## 3 Outage Probability Analysis  
In this section, we analyze the decoding outage probability at each sensor, where the transmit power level of \(s_{i}(t)\) is denoted by \(P_{i}\), \(i=1,\ 2,\cdots,\ M\). We assume that \(P_{1}\geq P_{2}\geq\ \cdots\ \geq\ P_{M}\). Note that different from conventional SIC, the order of the transmit power levels is not only determined based on the order of magnitude of the channel power gains, where the optimal scheme for transmit power allocation is obtained using the DRL approach. Combined with the descriptions in Section 2, while noting that an imperfect SIC scheme is adopted for decoding the signals in a descending order of transmit power levels, the received signal-to-interference-and-noise ratio (SINR) of the UAV for decoding \(s_{i}(t)\) is calculated by  
\[SINR_{,i}=\ \ \ \frac{P_{i}}{(P_{i+1}+\cdots+P_{M})+u[i-2]\xi(P_{1}+\cdots+P_{ i-1})+\sigma^{2}/I_{SR}}. \tag{8}\]  
Here, \(\xi\) denotes the proportional coefficient of residual interference caused by imperfect decoding [31], \(u[.]\) denotes the unit step function. Using \(\gamma_{th}\) to denote the threshold of the SINR for successful information decoding, the outage probability of decoding \(s_{i}(t)\) can be denoted by  
\[\begin{split} 1-\prod_{k=1}^{i}(1-\Pr[SINR_{,k}<\gamma_{th}])=\\ 1-\prod_{k=1}^{i}(1-\frac{Q_{k}\epsilon_{SR}^{2}G_{2A}^{3,1}[Q_ {k}]^{0,\epsilon_{SR}^{2}}_{\epsilon_{SR}-1,\ \epsilon_{SR}-1,\ -1}}{\Gamma(\alpha_{SR})\Gamma(\beta_{SR})}),\end{split} \tag{9}\]  
where \(Q_{k}\) denotes \(\frac{\alpha_{SR}\beta_{SR}\gamma_{th}\sigma^{2}/(A_{SR}l_{SR}^{l})}{P_{k}- \gamma_{th}(P_{k+1}+\cdots+P_{M}+u[k-2]\xi(P_{1}+\cdots+P_{k-1}))}\). \(\Pr[SINR_{,k}<\gamma_{th}]\) can be calculated by performing an integral operation for \(f_{I_{SR}}(x)\) from 0 to \(A_{SR}l_{SR}^{l}Q_{k}/(\alpha_{SR}\beta_{SR})\). The corresponding integral result can be obtained based on Equation (26) of [32]. During the second-hop transmission from the UAV to all sensors, the UAV utilizes spatial modulation to generate multiple directional light beams to point at the corresponding sensors [29]. Applying the imperfect SIC, in the case that the eavesdropper does not obtain security authentication from the UAV, the received SINR of sensor \(j,\,j=1,\,2,\cdots,\,M\), for decoding \(s_{i}(t)\) can be denoted by  
\[SINR_{D_{j\cdots i}}=\frac{P_{i}}{P_{i+1}+\cdots+P_{M}+u[i-2]\xi(P_{1}+\cdots+P_{ i-1})+\frac{\sigma^{2}}{I_{RD_{j}}}}. \tag{10}\]  
Accordingly, the resulting outage probability at sensor \(j\) for decoding \(s_{i}(t)\) is derived as below  
\[\Pr[SINR_{D_{j\cdots i}}<\gamma_{th}]=\int_{0}^{Q_{RD}^{i}}f_{I_{RD_{j}}}(x)dx= F_{I_{RD_{j}}}(Q_{RD}^{i}), \tag{11}\]  
where \(Q_{RD}^{i}\) denotes \(\frac{\gamma_{th}\sigma^{2}}{P_{i}-\gamma_{th}(P_{i+1}+\cdots+P_{M}+u[i-2]\xi( P_{1}+\cdots+P_{i-1}))}\). Note that a decoding outage will occur in cases where either the received SINR of the first-hop link or that of the second-hop link is not high enough for the decoding the information properly. As such, the decoding outage probability for sensor \(i,\,i=1,\,2,\,\,\cdots,\,M\), can be calculated as follows  
\[P_{out,i}=1-\quad(1-P_{scr})\prod_{q=1}^{i}\Pr[SINR_{D_{i\cdots q}}\geq\gamma _{th}]\prod_{k=1}^{i}\Pr[SINR_{R,k}\geq\gamma_{th}]. \tag{12}\]  
Combining Equations (9) and (11), a closed-form expression for Equation (12) can be derived accordingly. Note that a secrecy outage with the probability of \(P_{scr}\) is also regarded as a decoding outage in this case, where the eavesdropper also obtains the security authentication from the UAV.