# DDPG-Based UAV-RIS Framework for Optimizing Mobility in Future Wireless Communication Networks
## 2 System Model  
This section introduces the system model for downlink data transmission to manage GU mobility in 5G/B5G networks by utilizing a mobile RIS-assisted UAV wireless communication network. The detailed architecture of the system model is depicted in Figure 1, which consists of a BS operating at the mmWave frequency band, equipped with multiple antennas [32]. We assume that the direct communication links between the GBS and the GUs are obstructed by tall buildings or other environmental impediments, so we employ UAV-RIS technology to improve the downlink data transmission service and GUs mobility performance. The BS is located at the center point of an urban area denoted by \(C\) and serve GUs are randomly distributed in that area denoted by \(U\). These GUs are partitioned into different groups based on SINR to enhance the system's performance. In NLoS scenarios, the communications between the GBS and the GUs is assisted by a mobile UAV-RIS, modeled as a uniform planar array (UPA). The total number of reflective elements is \(F=FxFy\), where \(Fx\) and \(Fy\) are the number of RIS reflecting elements along the X-axis and Y-axis, respectively. The RIS learns the optimal method to reflect incident signals by adjusting the phase shift, which helps improve the mmWave network's performance. In this model, we consider that a single UAV-RIS flies at a fixed altitude over a specific area and its position remains the same during one time slot and the flight is stable. Without loss of generality, thecoordinates of GBS, user location, and UAV-RIS can be defined as \(q_{B}=(x^{\text{BS}}=0,y^{\text{BS}}=0,h^{\text{BS}})\), \(q_{U}=(x^{\text{GU}},y^{\text{GU}},h^{\text{GU}})\), and \(q_{\text{UR}}=(x^{\text{UR}},y^{\text{UR}},h^{\text{UR}})\), respectively. To facilitate the trajectory design, the total UAV-RIS flying time, \(T\), is divided into \(N\) time slots within equal time intervals (\(T=N\delta_{t}\)), where \(\delta_{t}\) is a single slot length. The movement of UAV-RIS satisfies the following mobility constraints:  
\[\parallel\text{q}_{\text{UR}}[n+1]-q_{\text{UR}}[n]\|^{2}\leq V^{2},n=1,\dots, N-1, \tag{1a}\] \[\parallel q_{\text{UR}}[N]-q_{F}\|^{2}\leq V^{2},q_{\text{UR}}[1]=q_{0}, \tag{1b}\]  
or can be written as follows:  
\[\parallel\text{q}_{\text{UR}}[n+1]-q_{\text{UR}}[n]\|^{2}\leq V^{2},n=1,\dots, N-1, \tag{2}\]  
where \(q_{F}\) and \(q_{0}\) represent the final and initial horizontal positions of UAV-RIS, respectively. The values of \(q_{0}\) and \(q_{F}\) are determined by the centroids of the user groups obtained through the modified K-means clustering algorithm described in Section 3.1. This clustering process considers both user locations and SINR values to ensure optimal UAV-RIS positioning at the start and end of the mission within the feasible flight zone. \(V=v_{\text{max}}\delta_{t}\) is the maximum horizontal distance that the UAV-RIS travels in a single time slot, and \(v_{\text{max}}\) denotes the maximum UAV-RIS speed in m/s. The UAV operates at a fixed altitude within each time slot due to airspace safety regulations and energy efficiency considerations, while horizontal coordinates are dynamically optimized across slots. Figure 1: UAV-assisted RIS framework for GUs mobility management. The Euclidean distance from GBS to the UAV-RIS and from the UAV-RIS to the GUs is repressed by \(d1\) and \(d2\), respectively, and can be calculated as  
\[d_{1}=\sqrt{\left(x^{\text{BS}}-x^{\text{UR}}\right)^{2}+\left(y^{\text{BS}}-y^{ \text{UR}}\right)^{2}+\left(h^{\text{BS}}-h^{\text{UR}}\right)^{2}} \tag{3}\]  
\[d_{2}=\sqrt{\left(x^{\text{UR}}-x^{\text{GU}}\right)^{2}+\left(y^{\text{UR}}-y^ {\text{GU}}\right)^{2}+\left(h^{\text{UR}}-h^{\text{GU}}\right)^{2}} \tag{4}\]  
There may exist LoS (direct) and NLoS (indirect) links between UAV-RIS and GUs communication. These indirect links, caused by obstacles such as trees and high-rise buildings, introduce a multipath propagation effect that can degrade transmission signal quality and distort QoS in urban HetNet.