## 1 Introduction  
In recent years, advancements in multimedia technologies, such as smartphones and televisions, have made high-capacity, high-speed communication a standard expectation. However, these advancements rely on the use of frequency bands, and the available spectrum for Radio Frequency (RF) communication is limited. Consequently, issues such as network congestion and connectivity difficulties have become increasingly common [1, 2, 3]. To address this challenge, there is growing demand for access to broader frequency resources. In this context, VLC, which utilizes visible light as a transmission medium, has garnered increasing attention. VLC offers significant advantages by exploiting the wide bandwidth of visible light (430 THz to 790 THz), which is substantially larger than the bandwidth of RF communication (3 kHz to 300 GHz). Furthermore, VLC does not overlap with existing RF frequency bands, making it a promising solution for mitigating spectrum scarcity [4]. Moreover, VLC commonly employs the Intensity Modulation/Direct Detection (IM/DD) scheme, where information is transmitted through variations in light intensity achieved by the high-speed switching of LEDs. This approach enables the construction of communication systems using existing LED lighting and cost-effective photodiodes, making VLC a promising candidate for rapid adoption in the near future [5, 6, 7]. Recently, VLC systems integrated with OFDM, referred to as VLC-OFDM systems, have gained significant attention for their efficient utilization of frequency resources [8, 9]. However, the LEDs used in VLC exhibit nonlinear characteristics between the driving current and emitted optical power, which introduces signal distortion during transmission [10, 11, 12]. In VLC-OFDM systems, such nonlinearities compromise the orthogonality between subcarriers, leading to substantial degradation of the communication system's performance [11]. Moreover, the nonlinear characteristics vary significantly not only between different LED types but also among individual LEDs within the same type [10]. This variability becomes even more pronounced in modern LED lighting systems that incorporate multiple LED chips, resulting in increasingly complex nonlinear behaviors. As a result, recent research has focused on developing compensation techniques to mitigate these nonlinear effects and improve the performance and reliability of VLC systems [13, 14, 15, 16, 17]. In conventional compensation methods for LED nonlinear characteristics, the transmitter receives the transmitted signal and estimates the nonlinear parameters, which necessitates sophisticated signal processing [14, 15]. Consequently, high-performance computational resources must be incorporated into the transmitter. This approach results in prohibitively high costs for individual LED luminaires, rendering it impractical. Moreover, while machine learning-based nonlinear compensation techniques are available, those methods that require offline training at both the transmitter and receiver incur an enormous computational burden [16, 17]. Therefore, for adaptive pre-distortion compensation designed to reduce the computational resources required at the transmitter, we propose a feedback-based adaptive pre-distortion method that employs a nonlinear parameter estimator at the receiver. This proposed method estimates the nonlinear characteristics of the transmitting LED using a parameter estimator at the receiver. The estimated parameters are then sent back to the transmitter using FeedBack Information (FBI), generally called Channel State Information (CSI), enabling the transmitter to perform adaptive pre-distortion based on this information. Furthermore, this study demonstrates that channel distortion effects can be mitigated by applying frequency symbol spreading (FSS) [18] to our proposed method, which equalizes the SNR of received signals through symbol spreading.