## 2 System and Channel Models  
We consider a RIS-Equipped UAV wireless communication system in an emergency scenario where a malicious jammer employs a RIS-Equipped UAV to disrupt legitimate signals. The legitimate signal is transmitted from the transmitter (Tx) and relayed through the RIS to reach the receiver (Rx). The signal from the jammer is relayed via a RIS-Equipped UAV, jamming the legitimate signal at the Rx. The system model is shown in Figure 1.  
In the considered system, the RIS is composed of \(N\) passive reflective units. Assuming that the RIS can fully adjust phase shifts, the received signal, denoted as \(y\), at the Rx can be formulated as follows:  
\[y=\sqrt{\frac{P_{s}}{d_{SR}^{\epsilon}d_{RD}^{\epsilon}}}\left[\sum_{i=1}^{N} \alpha_{i}\beta_{i}\right]x_{s}+\sqrt{\frac{P_{J}}{d_{J\cup}^{\epsilon}d_{UD }^{\epsilon}}}\left[\sum_{t=1}^{N}\eta_{t}\mu_{t}\right]\Lambda x_{J}+n \tag{1}\]  
where \(P_{s}\) is the transmission power of the source; \(x_{s}\) represents the normalized transmitted signal with unit power; \(n\sim(0,N_{0})\) indicates additive white Gaussian noise; \(P_{j}\) is the jammer transmission power; and \(x_{J}\) is the jamming signal symbol. \(d_{SR}\), \(d_{RD}\), \(d_{J\cup}\), and \(d_{UD}\) are the distances from the Tx to the RIS 1, the RIS 1 to the Rx, the jammer to the RIS 2, and the RIS 2 to the destination, respectively, with \(\epsilon\) being the path loss exponent. Figure 1: The system model. The channel gains \(\alpha_{i}\) and \(\eta_{t}\) follow the Rician distribution [21], whereas \(\beta_{i}\) and \(\mu_{t}\) follow the Nakagami-m distribution [24]. As a result, the signal-to-jamming-noise ratio (SJNR) at the Rx can be expressed as follows:  
\[\gamma_{SJNR}=\frac{\frac{P_{s}}{\frac{d_{SR}^{\epsilon}d_{RD}^{\epsilon}}{ \left[\sum\limits_{i=1}^{N}\alpha_{i}\beta_{i}\right]^{2}}}{\frac{P_{J}}{d_{ JU}^{\epsilon}d_{UD}^{\epsilon}}\left[\sum\limits_{t=1}^{N}\eta_{t}\mu_{t} \right]^{2}+N_{0}} \tag{2}\]  
where \(\Lambda\) stands for the state of jamming, which is modeled by means of a Bernoulli-distributed random variable [31; 32]. Hence, the probability distribution of \(\Lambda\) is provided as follows:  
\[\left\{ \begin{array}{l}P(\Lambda=1)=\rho\\ P(\Lambda=0)=1-\rho\end{array} \right. \tag{3}\]  
where \(\rho\) denotes the probability of jamming. The average jamming power \(E_{J}\) is defined as \(P_{J}=E_{J}/\rho\). Let \(H_{S}=\left[\sum\limits_{i=1}^{N}\alpha_{i}\beta_{i}\right]^{2}\) and \(H_{J}=\left[\sum\limits_{t=1}^{N}\eta_{t}\mu_{t}\right]^{2}\). Here, \(H_{S}\sim Gamma(a_{S}+1,b_{S})\) and \(H_{J}\sim Gamma\big{(}a_{J}+1,b_{J}\big{)}\), where \(a_{S}+1\) and \(a_{J}+1\) are shape parameters, and \(b_{S}\) and \(b_{J}\) are the scale parameters of the Gamma distribution [24]. Thus the PDF of \(H_{x}\) is calculated as follows:  
\[f_{H_{x}}(h_{x})=\frac{h_{x}^{g_{X}-1}\exp\left(-\frac{h_{x}}{b_{x}}\right)}{ b_{x}^{g_{X}}T(g_{x})} \tag{4}\]  
where \(x\in\{S,J\}\), \(g_{S}=a_{S}+1\), and \(g_{J}=a_{J}+1\). From Equation (2), assuming the dominance of jamming power, it can be obtained that the SJR is:  
\[\gamma_{SJR}=\frac{\frac{P_{s}}{\frac{d_{SR}^{\epsilon}d_{RD}^{\epsilon}}{d_{ RD}^{\epsilon}}\left[\sum\limits_{i=1}^{N}\alpha_{i}\beta_{i}\right]^{2}}}{ \frac{P_{J}}{d_{Jul}^{\epsilon}d_{UD}^{\epsilon}}\left[\sum\limits_{t=1}^{N} \eta_{t}\mu_{t}\right]^{2}}=\frac{D\overline{\gamma}\left[\sum\limits_{i=1}^{ N}\alpha_{i}\beta_{i}\right]^{2}}{\rho\left[\sum\limits_{t=1}^{N}\eta_{t}\mu_{t} \right]^{2}} \tag{5}\]  
where \(D=\frac{d_{Jul}^{\epsilon}d_{UD}^{\epsilon}}{d_{SR}^{\epsilon}d_{RD}^{\epsilon}}\) and \(\overline{\gamma}=\frac{P_{s}}{E_{J}}\) is the average SJR. **Remark 1**.