## 2 System Model
### Multi-User UAV Communication Channel Model with RIS  
Figure 4 presents the RIS-assisted multiuser UAV communication system model. The total number of users is expressed in \(K\), and the number of data streams is expressed in \(N_{s,K}\). The transmitter for UAVs communication is equipped with two transmitting antennas, denoted by \(N_{T}\), with an \(N_{T}^{RF}\) chain, where \(N_{s,K}\leq N_{T}^{RF}\leq N_{T}\). RIS consists of \(\mathcal{T}^{{}^{\prime}}\) reflective elements, and the set of reflective elements is expressed as \(\mathcal{T}^{{}^{\prime}}=\left\{1,\cdots,T^{{}^{\prime}}\right\}\). Typically, RIS can communicate with UAVs using specific links to exchange information about the channel status of the system while allowing for better coordination of the transmission signals of downlinks to multiple users. The reflection coefficient of RIS is expressed as \(\varrho_{\ell^{{}^{\prime}}}=e^{i\theta_{\ell^{{}^{\prime}}}},\forall i\in \mathcal{T}^{{}^{\prime}}\). \(\theta_{\ell^{{}^{\prime}}}e[0,2\pi)\) denotes the first \(t^{{}^{\prime}}\) phase shift of the first RIS reflection element. The RIS reflection matrix is expressed as \(\Phi=diag\{\varrho_{1^{{}^{\prime}}},\cdots,\varrho_{\mathcal{T}^{{}^{\prime} }}\}\), and \(|\varrho_{\ell^{{}^{\prime}}}|=1,\forall t^{{}^{\prime}}\in\mathcal{T}^{{}^{ \prime}}\). Similarly, the phase shift of the RIS reflector satisfies the discrete value \(\theta_{\ell^{{}^{\prime}}}e\boldsymbol{\Upsilon}\triangleq\left\{\frac{2\pi ^{{}^{\prime}}}{2^{\tilde{\imath}}}\right|\tilde{\imath}=0,1,\cdots,2^{ \tilde{\imath}}-1\right\}\). \(\boldsymbol{\Upsilon}\) represents the resolution of each reflector. Let \(s_{1}=\sqrt{P_{R}}y_{FSO}\) denote the signal forwarded by the node R. For this system, for \(K\) terrestrial users, the signal first enters the digital signal vector through the baseband  
Figure 4: RIS-assisted multiuser UAV communication system model. Figure 3: BiGRU-Attention model. beamforming matrix \(F_{BB}\). Then, the simulated beamforming matrix \(F_{RF}\) obtains the UAV transmit signal as:  
\[x=\sum_{k=1}^{K}F_{RF}F_{BB,k}s_{1k} \tag{18}\]  
where \(F_{RF}\epsilon\mathbb{C}^{N_{T}\times N_{RF}^{T}}\), \(F_{BB,k}=[F_{BB,1},\cdots F_{BB,K}]\epsilon\mathbb{C}^{N_{RF}\times N_{k,k}}\), \(N_{s,k}=\sum_{k=1}^{K}N_{s,k}\). \(s_{1k}=[s_{1}^{T},\cdots,s_{K}^{T}]\epsilon\mathbb{C}^{N_{k}\times 1}\) represents the connection of a single user's parallel data stream. \(s_{k}\epsilon\mathbb{C}^{N_{S_{k}}\times 1}\) denotes the first \(k\) Gaussian encoded data stream vector for the first user satisfying \(\mathbb{E}\big{[}s_{k}s_{k}^{H}\big{]}=I_{N_{s,k}}\). The maximum signal transmission power \(P\) satisfies \(\|F_{RF}F_{BB}\|_{F}^{2}\leq P\). The UAV transmits a communication signal to the RIS, and the RIS passes the communication signal to the user. The user is equipped with \(N_{R}\) receiving antennas and \(N_{R}^{RF}\) RF chains, where \(N_{S,k}\leq N_{R}^{RF}\leq N_{R}\). For signal accuracy, an analog combiner matrix is designed as \(W_{RF,k}\) and a digital combiner matrix \(W_{BB,k}\big{(}W_{RF,k}\epsilon\mathbb{C}^{N_{R}\times N_{R}^{R}}\) and \(W_{BB,k}\epsilon\mathbb{C}^{N_{RF}\times N_{k,k}}\)). Therefore, the received signal \(y_{k}\in\mathbb{C}^{N_{s,k}\times 1}\) at the \(k\)th terrestrial user can be expressed by the following equation:  
\[ \begin{array}{l}y_{k}(t)=W_{BB,k}^{H}W_{RF,k}^{H}\Big{(}\tilde{M}_{k}(t) \,\Phi\tilde{R}(t)\Big{)}F_{RF}F_{BB,k}s_{k}\\ +W_{BB,k}^{H}W_{RF,k}^{H}\Big{(}\tilde{M}_{k}(t)\,\Phi\tilde{R}(t)\Big{)}_{j \
eq k,j\in\mathcal{K}}W_{BB,k}^{H}W_{RF,k}^{H}F_{RF}F_{BB,k}s_{k}+W_{BB,k}^{ H}W_{RF,k}^{H}n\ (t)\end{array}  \tag{19}\]  
where \(W_{BB,k}^{H}W_{RF,k}^{H}\Big{(}\tilde{M}_{k}(t)\,\Phi\tilde{R}(t)\Big{)}F_{RF }F_{BB,k}s_{k}\) represents the received signal excluding other interference. \(W_{BB,k}^{H}W_{RF,k}^{H}\Big{(}\tilde{M}_{k}(t)\,\Phi\tilde{R}(t)\Big{)}_{j \
eq k,j\in\mathcal{K}}W_{BB,k}^{H}W_{RF,k}^{H}F_{RF}F_{BB,k}s_{k}\) is the interference signal, and \(W_{BB,k}^{H}W_{RF,k}^{H}n_{k}\) represents the total noise.