# DDPG-Based UAV-RIS Framework for Optimizing Mobility in Future Wireless Communication Networks
## 2 System Model
To address this challenge, UAV-RIS is deployed to enhance the probability of LoS links, thus enabling high-speed data transmission with improved connectivity and HO performance. The probability of LoS between UAV-RIS and GUs is given as  
\[p_{\text{LoS}}^{\text{UR}}=\frac{1}{1+\xi exp\left[\Psi\left(\frac{180}{\pi}tan ^{-1}\frac{h^{\text{UR}}}{d_{2}}\right)-\xi\right]} \tag{5}\]  
Here, \(\Psi\) and \(\xi\) are constant values representing the environmental influence such as urban, and suburban environments. The probability of NLoS between the UAV-RIS and GU \(u\) is  
\[p_{\text{NLoS}}^{\text{UR}}=1-p_{\text{LoS}}^{\text{UR}} \tag{6}\]  
Based on the above LoS and NLoS probability formulations, the path loss (PL) for the LoS and NLoS links between the UAV-RIS and the GU \(u\) are written [33] as  
\[PL_{\text{LoS}}^{\text{UR}}=\delta_{1}\left[\frac{4\pi f_{c}h^{\text{UR}}}{c_{ l}}\right]^{\alpha}p_{\text{LoS}}^{\text{UR}} \tag{7}\]  
\[PL_{\text{NLoS}}^{\text{UR}}=\delta_{2}\left[\frac{4\pi f_{c}h^{\text{UR}}}{c_ {l}}\right]^{\alpha}p_{\text{NLoS}}^{\text{UR}} \tag{8}\]  
where \(\delta_{1}\) and \(\delta_{2}\) are the PL coefficients for LoS and NLoS links, respectively, and their values depend on the area type. The PL coefficients \(\delta_{1}\) and \(\delta_{2}\) vary according to the environment type: (i) 0.1 dB and 21 dB in suburban, (ii) 1 dB and 20 dB in urban, (iii) 1.6 dB and 23 dB in dense urban, and (iv) 2.3 dB and 34 dB in high-rise urban environments, respectively. Moreover, \(f_{c}\) is the carrier frequency, \(\alpha\) is the PL exponent, and \(c_{l}\) is the speed of light. Furthermore, the average PL between UAV-RIS and GU \(u\) can be calculated by utilizing (7) and (8):  
\[\parallel q_{\text{UR}}[N]-q_{F}\|^{2}\leq V^{2},q_{\text{UR}}[1]=q_{0}, \tag{1b}\]0  
We consider UAV-mounted RIS to facilitate GUs in dense urban areas, where obstacles block direct communication links between GBS and GUs. The channel gain of GBS-(UAV-RIS)-GUs is expressed [34] as  
\[\parallel q_{\text{UR}}[N]-q_{F}\|^{2}\leq V^{2},q_{\text{UR}}[1]=q_{0}, \tag{1b}\]1  
Here, \(\Phi\) is the RIS phase shifts matrix and is denoted by  
\[\parallel q_{\text{UR}}[N]-q_{F}\|^{2}\leq V^{2},q_{\text{UR}}[1]=q_{0}, \tag{1b}\]2  
where \(\theta_{f}\in[0,2\pi]\), \(t\in F=\{1,2,\ldots,F\}\) is the phase shift of the \(F\)th reflecting element. The channels between GUs and UAV-RIS contain both LoS and NLoS links. Using Rician channel modeling, these channel gains are modeled as  
\[\parallel q_{\text{UR}}[N]-q_{F}\|^{2}\leq V^{2},q_{\text{UR}}[1]=q_{0}, \tag{1b}\]3  
where \(R\) is the Rician fading factor, and \(h_{LoS}\) and \(h_{NLoS}\) are the fast fading components of LoS and NLoS channels between UAV-RIS and GUs, respectively. \(\gamma\), \(\eta\), and \(d_{2}\) represent PL exponent, large-scale fading, and Euclidean distance among UAV-RIS and GUs, respectively. R-value decides whether the channel is a Rayleigh or Rician channel. When \(R=0\), then H is a Rayleigh channel; otherwise, it becomes a Rician channel. The Rician factor \(R=2\) is selected to model realistic urban UAV-to-ground links where moderate LoS dominance is observed, balancing strong direct components with multipath scattering effects. \(h_{NLoS}\) is the non-deterministic LoS component and is modeled as complex Gaussian distributed with zero mean and unit variance. On the other hand, \(h_{LoS}\) is the deterministic LoS component and is expressed as  
\[\parallel q_{\text{UR}}[N]-q_{F}\|^{2}\leq V^{2},q_{\text{UR}}[1]=q_{0}, \tag{1b}\]4 \[\parallel q_{\text{UR}}[N]-q_{F}\|^{2}\leq V^{2},q_{\text{UR}}[1]=q_{0}, \tag{1b}\]5 \[\parallel q_{\text{UR}}[N]-q_{F}\|^{2}\leq V^{2},q_{\text{UR}}[1]=q_{0}, \tag{1b}\]6  
where \(\sin\varphi_{u}\cos\phi_{u}=\frac{x^{\text{UR}}-x^{\text{CU}}}{d_{2}}\) and \(\cos\phi_{u}=\frac{h^{\text{UR}}-h^{\text{CU}}}{d_{2}}\) with \(\phi_{u}\) and \(\varphi_{u}\) represent the azimuth and elevation angles of arrival of the UAV-RIS and the GU \(u\), respectively.