# A Novel System of Mixed RF/FSO UAV Communication Based on MRR and RIS by Adopting Hybrid Modulation
## 2 System and Theoretical Model
### FSO Link  
The FSO channel follows the Gamma-Gamma distribution considering atmospheric turbulence and pointing error. We consider the UAV relay at low altitude, where MRR is installed.The intensity modulation/direct detection (IM/DD) technique is adopted at the optical receiver. Specifically, the retro-reflector in the MRR we use is the CCR. Note that the incident beam enters the CCR after being modulated by the optical modulator, then is reflected by mutually perpendicular reflective surfaces in turn, and finally exits in the opposite direction to the incident beam. The advantage is that the ATP system and the laser transmitter can be omitted at the relay. However, the use of MRR at the relay leads to differences between the uplink and downlink of the system, which is mainly reflected in the FSO link. For bidirectional communication in our system, the FSO uplink refers to the data transmission from the relay to the destination (i.e., Relay \(\rightarrow\) Destination), while the FSO downlink is the opposite (i.e., Destination \(\rightarrow\) Relay). Therefore, the principle of the FSO uplink and the FSO downlink is detailed in Figure 2. The FSO uplink implements the data transmission from the relay to the destination. Note that the data to be transmitted at the relay are sent by the user over the RF link. When the relay receives the data from the user, the next step is to send the data from the relay to the destination. First, the destination needs to transmit a beam without data to the relay through the forward path (i.e., Destination \(\rightarrow\) Relay), and then the relay loads the data onto the optical carrier in the forward path through the optical modulator. Hence, the backward path (i.e., Relay \(\rightarrow\) Destination) carries the data and reflects it to the destination via MRR. For the FSO downlink, it is the implementation of the data transmission from the destination to the relay. The principle is the same as that of traditional FSO communication. That is, data are loaded into the beam at the destination and then sent to the relay via the FSO downlink. Since the FSO uplink experiences twice the distance from the destination to the relay, the channel coefficient of the FSO uplink is expressed as:  
\[h_{2}=h_{f}h_{b}, \tag{3}\]  
where \(h_{f}\) and \(h_{b}\) are the channel coefficients of the forward path and the backward path, respectively. Owing to the characteristics of MRR, the forward path considers atmospheric turbulence and pointing error, while the backward path takes atmospheric turbulence into account. Hence, the channel coefficients of the forward path and the backward path are written as \(h_{f}=h_{a1}h_{p}\), \(h_{b}=h_{a2}\), where \(h_{a1}\) and \(h_{a2}\) are the channel coefficients due to atmospheric turbulence, and \(h_{p}\) is the channel coefficient caused by the pointing error. Therefore, the PDF of instantaneous SNR for the FSO uplink is expressed as [32]:  
\[f_{\gamma_{2}}(\gamma_{2})=\frac{\xi^{2}}{2\gamma_{2}\Gamma(\alpha_{1})\Gamma( \alpha_{2})\Gamma(\beta_{1})\Gamma(\beta_{2})}G_{1,5}^{5}\bigg{(}\frac{\alpha_ {1}\alpha_{2}\beta_{1}\beta_{2}}{A_{0}}\sqrt{\frac{\gamma_{2}}{\gamma_{2}}} \bigg{|}\xi^{2}+1\bigg{.}\xi^{2},\alpha_{1},\alpha_{2},\beta_{1},\beta_{2} \bigg{.}\bigg{)}, \tag{4}\]  
where \(\gamma_{2}\) and \(\gamma_{2}\) are the instantaneous SNR and the average SNR of FSO link. \(\xi=\omega_{eq}/2\sigma_{s}\) denotes the pointing error parameter, \(\omega_{eq}\) is the equivalent beamwidth, \(\sigma_{s}\) is the jitter standard deviation. \(A_{0}=(erf(\
u))^{2}\) is the received optical power at radial displacement of 0, \(\
u=(a/\omega_{z})\sqrt{\pi/2}\), \(a\) is the radius of the optical receiver, \(\omega_{z}\) is the beamwidth at distance from the laser emitter. \(G(\cdot)\) is the Meijer's G function. \(\alpha_{1}\), \(\beta_{1}\) are the parameters of atmospheric turbulence in the forward path, and \(\alpha_{2}\), \(\beta_{2}\) are the parameters of atmospheric turbulence in the backward path, which is calculated by (5) and (6) as below [33].