sum\limits_{k=1}^{M_{RF}}P_{RF}G_{RF}\Bigg{)} \tag{5}\] \[=log_{2}(1+M_{RF}P_{RF})\]  
Considering the difference in transmission rate between RF and FSO links, the above equation becomes  
\[I_{FSO}^{CC}=\Psi log_{2}(1+M_{RF}P_{RF}) \tag{6}\]  
where \(\Psi\) represents the relative symbol rates of the RF link over the \(FSO\) link [21]. It can be determined by the actual scenario. The outage probability is defined as the probability of the event that the accumulated mutual information of the two links combined is less than the transmission rate R [22], which is  
\[P_{out}=Pr\{I<R\} \tag{7}\]  
where the transmission rate R can be represented by the spectral efficiency (\(\text{bps}/\text{Hz}\)). The outage probability expression of the system is obtained by substituting the two mutual information formulas and considering the pdf of the channel gain  
\[ \begin{array}{ll}P_{out}&=Pr\Bigg{\{}log_{2}\Bigg{(}1+\sum\limits_{k=1}^{M_ {FSO}}P_{FSO}G_{FSO}\Bigg{)}+\Psi log_{2}(1+M_{RF}P_{RF})\leq R\Bigg{\}}\\ &=Pr\Bigg{\{}\sum\limits_{k=1}^{M_{FSO}}G_{FSO}\leq\frac{2^{[R-\Psi log_{2}(1+ M_{RF}P_{RF})]}-1}{P_{FSO}}\Bigg{\}}\end{array}  \tag{8}\]  
Figure 5: The RF link remains constant in the retransmissions, while in each retransmission HARQ round, different channel realizations are experienced in the FSO link. When \(M_{FSO}=1\), that is, the FSO link transmits only once, the above formula can be simplified to  
\[