## 3 Experiment Setup and Results
### Results Discussion  
Figure 5 shows the frequency response of the transmission system. We can see that the 3 dB bandwidth is only 26 GHz. In this case, the power fading in the high-frequency region caused by insufficient bandwidth will cause the signal to produce inter-code crosstalk, thus degrading the quality of the transmitted signal. The transmission rate is 56 GBaud/s and 64 GBuad/s. In order to compensate for the signal damage caused by insufficient \begin{table}
\begin{tabular}{c c c} \hline \hline
**Equalizer** & **Taps** & **Multiplication** \\ \hline DFE & \(L_{1}+K_{1}\) & \(L_{1}+K_{1}\) \\ Volterra-DFE & \(L_{1}+(L_{2}+1)L_{2}/2\) & \(L_{1}+(L_{2}+1)L_{2}\) \\  & \(+K_{1}+(K_{2}+1)K_{2}/2\) & \(+K_{1}+(K_{2}+1)K_{2}\) \\ Simplified Volterra-DFE & \(L_{1}+L_{2}+K_{1}+K_{2}\) & \(L_{1}+L_{2}+K_{1}+K_{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Equalizer complexity comparison. Figure 4: Experiment Setup. system bandwidth, the roll-off factor is set to 0.25 when pulse-shaping is performed at the transmitter. Figures 6 and 7 show the BER curves of signals with different transmission rates under different conditions. The feedforward taps and feedback taps in the DFE equalizer are 31 and 17, respectively. The number of first-order and second-order taps in the feedforward part of Volterra-DFE is 31 and 45, respectively, and the number of taps in the feedback part is 17 and 15, respectively. The number of taps in the simplified Volterra-DFE is composed of 31 and 9 taps in the feedforward part and 17 and 5 taps in the feedback part. In the second-order part, the absolute value operation is used instead of the square operation, which significantly reduces complexity. After simplification, the number of taps is reduced from 108 to 62, which is reduced by 42%. As can be seen from Figure 6, when the transmission rate is 112 Gbit/s, the main factor affecting the transmission BER is the device bandwidth. The signal is not damaged by dispersion; thus, the BER level is low. Using the proposed simplified Volterra-DFE equalizer, BER can reach the KP4-FEC threshold (2 \(\times\) 10\({}^{-4}\)) at \(-\)1 dBm received optical power. When the transmission rate is 128 Gbit/s, the HD-FEC BER threshold (3.8 \(\times\) 10\({}^{-3}\)) can be reached using each equalizer. The simplified Volterra-DFE equalizer has a 1 dB improvement over the traditional DFE equalizer. In addition, the results show that the effect of Volterra-DFE equalization is similar before and after simplification, which means the simplification is effective. Figure 5: Frequency Response of BTB Transmission System. Figure 6: BER Performance of 112 Gbit/s PAM4 after BTB Transmission. Figures 8 and 9 show the BER curves of different equalizers after signals with different transmission rates after transmitting through the 10.8 km SSMF. The feedforward taps and feedback taps in the DFE equalizer are 41 and 21, respectively. The number of first-order and second-order taps in the feedforward part of Volterra-DFE is 41 and 91, and the number of taps in the feedback part is 21 and 28, respectively. After simplification, the number of taps consists of 41 and 13 feed-forward taps with 21 and 7 feed-back taps. After simplification, the number of taps is reduced from 181 to 82, which is reduced by 55%. Figure 8 shows the transmission with a bit rate of 112 Gbps. It can be seen that the equalization effect of traditional Volterra-DFE and simplified Volterra-DFE is close to each other, and both can reach the threshold of the KP4-FEC bit error rate (\(2\times 10^{-4}\)), while the equalization effect of ordinary DFE equalizer is poor. Figure 10 shows the eye diagrams at 112 Gb/s, and it can be seen that the eyes open when using both the DFE equalizer and the proposed equalizer. However, using the latter equalizer can make the eyes clearer. This shows that the equalization effect is better in this case. Figure 9 shows the transmission with a bit rate of 128 Gbps.