## 3 Materials and Methods
### Codebook Sizes and Data Split Ratios  
The main focus of this study is to investigate the impacts of codebook size and data split ratio on ML-driven beam prediction. The original dataset consists of indices \(M=64\) beams. To reduce complexity and beams' overlap, the beam codebook is downsampled from \(M=64\) beams to \(M\in\{32,16,8\}\) beams as shown in Table 2. We then analyze the impacts of this downsampling on the beam prediction performance (i.e., using accuracy and related metrics) for the considered ML algorithms (i.e., KNN, SVM, DT, and NB).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**64 Beams** & **32 Beams** & **16 Beams** & **8 Beams** \\ \hline \(1,2\) & \(1\) & & \\ \hline \(3,4\) & \(2\) & & \\ \hline \(5,6\) & \(3\) & & \(1\) \\ \hline \(7,8\) & \(4\) & & \(2\) & \\ \hline \(9,10\) & \(5\) & & \(3\) & \\ \hline \(11,12\) & \(6\) & & \(2\) \\ \hline \(13,14\) & \(7\) & & \(4\) & \\ \hline \(15,16\) & \(8\) & & \(5\) & \\ \hline \(17,18\) & \(9\) & & \(3\) \\ \hline \(19,20\) & \(10\) & & \(6\) & \\ \hline \(21,22\) & \(11\) & & \(3\) \\ \hline \(23,24\) & \(12\) & & \(6\) & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Beam Codebook Downsampling.  
Figure 3: Study methodology flowchart.  
In Figures 4 and 5, we compare the \(M\in\{64,32,16,8\}\) multi-beam patterns for the ideal [21] and measured [19] cases, respectively. Unlike the ideal patterns in Figure 4 with uniform received powers and gains, the measured beam patterns in Figure 5 have non-uniform powers/gains across the beams, which indicate that the choice of beams in the downsampled codebooks may have impacts on performance. In Figure 6a-c, however, we show that the impact of beam codebook downsampling is not significant with respect to beam powers that determine the beam indices used as the ML output. Taking \(M=32\) as an example, downsampling by a factor of 2 implies taking either odd-numbered \(\{1,3,5,\ldots,63\}\) or even-numbered \(\{2,4,6,\ldots,64\}\) beams for the 32 classes. The same patterns can be observed for \(M=16\) and \(M=8\). For all cases, the corresponding beam powers are comparable, except beam indexes 1 and 64 with significantly lower beam powers due to measurement design [19]. We note that the results in Figure 6 are averaged over the total 9454 samples used in this study (i.e., for Scenarios 1, 2, 5, 6, and 7 combined).  
Further, this study also examines the impacts of the different data splits on the beam prediction accuracy performance of KNN, SVM, DT, and NB algorithms on the dataset. The different data splits used in the ML-based beam prediction training to testing sample ratios are as presented in Table 1 (i.e., {80:20, 70:30, 60:40}%). The hold-out partitioning method was used for data split.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**64 Beams** & **32 Beams** & **16 Beams** & **8 Beams** \\ \hline  
\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._Figure 4: Ideal multi-beam patterns for \(M\in\{64,32,16,8\}\) (Generated using MATLAB code from [21]).  
Figure 5: Measured multi-beam patterns for \(M\in\{64,32,16,8\}\) (Generated using data and MATLAB code from [19]).  
Figure 6: _Cont._