## 3 Proposed Solution to Predict the AoA
### Curvature-Adaptive Kernel for Non-Linear Mobility  
The performance of SVR in dynamic AoA prediction is susceptible to kernel choice, especially the Gaussian (RBF) kernel width \(\sigma\). Using a fixed \(\sigma\) may be adequate in stable linear-mobility cases, but cannot adapt to the fast non-linear AoA shifts commonly seen in urban or vehicular scenarios. To address this, our model employs a Curvature-Adaptive Kernel, in which the kernel width is updated in real-time according to the local curvature of the AoA trajectory. This approach enables the SVR to adjust its locality and smooth it flexibly, tracking both gradual and abrupt AoA changes without the need for retraining or system reconfiguration. This method allows for the SVR model to respond to trajectory nonlinearities in real-time, enhancing its prediction accuracy under variable mobility without requiring architectural or training changes. In a trajectory defined by discrete AoA observations \(\theta(t_{i})\), the curvature reflects how sharply the AoA changes with respect to time. A nearly linear AoA change indicates low curvature, where wide kernels (i.e., large \(\sigma\)) are beneficial due to smooth variations. In contrast, rapid AoA transitions (e.g., due to turns or multipath transitions) induce high curvature and require narrower kernels to maintain local sensitivity. Thus, we define a time-dependent kernel width \(\sigma(t)\) based on the instantaneous angular curvature \(\kappa(t)\), which is calculated from the recent AoA window using finite differences:  
\[\kappa(t)=\theta(t+1)-2\theta(t)+\theta(t-1) \tag{18}\]  
This expression resembles the second derivative of \(\theta(t)\) and quantifies angular acceleration. A significant value of \(|\kappa(t)|\) implies a sharp AoA transition. We define the kernel width \(\sigma(t)\) for the RBF kernel as a function of AoA curvature:  
\[\sigma(t)=\alpha+\beta\cdot\mid\kappa(t)\mid \tag{19}\]where \(\alpha>0\) is a baseline kernel width (ensures non-zero minimum smoothing), \(\beta>0\) scales the influence of curvature on kernel size, and \(|\;\kappa(t)\;|\;\) is the absolute curvature, ensuring positive \(\sigma(t)\). Substituting this into the standard RBF kernel, we obtain the curvature-adaptive kernel:  
\[K(t_{i},t_{j})=exp\left(-\frac{\left(t_{i}-t_{j}\right)^{2}}{2\sigma(t)^{2}}\right) \tag{20}\]  
Note that \(\sigma(t)\) is recomputed at every prediction step using the most recent AoA window, making the SVR kernel adaptive and responsive to current trajectory dynamics. This is a practical implementation strategy starting from compute \(\kappa(t)\) from the most recent AoA window \(\{\theta(t-1),\theta(t),\theta(t+1)\}\). Set \(\sigma(t)\) using Equation (18), with the parameters \(\alpha\) and \(\beta\) chosen based on empirical observations and systematic cross-validation using representative training data, reflecting various mobility scenarios and propagation conditions. To further enhance performance robustness and generalisation, future implementations may incorporate online parameter optimisation methods to dynamically tune \(\alpha\) and \(\beta\) according to observed real-time trajectory curvature and mobility characteristics, with empirically chosen or cross-validated parameters \(\alpha\) and \(\beta\). Pass \(\sigma(t)\) to the SVR model kernel function for the next prediction. Repeat the adaptation at every new slot, ensuring real-time kernel adjustment for each user's mobility pattern. This method's benefits include responsiveness, stability, and continuity. When users undergo rapid directional changes, the model adaptively narrows the kernel width to preserve local learning accuracy. During linear or slow movement, a wider kernel suppresses overfitting and promotes smoother predictions. This dynamic adjustment eliminates the need for explicit switching logic or model replacement, relying solely on real-time kernel recalibration.