## 4 Experiments and Results
### Distance Prediction  
Figure 5 presents the graphics of the \(MSE\) values of the initial and final distances between the SU and PU during the spectrum sensing with the variation in \(N_{0}\) in the proposed regression methods. It is noticeable that SVR and decision tree had the worst performance at all levels of noise. Random forest, XGB, transformer, LGBM, and extra trees demonstrated similar performance, as shown in the graph. However, LGBM exhibited slightly better performance than the others, especially at the lowest level of noise, achieving \(100.67\). In the final distance prediction, the extra trees model exhibited slightly better performance, achieving \(107.77\). Figure 6 presents the graphics of the \(MAE\) values of the initial and final distances between the SU and PU during the spectrum sensing with the variation in \(N_{0}\) in the proposed regression methods. It is also noticeable that SVR and decision tree had the worst performance at all levels of noise. Random forest, XGB, LGBM, transformer, and extra trees showed similar performance, as indicated in the graph. However, XGB exhibited slightly better performance than the others, achieving \(7.19\). In the final distance prediction, the extra trees model exhibited slightly better performance, achieving \(7.33\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Metric** & **RF** & **DT** & **ET** & **SVR** & **XGB** & **LGBM** & **Transformer** \\ \hline CC & 0.9801 & 0.9521 & 0.9794 & 0.0079 & **0.9806** & 0.979 & 0.9697 \\ \(MSE\) & 16.084 & 38.6547 & 16.8942 & 404.64335 & **15.53** & 16.35 & 19.2086 \\ \(MAE\) & **1.9473** & 2.32738 & 2.0186 & 17.2736 & 2.23 & 2.32 & 3.4854 \\ \(RMSE\) & 4.0104 & 6.2172 & 4.11026 & 20.11575 & **3.94** & 4.04 & 4.3827 \\ \(MAPE\) & **1.2534** & 1.49406 & 1.2971 & 12.3579 & 1.48 & 1.52 & 2.4489 \\ R\({}^{2}\) & 0.96025 & 0.9044 & 0.9582 & \(-4.0934\times 10^{-6}\) & **0.9616** & 0.959 & 0.9365 \\ \hline \hline \end{tabular}  
* CC is the abbreviation of correlation coefficient. RF is the abbreviation of random forest. DT is the abbreviation of decision tree. ET is the abbreviation of extra trees.  
\end{table} 
Table 6: Noise regression comparison metrics of the proposed methods. Figure 4: Graphic of the \(RMSE\) (**left**) and \(MAPE\) (**right**) of the proposed methods with \(N_{0}\) between \(-114\) dBm/Hz and \(-174\) dBm/Hz. Figure 7 presents the graphics of the \(RMSE\) values of the initial and final distances between the SU and PU during the spectrum sensing with the variation in \(N_{0}\) in the proposed regression methods. It is also noticeable that SVR and decision tree had the worst performance at all levels of noise. Random forest, XGB, LGBM, transformer, and extra trees showed similar performance, as indicated in the graph. However, LGBM exhibited slightly better performance than the others, achieving 10.03. In the final distance prediction, the extra trees model exhibited slightly better performance, achieving 10.38. Figure 8 presents the graphics of the \(MAPE\) values of the initial and final distances between the SU and PU during spectrum sensing with variations in \(N_{0}\) using the proposed regression methods. It is also noticeable that SVR and decision tree had the worst performance levels across all levels of noise. Random forest and extra trees showed similar performance, as displayed in the graph on the left. However, transformer exhibited slightly better performance than random forest, especially at \(-174\) dBm\(/\)Hz, \(-164\) dBm\(/\)Hz, and \(-155\) dBm\(/\)Hz, achieving 30.23. In the graph on the right, random forest, XGB, LGBM, and  
Figure 5: Graphic of the \(MSE\) (initial distance on the left and final distance on the right) of the proposed methods with \(N_{0}\) between \(-114\) dBm\(/\)Hz and \(-174\) dBm\(/\)Hz. Figure 6: Graphic of the \(MAE\) (initial distance on the left and final distance on the right) of the proposed methods with \(N_{0}\) between \(-114\) dBm\(/\)Hz and \(-174\) dBm\(/\)Hz.