# Hybrid VLC-RF Channel Estimation for GFDM Wireless Sensor Networks Using Tree-Based Regressor
## 6 Simulation and Results
These results highlight tree's scalability and data adaptability as the SNR improves. Figures 5 and 6 show that both precision and recall grew significantly with the SNR. At 0 dB, tree's precision was 61.98% and its recall was 61.41%, while RF and SVM were slightly better (62-63%). At 10 dB, tree's precision was 90.57% and its recall was 90.40%, just behind RF (91.27% and 91.01%, respectively) and SVM (91.09% and 90.91%, respectively). At 30 dB, tree achieved 97.89% precision and 97.83% recall, demonstrating strong balance. MMSE and LMMSE plateaued around 89%, showing limited adaptability, even at high SNR. Figure 4: Regression accuracy vs. SNR for tree, MMSE, LMMSE, SVM, RF, and linear regression. Figure 5: Precision vs. SNR for tree, MMSE, LMMSE, SVM, RF, and linear regression. Figure 7 further confirms the tree model's well-rounded performance through the F1-score curve. At 0 dB, tree scored 61.69%, with RF and SVM close behind. At 10 dB, tree reached 90.48% compared to MMSE's 86% and RF's 91.13%. At 30 dB, the tree model hit 97.86%, closely trailing RF (98.22%) and outperforming SVM (97.31%) and linear regression (95.94%). The consistent rise of the tree curve indicates its ability to maintain both high precision and high recall as channel conditions improve. Figures 8-10 provide signal estimation plots. At 0 dB, the tree model retained more signal shape compared to MMSE, which displayed smoothing and attenuation. At 10 dB, tree better approximated peaks and valleys, with RF and SVM also showing improvement. At 30 dB, the tree model's estimated waveform was nearly indistinguishable from the original signal, demonstrating excellent structural fidelity, and it was similar to RF and superior to the traditional estimators. Figure 6: Recall vs. SNR for tree, MMSE, LMMSE, SVM, RF, and linear regression. Figure 7: F1-score vs. SNR for tree, MMSE, LMMSE, SVM, RF, and linear regression. Figure 8: Original and estimated signals at SNR = 0 dB for all models. Figure 9: Original and estimated signals at SNR = 10 dB for all models. Figure 10: Original and estimated signals at SNR = 30 dB for all models. Figure 12: Scatter plot of the predicted vs. actual values at SNR = 10 dB. Beyond accuracy and error metrics, inference time is a key consideration for real-time channel estimation in wireless sensor networks. Table 3 presents the average inference time for each model. As expected, classical estimators, such as MMSE (0.007374 s) and MMSE (0.007374 s), MMSE (0.007374 s) and MMSE (0.007374 s), MMSE (0.007374 s), MMSE (0.007374 s) and MMSE (0.007374 s), MMSE (0.007374 s) and MMSE (0.007374 s). Figure 13: Scatter plot of the predicted vs. actual values at SNR = 30 dB. LMMSE (0.009032 s), were the fastest due to their low computational complexity. Linear regression also performed reasonably well with an inference time of 1.181935 s, although its estimation accuracy was limited. The proposed tree model required an average inference time of 45.531617 s. While this was significantly higher than that of MMSE and linear regression, it was still substantially lower than random forest (140.094001 s) and SVM (189.347879 s), which offer only marginal performance improvements in some scenarios. The tree model thus achieved a practical balance--delivering high estimation accuracy and low BER across all SNR levels while maintaining moderate computational demand. This makes it particularly well suited for deployment in real-world systems that require a compromise between performance and latency. In contrast, although the random forest and SVM models provided strong accuracy, their high inference times may limit applicability in time-sensitive or energy-constrained WSN environments. The tree model, therefore, offers an attractive middle ground: it outperforms traditional methods and avoids the excessive computational load associated with more complex ML ensembles (see Table 4).