# Hybrid VLC-RF Channel Estimation for GFDM Wireless Sensor Networks Using Tree-Based Regressor
## 6 Simulation and Results  
To evaluate the performance of the proposed tree decision-based model for hybrid VLC-RF channel estimation in GFDM wireless sensor networks, we conducted simulations across a wide SNR range from \(-5\) dB to \(30\) dB. The tree model was compared with five other methods: Minimum Mean Square Error (MMSE), Linear MMSE (LMMSE), support vector machine (SVM), random forest (RF), and linear regression. This comparison includes both traditional statistical estimators and machine learning models to ensure comprehensive benchmarkingFigure 3 illustrates the BER performance. At SNR = 0 dB, BER was found to be high across all models due to significant noise, with tree at 0.2591, MMSE at 0.2615, and RF slightly better at 0.2577. As the SNR increased, BER sharply declined. At 10 dB, the tree model improved drastically to 0.0917, while MMSE and LMMSE remained relatively high at 0.1448 and 0.1438, respectively. RF and SVM performed closely to tree with 0.0899 and 0.0866, respectively. At 30 dB, tree achieved an excellent BER of 0.0237, only slightly behind RF (0.0212) and SVM (0.0323), and far ahead of MMSE (0.1135) and LMMSE (0.1122), confirming tree's robustness in high SNR environments. The inference time presented in Table 3 refers to the total duration required by each model to complete the prediction process on the entire test set. Specifically, with a dataset consisting of 18,000 samples and a 70/30 train-test split, each model performed inference on 5400 test samples. Given that each sample had 160 output features, this resulted in a total of 864,000 individual predictions per model. Inference time strictly measures how quickly a trained model can generate these predictions during the deployment phase, excluding any training or preprocessing time. This inference time is crucial in evaluating the practicality of different models, particularly for real-time and latency-sensitive applications where fast and efficient prediction is essential. While random forest achieved slightly superior BER performance across most SNR levels, the proposed tree model offers a compelling trade-off between accuracy and inference efficiency. As shown in Figure 3, tree achieved BER results close to the best-performing models: at 10 dB, it recorded a BER of 0.0956 compared to 0.0840 for random forest; and, at 30 dB, it reached 0.0216, only marginally behind RF's 0.0146. However, the inference time,  
Figure 3: The Bit Error Rate (BER) vs. SNR for tree, MMSE, LMMSE, SVM, RF, and linear regression. \begin{table}
\begin{tabular}{l c} \hline \hline
**Model** & **Inference Time (s)** \\ \hline MMSE & 0.007374 \\ LMMSE & 0.009032 \\ Linear Regression & 1.181935 \\ Random Forest & 140.094001 \\ SVM & 189.347879 \\ Tree (Proposed) & 45.531617 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The average inference time of each estimator. as detailed in Table 3, highlighted a crucial advantage of the tree model. On a test set of 5400 samples with 864,000 total predictions, the tree model completed inference in 45.53 s, significantly faster than random forest (140.09 s) and SVM (189.35 s). This considerable speed-up that is 3 times faster than RF and 4 times faster than SVM makes the tree model more suitable for real-time and latency-sensitive applications, where inference time is often as critical as prediction accuracy. Thus, despite not having the absolute lowest BER, the tree model attains a practical balance between robust accuracy and efficient inference, which makes it a strong candidate for deployment in real-world systems. As shown in Figure 4, regression accuracy improves with SNR. At 0 dB, the accuracy was modest: tree (74.09%), MMSE (73.85%), and RF (74.23%). Despite low values, the ML models already began outperforming the traditional estimators. At 10 dB, tree surged to 90.83%, while MMSE and LMMSE lagged at 85.52% and 85.62%. RF led with 91.01%, and SVM followed closely (91.34%). At 30 dB, tree achieved 97.63%, slightly behind RF (97.88%) and well above MMSE (88.65%) and LMMSE (88.78%).