# Hybrid VLC-RF Channel Estimation for GFDM Wireless Sensor Networks Using Tree-Based Regressor

## TL;DR

This paper introduces a fast and efficient tree-based model for estimating hybrid VLC-RF channels in wireless sensor networks, offering significant speed improvements over traditional methods.

## Contribution

A novel tree-based regression approach for hybrid channel estimation in GFDM WSNs, emphasizing inference efficiency over marginal accuracy gains.

## Key findings

- The tree model achieved 90.83% accuracy at 10 dB and 97.63% at 30 dB with lower BER compared to SVM and random forest.
- The tree model's inference time was 45.53 seconds, over three times faster than random forest and four times faster than SVM.
- The model is well-suited for real-time, resource-constrained wireless systems due to its low computational overhead.

## Abstract

This paper proposes a tree-based regression model for hybrid channel estimation in wireless sensor networks (WSNs) in generalized frequency division multiplexing (GFDM) over both visible light communication (VLC) and radio frequency (RF) links. The hybrid channel incorporates both additive white Gaussian noise (AWGN) and Rayleigh fading to mimic realistic environments. Traditional estimators, such as MMSE and LMMSE, often underperform in such heterogeneous and nonlinear conditions due to their analytical rigidity. To overcome these limitations, we introduce a data-driven approach using a decision tree regressor trained on 18,000 signal samples across 36 SNR levels. Simulation results show that support vector machine (SVM) achieved 91.34% accuracy and a BER of 0.0866 at 10 dB, as well as 96.77% accuracy with a BER of 0.0323 at 30 dB. Random forest achieved 91.01% accuracy and a BER of 0.0899 at 10 dB, as well as 97.88% accuracy with a BER of 0.0212 at 30 dB. The proposed tree model attained 90.83% and 97.63% accuracy with BERs of 0.0917 and 0.0237, respectively, at the corresponding SNR values. The distinguishing advantage of the tree model lies in its inference efficiency. It completes predictions on the test dataset in just 45.53 s, making it over three times faster than random forest (140.09 s) and more than four times faster than SVM (189.35 s). This significant reduction in inference time makes the proposed tree model particularly well suited for real-time and resource-constrained WSN scenarios, where fast and efficient estimation is often more critical than marginal gains in accuracy. The results also highlight a trade-off, where the tree model provides sub-optimal predictive performance while significantly reducing computational overhead, making it an attractive choice for low-power and latency-sensitive wireless systems.