## 3 Proposed Solution to Predict the AoA
### Support Vector Regression (SVR) for Non-Linear AoA Prediction  
While LR provides a computationally efficient solution for short-term AoA forecasting, it is inherently limited to linear angular trajectories. In dynamic or non-linear user mobility scenarios, such as abrupt direction changes, curved pedestrian movement, or multipath-induced angular deviation, the linearity assumption breaks down. To address this, we extend the DE-ACSW-R framework with SVR, a kernel-based non-linear model capable of learning complex AoA evolution patterns from historical data. SVR operates at the O-DU layer, where more computational resources and a broader temporal context are available. SVR predictions complement those of LR and are dynamically fused via a confidence and error-weighted scheme, as detailed in our adaptive fusion logic. Given a window of AoA observations \(D_{t}=\{(t_{i},\theta_{i})\}_{i=t-W+1}^{t}\), the SVR aims to find a non-linear \(f(t)\) that approximates the underlying AoA trajectory:  
\[\hat{\theta}_{SVR}(t+\Delta)=f(t+\Delta)=\langle W,\phi\ (t+\Delta)\rangle+b_{SVR} \tag{14}\]  
where \(\phi\ (t)\) is a non-linear mapping to a high-dimensional feature space, \(W\) is the weight vector in the transformed space, \(b_{SVR}\) is the SVR bias term, and \(\langle\cdot,\cdot\rangle\) denotes the inner product. The SVR learning problem minimises a regularised hinge-loss objective  
\[\underset{w,\phi_{t},\phi_{t}^{*}}{\text{min}}\frac{1}{2}\|w\|^{2}+C\sum_{i=1 }^{w}(\xi_{t}+\xi_{t}^{*}) \tag{15}\]  
subject to the following constraints:  
\[\left\{ \begin{aligned} &\theta_{i}-\langle 2,\ \phi(t_{i})\rangle-b_{SVR}\leq\ \epsilon+\xi_{t}\\ &\langle w,\phi(t_{i})\rangle+b_{SVR}-\theta_{i}\leq\epsilon+ \xi_{t}^{*}\\ &\xi_{t},\xi_{t}^{*}\ \geq 0\end{aligned} \right.\quad\text{for }i-1,\ \ldots,W \tag{16}\]  
where \(\epsilon\) is the maximum allowable prediction error (insensitive margin), \(\xi_{t},\xi_{t}^{*}\) are slack variables penalising violations beyond \(\epsilon\), and C \(>0\) is the regularisation parameter controlling the trade-off between margin width and tolerance to error. In practice, the SVR is implemented using a Gaussian (RBF) kernel whose width is dynamically adapted according to the estimated curvature of the AoA trajectory within the window. This curvature-adaptive kernel allows for the SVR model to respond to both slow and sharp changes in user motion. The SVR prediction for time \(t+\Delta\) is computed as a weighted sum over support vectors, utilising the curvature-adapted kernel:\[\hat{\theta}_{SVR}(t+\Delta)=\sum_{i=1}^{\infty}\left(\alpha_{i}-\alpha_{i}^{*} \right)K(t_{i},t+\Delta)+b_{SVR} \tag{17}\]  
where \(\alpha_{i}-\alpha_{i}^{*}\) are dual coefficients learned from training and \(K(t_{i},t)=\left\langle\phi(t_{i}),\phi\big{(}t_{j}\big{)}\right\rangle\) is a kernel function (Radial Basis Function kernel) defining the similarity between inputs. SVR-based AoA prediction is particularly beneficial in the following scenarios:  
* Non-linear or curved mobility patterns, such as turns, roundabouts, or urban obstacles. * Multipath-dominated environments, where reflection-induced AoA shifts create non-monotonic signal behaviour. * Longer-term history exploitation, where patterns are not well approximated by short-window linear trends. Compared to LR, SVR can exploit a more extended history and capture non-linear AoA evolution, providing improved generalisation for irregular mobility or channel conditions. However, SVR's computational cost and the need for additional parameters make it better suited for O-DU or near-real-time RIC layers rather than for immediate O-RU prediction. At each slot, the O-DU runs the SVR model based on the recent AoA history (provided by the O-RU). The predicted value \(\hat{\theta}_{SVR}(t+\Delta)\) is combined with the LR prediction through a confidence- and error-weighted fusion logic (see Section 3.3.5).