# Design of PAM-8 VLC Transceiver System Employing Neural Network-Based FFE and Post-Equalization
## 5 Simulation Results and Discussion
### Post-Equalization Performance Evaluation  
To evaluate the post-equalization performance, the bandwidth of the AFE on the receiver side was analyzed first. The \(-3\) dB bandwidth of the AFE in the receiver, including the PD model and the corresponding total gain, were simulated as shown in Figure 15. It can be noticed that the total bandwidth was 906.8 MHz, with a TIA gain of 73.9 dB.  
The BER is one of the most important evaluation criteria of data transmission quality, and the relationship of the BER with the data rate was studied to find the maximum data rate that the VLC system could support with the BER criteria of 3.8 \(\times\) 10\({}^{-3}\). The data transmission quality of using the RBF-NN as the post-equalizer, using a DNN, and using a traditional equalization scheme of FFE were compared under a 3 m free-space channel, and the results are presented in Figure 16a. The highest data rate of using the RBF-NN as a post-equalizer was 3.6 Gbps, while the highest data rates that could be achieved with the DNN equalizer or FFE were 3.3 Gbps and 2.7 Gbps, respectively. By utilizing the RBF-NN as the equalization scheme, the communication data rate could be improved by 20% when compared with the DNN due to the more suitable activation function. In addition, the highest data rate that this system could support with different types of channels was also studied. As shown in Figure 16b, the highest achievable data rate for a 1.2 m water channel was 4.2 Gbps, which was higher than the 3 m free-space channel due to less channel loss with the RBF-NN.  
Figure 16: Simulated results of BER vs. data rate: (**a**) using RBF-NN, DNN, or FFE as a post-equalizer with 3 m free-space channel; (**b**) 3 m free-space and 1.2 m water channel with RBF-NN.  
Figure 15: \(-3\) dB bandwidth and gain of receiver AFE including PD.  
The simulated received eye diagrams using the RBF-NN as a post-equalization scheme at two different data rates with two types of channels are presented in Figure 17. Figure 17a,b shows the eye diagrams acquired with a 3 m free-space channel model utilized as the VLC channel under the data rates of 2.7 Gbps and 3.6 Gbps, respectively. Comparing Figure 17a to Figure 17b, it can be noticed that the eye quality decreased with the increase in data rate. Figure 17a shows an eye diagram acquired with a BER of \(10^{-5}\), while Figure 17b is the case a BER equal to 3.8 \(\times\)\(10^{-3}\). These two figures also present the case of error-free and the case of maximum BER tolerated for signal transmission. Meanwhile, Figure 17c,d displays the eye diagrams acquired with a 1.2 m underwater channel model under the data rates of 3.3 Gbps and 4.2 Gbps. According to Figure 4, the path loss of the 3 m free-space channel was around 5 dB larger than the 1.2 m underwater channel. Therefore, by comparing the upper two figures with the lower two figures, it can be concluded that, under the same BER criteria, the communication data rate increased when the path loss decreased. In addition, when taking Figure 14b,d into comparison, the feasibility of the RBF-NN enabled post-equalization could be proved. Since Figure 14b,d represent the eye diagrams acquired with the FFE and passive equalizers on the transmitter side, the upper two eye diagrams are the results of transmission through the 3 m free-space channel and processing by the receiver. It can be noticed that the eye quality was hugely increased when comparing Figure 14b,d.  
Figure 17: Simulated eye diagrams of PAM-8 signal with RBF-NN as post-equalizer: (**a**) communication data rate of 2.7 Gbps with 3 m free-space channel; (**b**) communication data rate of 3.6 Gbps with 3 m free-space channel; (**c**) communication data rate of 3.3 Gbps with 1.2 m underwater channel; (**d**) communication data rate of 4.2 Gbps with 1.2 m underwater channel.