## 3 Proposed Solution to Predict the AoA
### System Model and Mathematical Formulation
#### 3.3.2 Predictive Signal Model Under User Mobility  
To realistically capture the dynamic propagation environment in high-mobility O-RAN scenarios, we adopt a predictive baseband signal model that incorporates both deterministic and stochastic signal components. This model is designed to reflect the composite nature of the received signal under time-varying user movement, multipath reflections, fading, and background noise. It serves as the basis for slot-level AoA tracking and prediction using a clustered, adaptive sliding window pipeline, which includes in-window jump detection and cluster-specific regression modelling. The user signal received at the \(i\)th antenna element from user \(u\) at time \(t\) is modelled as follows:  
\[ \begin{split} r_{i,u}(t)&=G_{\text{u}}e^{i(\omega_{ \text{c}}t-\frac{\omega_{\text{c}}}{\kappa}(i-1)d\,\sin\left(\theta_{u}(t) \right))}+s_{\text{mp,u}}(t)+f_{\text{NLOS,u}}(t)+n_{i,u}(t)\\ &\text{\emph{For}}\ i=1,2,\ldots,N(i-th\ \text{antenna\ element})\ \text{and}\ u=1,2,\ldots,U(User\ index)\end{split}  \tag{1}\]  
where \(G_{\text{u}}\) denotes the amplitude gain of the line-of-sight (LOS) signal component for the user \(u\), and \(\omega_{\text{c}}=2\pi f_{c}\) is the angular frequency corresponding to the carrier frequency \(f_{c}\). The term \(\frac{\omega_{\text{c}}}{c}(i-1)d\,\sin(\theta_{u}(t))\) accounts for the phase difference introduced by spatial delays between antenna elements, where ccc is the speed of light, \(d=\lambda/2\) is the inter-antenna spacing, and \(\theta_{u}(t)\) represents the instantaneous AoA of the dominant signal path at time \(t\). \(M_{\text{multipath}}(t)\) present the multiple paths due to reflections, diffractions, and scattering. The total received signal includes contributions from \(M\) number of multipath components (\(s_{\text{mp,u}}(t)\)). The \(f_{\text{NLOS,u}}(t)\) represents the effect of scattered signals in non-line-of-sight (NLOS) environments, it is generally modelled as a complex Gaussian random variable. The \(n_{i,u}\) additive Gaussian noise at the \(i\)th antenna. These components cause phase and amplitude distortions, increasing the complexity of AoA estimation. The model accounts for both spatial diversity across the antenna array and temporal variation induced by user mobility, forming a foundation for evaluating AoA tracking and prediction algorithms in realistic O-RAN deployments. The choice of this hybrid deterministic-stochastic signal model is guided by its close approximation to real-world wireless propagation, particularly under the constraints and capabilities of O-RAN Category B deployments. In practice, the signal received at each antenna results from a superposition of direct LOS components, scattered multipath replicas, fast-fading variations, and thermal noise. Our model integrates all of these aspects and introduces time dependency through \(\theta_{\text{u}}(t)\), which evolves non-linearly over time. This non-linear AoA trajectory is especially relevant for high-mobility users (e.g., vehicular or pedestrian motion through cluttered environments), where abrupt changes in direction or velocity can drastically alter the spatial signature of the received signal. Such behaviour challenges static beamforming systems and motivates the need for predictive models capable of forecasting AoA with low latency. Our framework explicitly detects such abrupt changes within the AoA window and adaptively selects clusters of recent samples for linear or SVR-based regression, ensuring robust prediction even during non-linear user trajectories. By incorporating multipath \(s_{\text{mp,u}}(t)\) and fading \(f_{\text{NLOS,u}}(t)\) components, the simulation environment also allows us to evaluate the robustness of prediction-enhanced beamforming under challenging channel conditions, such as inter-cell interference, non-line-of-sight (NLoS) dominance, and fading-induced signal dropout. Furthermore, the statistical properties of each term in Equation (1) allow for controlled experimentation.