## 4 Performance Evaluation Results
### Impact of Codebook Size  
The impact of codebook size \(M=\{8,16,32\}\) (as given in Table 2) has been examined using the four algorithms considered in this work, across five different scenarios and the combined scenario (as given in Table 1). Figure 7a-c show the beam prediction accuracy plots of all five scenarios and the combined scenario for the [80:20]% data split for \(M=8\), 16, and 32, respectively. Figure 7a-c shows that the accuracy of beam prediction decreases with increase in codebook size. Specifically, the 8-beam codebook (Figure 7a) has the best performance, while the 32-beam codebook (Figure 7c) has the least performance across the considered algorithms and scenarios. This is because the lower the number of beams in the codebook, the higher the beam pairing or prediction accuracy. Here, we note that the codebook is oversampled and the beams overlap. In systems with non-overlapping beams, covering the FoV with a lower number of beams will translate to a wider beamwidth per beam with reduced gain.  
Higher-dimension codebooks with narrower beams (and higher gains) will translate to a higher probability of beam misalignment and, by implication, lower beam prediction accuracies. There is, therefore, a tradeoff between the beam prediction accuracy (choice of beam) and the system performance (with respect to received power and gain, and by extension, SNR).  
For scenario-by-scenario analyses for \(M=8\), Figure 6(a) shows that SVM achieves an accuracy of over 90% in Scenario 1, followed by KNN with 90%, while DT and NB's accuracies are 88% and 78%, respectively. In Scenario 2, SVM maintains its performance as the best algorithm, followed by DT, KNN, and NB. For Scenario 5, the best performing algorithm is DT with 90% accuracy, followed by SVM, KNN, and NB. In Scenario 6, SVM outperforms the other algorithms, followed by DT and KNN, with NB performing better than in Scenarios 2 and 5. Lastly, in Scenario 7, SVM is again the best performing algorithm, followed by DT and KNN, with NB ranking last. For \(M=16\) and \(M=32\), the performances follow the same trend as those of \(M=8\). However, for the combined scenarios across all considered \(M\), DT has the best performance, followed by KNN, SVM, and NB in decreasing order of performance. For \(M=8\) in Figure 6(a), the best accuracy results are \(\sim\)90%. For \(M=16\) in Figure 6(b), the best accuracy results are \(\sim\)80%, while for \(M=32\) in Figure 6(c), the best accuracy results are \(\sim\)60%. The results generally show higher degradation moving from \(M=16\) to \(M=32\) than moving from \(M=8\) to \(M=16\).  
Overall, the beam accuracy results in Figure 7 show that the naive Bayes algorithm consistently has the least beam prediction accuracy across the different codebooks and  
Figure 7: Beam Prediction accuracy comparison for different codebook sizes and 80:20% dataset split.  
scenarios. This can be attributed to the fact that the longitude and latitude features are correlated or related, contrary to NB's assumption of unrelated features. The results also reveal that the other three algorithms (KNN, SVM, and DT) have comparable performances across the codebooks and scenarios, with SVM outperforming others on the scenario-by-scenario case while DT outperforms other algorithms in the combined scenario with larger data samples than the per-scenario cases.