## 4 Discussions
Figure 9 illustrates the maximum AIRs versus transmission distances for the DP-QPSK, the DP-16 QAM, the DP-64 QAM, and the field-link Nyquist-spaced transmission systems with and without the application of EEPN. Here, the product between AIR and transmission distance \(AIR\cdot\sqrt{L}\) is employed as an indicator to evaluate the transmission quality of optical communication systems, the three hyperbolas in Figure 9 are provided using the formula of \(AIR\cdot\sqrt{L}=C\) based on the 9-channel 32-Gbaud Nyquist-spaced DP-QPSK system under the transmission distance of 8000 km and three LO laser linewidths (0 Hz, 100 kHz, 1 MHz). The AIR-distance product can reach 103.00 Tbit s\({}^{-1}\)km\({}^{1/2}\) and 102.82 Tbit s\({}^{-1}\)km\({}^{1/2}\) for the DP-QPSK system when the LO linewidths are 0 Hz and 100 kHz, respectively. However, it can only achieve 96.88 Tbit s\({}^{-1}\)km\({}^{1/2}\) when the LO linewidth is 1 MHz. It is very interesting that the AIR-distance products of the 9-channel 32-Gbaud Nyquist-spaced DP-16 QAM system are basically equal to the AIR-distance products in the DP-QPSK system for all different values of EEPN. For the 9-channel 32-Gbaud Nyquist-spaced DP-64 QAM system, the AIR-distance products are 114.63 Tbit s\({}^{-1}\)km\({}^{1/2}\) and 111.68 Tbit s\({}^{-1}\)km\({}^{1/2}\) for the LO linewidths of 0 Hz and 100 kHz, respectively. This shows a better performance (based on the indicator of the AIR-distance product) compared to the DP-QPSK and the DP-16 QAM systems. However, the product drops to 95.05 Tbit s\({}^{-1}\)km\({}^{1/2}\) when the LO linewidth rises to 1 MHz, which is similar to the indicators in the DP-QPSK and the DP-16 QAM systems. For the 820 km field-link transmission, the system shows a significant performance degradation compared to all above three systems in terms of the AIR-distance product. It can only reach 82.88 Tbit s\({}^{-1}\)km\({}^{1/2}\) in the case of FF-BDP when the LO laser linewidth is 1 MHz. Figure 9: Maximum AIRs versus transmission distance for the DP-QPSK, the DP-16 QAM, the DP-64 QAM, and the 820 km field-link Nyquist-spaced transmission systems with and without EEPN. The three hyperbolas are obtained by \(AIR\cdot\sqrt{L}=C\) based on the 9-channel 32-Gbaud Nyquist-spaced DP-QPSK system under the transmission distance of 8000 km and three LO laser linewidths (0 Hz, 100 kHz, 1 MHz). In this research, the impact of EEPN is investigated in optical communication systems based on the use of MC-DBP, which is one of the most promising approaches for nonlinearity compensation in next-generation optical fiber networks, due to its flexible implementation and optimization in the hardware. Meanwhile, the optical phase conjugation (OPC) is another promising technique to compensate for fiber nonlinearities in WDM optical transmission systems [34; 35]. In such systems, the phase fluctuation from the high-power pump laser, which is used for realizing the FWM-based OPC, will be transferred into the phase of output signals [13]. Therefore, the EEPN in OPC-based systems arises from the interactions between the phase noise from the high-power pump laser and the fiber dispersion experienced by the phase-conjugated optical signals.