# Hybrid VLC-RF Channel Estimation for GFDM Wireless Sensor Networks Using Tree-Based Regressor
## 1 Introduction  
Wireless sensor networks (WSNs) represent a significant advancement in the deployment of intelligent systems across multiple domains, including smart cities, environmental monitoring, healthcare, and industrial automation. These networks consist of distributed sensor nodes that are energy-constrained and operate in dynamic settings, necessitating communication protocols that prioritize energy efficiency, low latency, and resilience to environmental interference [1]. Traditional radio frequency (RF) communication methods have proven effective; however, they face major issues, such as spectrum congestion,electromagnetic interference, and security vulnerabilities, thus prompting research into alternative communication methods [1; 2].  
Recently, visible light communication (VLC) has been recognized as a promising alternative owing to its significant advantages, including extensive unlicensed bandwidth and immunity to electromagnetic interference [2; 3]. Nevertheless, VLC is intrinsically limited by its reliance on line-of-sight conditions and changes in ambient lighting, leading researchers to develop hybrid VLC-RF systems that combine the strengths of both communication methods. These hybrid systems enhance coverage and robustness while improving spectral efficiency, making them suitable for next-generation WSN applications [4].  
Despite these advantages, hybrid VLC-RF systems present new technical challenges, particularly in channel estimation. The deterministic nature of VLC channels, juxtaposed with the stochastic characteristics of RF channels, complicates traditional estimation techniques as RF channels are often subject to multipath propagation effects. Advanced methods further complicate the scenario with inherent non-orthogonal characteristics that lead to inter-symbol interference (ISI), such as generalized frequency division multiplexing (GFDM) [4]. Consequently, conventional means of channel estimation, including Minimum Mean Square Error (MMSE) and Linear MMSE (LMMSE) techniques, tend to perform sub-optimally in these mixed environments, necessitating the adoption of more sophisticated solutions [5].  
In light of these challenges, there is a growing trend toward leveraging machine learning (ML) algorithms to enhance channel estimation methods in hybrid systems. Recent studies have demonstrated the viability of data-driven approaches, particularly those employing deep learning architectures designed to learn channel characteristics directly from empirical data without rigid model assumptions [6]. Tree-based models, such as decision trees and random forests, have emerged as practical options due to their minimal computational overhead, making them ideally suited for resource-constrained environments [7; 8; 9]. This trend highlights a critical shift toward integrating ML strategies not only for channel estimation, but also for various roles in optimizing the performance and efficiency of WSNs.  
In fact, WSNs stand at the crossroads of advancing communication technologies and machine learning methods. The integration of VLC and RF in hybrid systems promises substantial improvements over traditional RF communication, although it introduces new challenges in channel estimation that must be effectively addressed through innovative techniques, particularly in the realm of machine learning. Ultimately, these advancements can significantly enhance the capabilities of WSNs in the face of increasing demands from diverse real-time applications. The outline of the paper is shown in Figure 1.