## 3 Results and Discussion
In the training and testing sets, the OFDM signal waveform intensities through the experimental channel and the channels based on different models are shown in Figure 5. It can be seen that in both the training and testing sets, the waveform through the BiLSTM model channel can well fit the experimental waveform. Figure 6 presents the data distribution and Probability Density Function (PDF) of the experimental OFDM data compared to the predicted data from the three different channel models. The figure illustrates that the predicted data distributions from all three proposed models closely match the original experimental OFDM data. This indicates that the proposed models accurately capture the statistical properties of the OFDM signals, providing a good fit to the experimental data. Figure 4: Model fitting performance. The establishment of end-to-end systems aims to optimize the structure of communication systems to achieve global system performance optimization and to help the receiver better receive signals. In traditional receivers, channel estimation usually employs methods like Least Squares (LS) and Minimum Mean Square Error (MMSE). However, LS performs poorly due to noise amplification, and MMSE is proven to be impractical due to its high complexity [18]. Recently, some typical schemes have used deep learning (DL) methods to replace the channel estimation part of traditional schemes, as shown in Figure 7a. In this paper, the established channel models are used to directly process the signals received by the receiver to evaluate the performance of the models as illustrated in Figure 7b. Unlike the approach in Figure 7a, which requires traditional DSP processing first, then uses the DL  
Figure 5: (**a–c**) Waveform fitting plots on the training set for the three algorithms. (**d–f**) Waveform fitting plots on the testing set for the three algorithms. Figure 6: The data distribution and PDFs of the experimental OFDM data and the predicted data from the three proposed models. (**a**) Data distribution and PDFs of the data predicted by the proposed Transformer algorithm structure and the original experimental data. (**b**) Data distribution and PDFs of the data predicted by the proposed BiLSTM algorithm structure and the original experimental data. (**c**) Data distribution and PDFs of the data predicted by the proposed BiGRU algorithm structure and the original experimental data. model, and finally performs traditional DSP processing again, the proposed method can directly equalize the waveform and perform simple DSP processing at the end. To validate the performance of the proposed end-to-end VLC system channel model, we evaluated the BER performance using traditional channel estimation methods, existing typical DL-based methods, and the proposed direct DL method. We collected 262,144 sample data points under different signal-to-noise ratio (SNR) conditions. These data include the transmission characteristics of VLC signals under various SNR conditions, and they are used to validate the performance and accuracy of the proposed model and method. In the experimental setup, the power at the transmitter is determined by the power of the LED. The LED power at the transmitter starts at 10 mW and gradually increases to vary the system's SNR. As shown in Figure 8, the direct reception scheme proposed in this paper effectively reduces the system BER, outperforming both traditional channel estimation schemes and existing DL-based schemes. Among the three proposed model structures, the Transformer model demonstrates significantly better BER performance in direct equalization compared to all other schemes. The bit error rate (BER) performance results show that the DL-based scheme achieves better BER performance without occupying additional spectrum resources, whereas traditional pilot-based schemes exhibit several orders of magnitude of disadvantage.