## 4 Conclusions  
Based on the chirp model of the EML laser, the second-order Volterra transmission model of the EML-IMDD system is deduced in this paper. It is found that in the second-order nonlinear terms, the signal square terms have a greater influence on the received signal than other nonlinear terms. According to this model, Volterra's nonlinear kernel matrix is simplified; at the same time, the absolute value operation is used instead of the square operation to reduce the number of multiplications required by the equalizer. Through simplification, a simplified nonlinear-DFE equalizer is proposed. Compared with the traditional Volterra-DFE equalizer, the simplified equalizer greatly reduces the number of taps and multiplications. The proposed equalizer is verified by 112 Gbit/s and 128 Gbit/s IM-DD system transmission using an EML laser. The complexity of the simplified equalizer is greatly reduced; thus, the operation time is also reduced to a great extent.  
Using the simplified Volterra-DFE equalizer proposed in this paper, the BER of the 112 Gbps PAM-4 signal can reach the threshold of KP4-FEC (BER = 2 \(\times\) 10\({}^{-4}\)) after 10.8 km standard single-mode fiber transmission. The 128 Gbps PAM-4 signal can reach the HD-FEC (BER = 3.8 \(\times\) 10\({}^{-3}\)) threshold, which has a 1 dB sensitivity improvement over the traditional DFE equalizer. At the same time, its equalization effect is basically the same as the Volterra-DFE equalizer before simplification in the EML-IMDD system, which also proves the derivation in this paper. Above all, the proposed equalization scheme can provide an effective and low-complexity choice for signal equalization in the EML-IMDD system in data communication.  
Figure 12: BER Performance of 112 Gbit/s PAM4 after 10 km Transmission with PNLE or Proposed Equalizer.  
Figure 13: BER Performance of 128 Gbit/s PAM4 after 10 km Transmission with PNLE or Proposed Equalizer.  
**Author Contributions:** Conceptualization, Y.X., P.H. and W.L.; methodology, Y.X. and P.H.; validation, P.H. and N.L.; investigation, Y.X. and P.H.; resources, W.L.; data curation, P.H. and N.L.; writing--original draft preparation, Y.X. and P.H.; writing--review and editing, Y.X., P.H. and W.L.; supervision, W.L. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.  
**Data Availability Statement:** Data is unavailable due to privacy.  
**Acknowledgments:** The authors are grateful to those who provided technical support for experiments in this paper. [PERSON] and [PERSON] provided the photoelectric devices and parameters used in the experiments, representing Hisense Broadband Multimedia Technologies Co., Ltd. [PERSON] provided transmission fibers and the DEMO board, representing Accelink Technologies Co., Ltd. [PERSON] provided test equipment and a test site, representing State Key Laboratory of Optical Communication Technologies and Networks.  
**Conflicts of Interest:** The authors declare no conflict of interest.