## 2 System and Channel Models  
### System Model  
We consider a parallel-UAV-relay-based FSO system consisting of a source node (S), \(M\) relay nodes ( \(\mathrm{R}_{1},\mathrm{R}_{2},\ldots,\mathrm{R}_{M}\)), and a destination node (D), as illustrated in Figure 1. In this system, node S and node D are installed on the top of buildings, and hovering UAVs are used as the relay nodes. We suppose that the direct transmission link between node S and node D is blocked. Moreover, node S uses laser diodes as its transmitter to send optical signals; each UAV relay node employs the DF protocol and node D uses photodiodes to receive the signal and perform photoelectric conversion.  
The entire communication system includes \(M\) parallel paths, and each path contains two hops. For the first hop, node S transmits the same signal \(x_{\mathrm{s}}\) to \(M\) UAV relay nodes; the signal received by UAV relay node \(\mathrm{R}_{m}\) can be written as  
\[y_{m,1}=Th_{m,1}x_{\mathrm{s}}+n_{m},\ \forall m\in\{1,2,\ldots,M\} \tag{1}\]  
where \(T\) denotes the photoelectric conversion efficiency of the receiver's photodiode at \(\mathrm{R}_{m}\), \(h_{m,1}\) is the channel gain between node S and node \(\mathrm{R}_{m}\), and \(n_{m}\) is the additive white Gaussian noise (AWGN) at \(\mathrm{R}_{m}\) with mean zero and variance \(\sigma_{\mathrm{r}}^{2}\).  
In addition, the transmitted signal consists of symbols that are randomly selected with equal probability from the on-off keying (OOK) constellation such that \(x_{\mathrm{s}}\in\{0,2\mathrm{R}_{1}\}\), where \(P_{\rm t}\) denotes the average optical power of transmission. After that, the received electrical SNR of the \(m\)th link is given by  
\[\gamma_{m,1}=\frac{2P_{\rm t}^{2}T^{2}}{\sigma_{\rm r}^{2}}h_{m,1}^{2} \tag{2}\]  
For the second hop, the node R\({}_{m}\) adopts the DF protocol. That is, the received signal is first decoded, and then the re-encoded signal \(x_{\rm r}\) is sent to node D. Therefore, the signal received at node D is expressed as  
\[y_{m,2}=Th_{m,2}x_{\rm r}+n_{d},\ \forall m\in\{1,2,\ldots,M\} \tag{3}\]  
where \(h_{m,2}\) is the channel gain between node R\({}_{m}\) and node D and \(n_{d}\) is the AWGN at node D with mean zero and variance \(\sigma_{\rm d}^{2}\).  
Similarly, the transmitted signal at each UAV relay is also considered as symbols were selected with equal probability from the OOK constellation such that \(x_{\rm r}\in\{0,2P_{\rm o}\}\), where \(P_{\rm o}\) is the average transmit power of each relay. Then, the SNR \(\gamma_{m,2}\) of the second hop is given by  
\[\gamma_{m,2}=\frac{2P_{\rm o}^{2}T^{2}}{\sigma_{\rm d}^{2}}h_{m,2}^{2} \tag{4}\]  
For each path, the end-to-end SNR \(\gamma_{m}\) can be written as  
\[\gamma_{m}=\min\{\gamma_{m,1},\gamma_{m,2}\} \tag{5}\]  
To combine the received signal, a selection combining (SC) receiver is used. Compared to other combining schemes, the SC receiver is easier to implement since only one path is used for transmission. Moreover, the SC receiver is more robust in dealing with channel estimation errors since the weakest paths are excluded from the combining process. Therefore, the total SNR \(\gamma\) of the system can be expressed as  
\[\gamma=\max\{\gamma_{1},\gamma_{2},\ldots,\gamma_{M}\} \tag{6}\]