# Optimization of RIS-Assisted 6G NTN Architectures for High-Mobility UAV Communication Scenarios
## 4 Joint Optimization Framework for RIS Configuration and UAV Mobility
### Performance Evaluation and Trade-Off Analysis
#### 4.3.4 Latency  
Latency is the sum of the processing delay and transmission delay:  
\[\text{Latency}=T_{\text{processing}}+T_{\text{transmission}}, \tag{22}\]  
where \(T_{\text{processing}}\) depends on the number of RIS elements \(M\), and \(T_{\text{transmission}}\) is a fixed delay. By optimizing the RIS configuration and predicting channel changes, we minimize the processing delay, thereby reducing the overall latency. The proposed predictive coordination framework between the NTN and RIS shows significant improvements in throughput, energy efficiency, and reliability while maintaining low latency. The proactive approach to channel prediction, RIS reconfiguration, and handover management ensures that the system can adapt to rapid changes in channel conditions, making it highly suitable for high-mobility scenarios. The detailed step-by-step procedure to implement this predictive coordination mechanism is outlined in Algorithm 1. ```
1:Initial phase vector \(\mathbf{\phi}^{(0)}\), step size \(\eta\in(0,1]\), threshold \(\epsilon\), max iterations \(K_{\max}\)
2:Optimized Doppler-compensated phase vector \(\mathbf{\phi}^{*}\) and performance metrics
3:Inputs: Channels at \(t-1,t\): \(\{h_{d}(t-1),h_{d}(t)\}\), \(\{h_{m}(t-1),h_{m}(t)\}_{m=1}^{M}\), \(\{g_{m}(t-1),g_{m}(t)\}_{m=1}^{M}\); user trajectory and velocity; time step \(\Delta t\); powers \(P_{\mathrm{NTN}},P_{\mathrm{RBS}}\); noise variance \(\sigma^{2}\); interference \(I\); bandwidth \(B\); SINR threshold \(\gamma\)
4:Initialize iteration counter: \(k\gets 0\)
5:while true do
6: Step 1: Channel and Doppler prediction
7: Predict next-slot CSI: \(\hat{h}_{d}(t+1)\) and \(\{\hat{h}_{m}(t+1),\hat{g}_{m}(t+1)\}_{m=1}^{M}\)
8: Estimate Doppler shifts: for each \(m\), \(\hat{f}_{D,h_{m}}=\frac{1}{2\pi\Delta t}\arg\left(\frac{h_{d}(t)}{k_{m}(t-1)} \right)\), \(\hat{f}_{D,h_{d}}=\frac{1}{2\pi\Delta t}\arg\left(\frac{\hat{g}_{m}(t-1)}{k_{ m}(t-1)}\right)\)
9: Step 2: Compute ideal phase shifts
10:for\(m=1\)to\(M\)do
11:\(\mathbf{\phi}_{m}^{\mathrm{ideal}}=-\arg(\hat{h}_{d}(t+1))+\arg(\hat{g}_{m}^{*}(t+1 )\,\hat{h}_{m}(t+1))-2\pi(\hat{f}_{D,g_{m}}+\hat{f}_{D,h_{m}})\,\Delta t\)
12:endfor
13:Step 3: Phase update (unit modulus)
14:for\(m=1\)to\(M\)do
15:\(\mathbf{\phi}_{m}^{(k)}=(1-\eta)\,\mathbf{\phi}_{m}^{(k)}+\eta\,\mathbf{\phi}_{m}^{\mathrm{ ideal}}\mod 2\pi\)
16:endfor
17:Step 4: Convergence check
18:if\(\|\mathbf{\phi}^{(k+1)}-\mathbf{\phi}^{(k)}\|_{2}\leq\epsilon\ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\bm* Mobility modeling: User velocities \(v\in[10,100]\) m/s follow scenario-specific UAV speed distributions representative of operational aerial platforms. * Interference profile: Log-normal distribution with environment-dependent standard deviations (\(\sigma_{\text{urban}}\) = 6 dB, \(\sigma_{\text{rural}}\) = 4 dB) that capture realistic NTN channel conditions. * Processing latency: Per-element delay \(\tau_{\text{RIS}}=1\) us; benchmarks state-of-the-art RIS controller architectures. * Doppler compensation: The frequency shift \(\Delta f=v\cdot f_{c}\cdot\cos\theta/c\) allows for the predictive alignment of the phase, where \(\theta\) denotes the angle of motion relative to the propagation of the signal. Parameters not explicitly varied (e.g., Rician \(K\) factor, mobility patterns) remained scenario-constant to isolate RIS-scaling effects. Future work will investigate the adaptation of dynamic parameters under practical constraints for the deployment of NTNs. The simulation results provide a comprehensive analysis of the performance of RIS-assisted NTNs in five scenarios (urban, rural, highway, indoor, emergency) with five metrics (SINR, throughput, energy efficiency, outage probability, latency), as shown in Figure 3. The following is a logical breakdown of the findings. ### Analysis of Plotted Results Across Different Scenarios

The performance of each scenario is analyzed based on five key metrics: SINR, throughput, energy efficiency, outage probability, and latency.