## 3 Results and Discussion  
A series of experiments were conducted to validate the performance of the proposed channel models for end-to-end VLC systems, and the results were analyzed. As shown in Figure 1a, OFDM signals were generated in MATLAB and transmitted using an arbitrary waveform generator (AWG, Tektronix AWG5012). The setup consisted of a set of \(X[K]\) with a length of 64, corresponding to an FFT length \(N_{fft}\) of 2 \(\times\) 64 + 2. The cyclic prefix \(N_{cp}\) was set to 1/4 of the length of \(X[K]\), resulting in a complete OFDM symbol length of \(N_{fft}+N_{cp}\). The signal data rate was 250 Mbps, with the LED (OSRAM LUW W5 SM) biased at 6 V and the signal driving voltage set to 1 V. At the receiving end, a commercial PD (Thorlabs PDA10A-EC) was used to receive the optical signal and perform photoelectric conversion at a distance of 3 m from the LED. A real-time oscilloscope (LeCroy SDA760 Zi) was then used to collect actual channel response data. We collected DCO-OFDM signal data from both ends of the channel to train the channel models. As shown in Figure 3, the loss functions of the proposed three channel models converge under 6000 training iterations. All models achieve a relatively low training loss level, indicating effective training and fitting of the channel models. Additionally, R-square was used to evaluate the fitting performance of the models [17], and it is calculated using the following formula:  
\[R^{2}=1-\frac{\sum_{i=0}^{n}(y_{i}-\hat{y_{i}})^{2}}{\sum_{i=0}^{n}(y_{i}-\hat{ y_{i}})^{2}} \tag{10}\]  
The formula used incorporates the following variables: \(n\) represents the length of the sequence, \(y_{i}\) denotes the \(i\)-th data point of the target sequence, \(\hat{y_{i}}\) is the \(i\)-th output from the neural network, and \(\hat{y_{i}}\) is the mean of the target sequence. The \(R^{2}\) value ranges from 0 to 1, with values closer to 1 indicating better fitting performance. Figure 3: Training loss functions of the three channel models. Figure 4 illustrates the fitting performance of the three proposed channel models: BiLSTM, BiGRU, and Transformer. The diagrams show the comparison between the actual values and the predicted values by each model. BiLSTM Model: The fitting performance demonstrates a good match between the actual and predicted values, capturing the overall trend and patterns in the data. BiGRU Model: Similar to the BiLSTM model, the BiGRU model shows strong fitting performance, effectively modeling the sequential data with slight variations from the actual values. Transformer Model: The Transformer model exhibits the best fitting performance among the three, closely aligning with the actual values due to its ability to capture complex dependencies through the multi-head attention mechanism. As shown in Figure 4, the channel model structures of the three proposed algorithms all achieve good fitting performance. However, compared to the Transformer model with multi-head attention mechanism, the data fitting performance of the BiLSTM and BiGRU models is slightly inferior, though they still demonstrate quite impressive performance. The R-square values for the models indicate that while the Transformer model achieves the highest fitting performance, the BiLSTM and BiGRU models also provide substantial accuracy and effectiveness in modeling the VLC channel. The multi-head attention mechanism in the Transformer allows it to capture more complex dependencies and interactions within the data, giving it an edge in performance. However, the BiLSTM and BiGRU models still offer robust solutions for channel modeling, especially in scenarios where computational simplicity and efficiency are desired. These fitting performance plots visually confirm the R-square evaluations, highlighting the strengths and slight differences in effectiveness among the three models in fitting the VLC channel data.