# Hybrid VLC-RF Channel Estimation for GFDM Wireless Sensor Networks Using Tree-Based Regressor
## 4 Model Configuration and Training Parameters  
This section outlines the numerical configuration of all AI-based models employed for channel estimation in hybrid VLC-RF GFDM systems. The chosen parameter values were carefully selected to balance model complexity, accuracy, and computational efficiency, ensuring robust performance across varying SNR conditions. The tree model was configured with 100 decision trees, each with a maximum of 160 splits to fully leverage the 160 input features, and 160 independent regressors were trained to estimate each output component. The random forest model followed a similar structure, using 100 trees with 13 predictors randomly selected at each split to encourage diversity among trees and a minimum leaf size of 5 to optimize generalization. For support vector machine (SVM) models, a linear kernel was used in combination with standardized input features to ensure efficient training and reliable prediction. The SVM configuration included a BoxConstraint of 1 and an Epsilon value of 0.1, which control the margin softness and the regression sensitivity zone, respectively. The linear regression models were implemented using ordinary least squares with a linear polynomial degree, offering fast training and interpretability. All models were trained using a dataset comprising 18,000 samples and 160 features, generated across 36 distinct SNR levels with 500 signal realizations per level. The dataset was partitioned into 70% for training and 30% for testing, and the numerical parameters listed contributed directly to the strong generalization and predictive capabilities observed in the AI-based estimators (see Table 2). \begin{table}
\begin{tabular}{l l} \hline
**Parameter** & **Value/Description** \\ \hline
**GFDM Parameters** & \\ \hline Number of subcarriers (\(K\)) & 16 \\ Number of time slots (\(M\)) & 10 \\ Total GFDM symbol length (\(N=K\times M\)) & 160 \\ Modulation scheme & BPSK \\ Roll-off factor (\(\alpha\)) & 0.25 \\ Cyclic prefix length & 16 samples \\ \hline
**VLC Channel Parameters** & \\ \hline Channel type & AWGN \\ Noise type & Additive white Gaussian noise \\ SNR range & \(-5\) dB to 30 dB \\ \hline
**RF Channel Parameters** & \\ \hline Channel model & Rayleigh fading \\ Number of paths (\(L\)) & 3 \\ Path delays (\(\tau_{l}\)) & [0, 1, 2] \(\upmu\)s \\ Path gains (\(G_{l}\)) & [0, \(-3\), \(-6\)] dB \\ \hline
**Simulation Parameters** & \\ \hline SNR range tested & \(-5\) to 30 dB \\ Signals per SNR & 500 \\ Monte Carlo runs & 50 \\ Dataset structure & Input, target, and label per sample \\ \hline \end{tabular}
\end{table} 
Table 1: Parameter descriptions for the GFDM-based hybrid VLC-RF system. The first approach utilizes a tree model based on bagging (bootstrap aggregation). This method was chosen for its ability to reduce variance and capture nonlinear patterns through multiple decision trees trained independently for each output. The Algorithm 1 outlines the full training and evaluation process for the tree-based model. The second method applies a random forest regressor, which extends the tree approach by introducing feature randomness at each split. This helps prevent overfitting and improves generalization. The Algorithm 2 below describes the training and evaluation pipeline for the random forest model, including parameter settings, such as the number of trees and predictors per split. The third technique is based on support vector machines using a linear kernel. SVMs are effective for high-dimensional data and provide stable, interpretable decision boundaries. The Algorithm 3 details the steps for training and testing individual SVM models for each output bit, including input standardization and prediction thresholding. The final model uses ordinary least squares (OLS) linear regression. While simpler than tree- and kernel-based methods, linear regression provides a useful performance baseline. The Algorithm 4 below summarizes the training of 160 independent linear models and the subsequent evaluation using classification metrics.