# Hybrid VLC-RF Channel Estimation for GFDM Wireless Sensor Networks Using Tree-Based Regressor
## 7 Conclusions  
This paper introduced a tree decision-based regression model for channel estimation in hybrid VLC-RF generalized frequency division multiplexing (GFDM) wireless sensor networks. Through comprehensive simulations across a broad range of SNR values from  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**SNR** & \multicolumn{2}{c}{**Tree (Our)**} & \multicolumn{2}{c}{**MMSE**} & \multicolumn{2}{c}{**LMMSE**} & \multicolumn{2}{c}{**RandomForest**} & \multicolumn{2}{c}{**SVM**} & \multicolumn{2}{c}{**LinearRegression**} \\  & **BER** & **Acc** & **BER** & **Acc** & **BER** & **Acc** & **BER** & **Acc** & **BER** & **Acc** & **BER** & **Acc** \\ \hline \(-\)5 & 0.3853 & 0.6147 & 0.3798 & 0.6202 & 0.3795 & 0.6205 & 0.38  
\(-5\) dB to 30 dB, the proposed model was benchmarked against five well-established techniques: Minimum Mean Square Error (MMSE), linear MMSE (LMMSE), support vector machine (SVM), random forest (RF), and linear regression.  
The tree model consistently achieved very good performance across the key evaluation metrics, particularly in the mid-to-high SNR region, where most practical wireless systems operate. At SNR = 10 dB, the tree model achieved an accuracy of **90.83%** with a BER of **0.0917**. In contrast, MMSE and LMMSE lagged at around **85.5%** accuracy, while random forest slightly led with **91.01%** and SVM achieved **91.34%**. At this level, the tree model also reduced the Bit Error Rate (BER) to **0.0917**, outperforming MMSE (**0.1448**) and LMMSE (**0.1438**), as well as closely tracking random forest (**0.0899**) and SVM (**0.0866**).  
At SNR = 30 dB, the tree-based model further improved, achieving **97.63%** accuracy with a BER of **0.0237**. The BER of the proposed model dropped to a value nearly **five times lower** than MMSE (**0.1135**) and closely matched random forest (**0.0212**) and SVM (**0.0323**). These results validate the tree model's ability to maintain robustness not only in ideal high-SNR conditions, but also in the more critical and realistic mid-SNR regime, where conventional estimators begin to saturate in performance.  
Moreover, the tree-based model achieved this balance with a moderate inference time of **45.53 s**, which was significantly faster than random forest (**140.09 s**) and SVM (**189.35 s**), as well as only moderately higher than linear regression (**1.1819 s**). While the MMSE (**0.0073 s**) and LMMSE (**0.0090 s**) models were faster, they lacked the accuracy and BER required in dynamic environments. Thus, the tree model offers an effective trade-off between accuracy and computational efficiency, making it highly suitable for time-sensitive WSN deployments.  
Conceptualization, A.I.A., T.A.A. and A.T.S.; Methodology, A.I.A. and T.A.A.; Software, A.I.A.; Validation, A.I.A. and T.A.A.; Formal analysis, A.I.A., T.A.A. and A.T.S.; Investigation, T.A.A., A.T.S. and I.R.K.; Resources, T.A.A., A.T.S. and I.R.K.; Writing--original draft, A.I.A.; Writing--review & editing, T.A.A.; Visualization, T.A.A.; Supervision, T.A.A., A.T.S. and I.R.K.; Project administration, T.A.A., A.T.S. and I.R.K. All authors have read and agreed to the published version of this manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author due to ongoing related research and data use agreements that limit immediate public sharing.  
The authors declare no conflicts of interest.