## 3 Simulation Results
Due to the EEPN (with an LO laser linewidth of 1 MHz), the best BER increases by two and a half orders of magnitude (from \(1.70\times 10^{-5}\) to \(6.95\times 10^{-3}\)) in the case of FF-DBP, while it only increases by less than an order of magnitude (from \(3.43\times 10^{-3}\) to \(1.41\times 10^{-2}\)) in the case of EDC. The relationship between the AIRs and optical launch powers in the 9-channel 32-Gbaud Nyquist-spaced DP-QPSK optical communication system was investigated, as described in Figure 3b. When there is no EEPN, the highest AIRs for the system are 1.11 Tbit/s, 1.13 Tbit/s, 1.14 Tbit/s, and 1.15 Tbit/s for the cases of EDC, single-channel, 5-channel, and full-field DBP, respectively. When the EEPN is applied with an LO linewidth of 100 kHz, it can be seen from Figure 3b that the AIRs of the transmission system are not significantly reduced in all compensation schemes for such an amount of EEPN. However, the degradation on AIRs becomes significant when the LO laser linewidth increases to 1 MHz. The best AIRs now become 1.03 Tbit/s, 1.05 Tbit/s, 1.07 Tbit/s, and 1.08 Tbit/s for the cases of EDC, single-channel, 5-channel, and full-field DBP, respectively. It is noted that, for all launch powers smaller than 0.5 dBm, the AIRs in the cases of single-channel and 5-channel DBP with the LO laser linewidth of 100 kHz are higher than the AIRs in the case of FF-DBP with the LO laser linewidth of 1 MHz. This indicates that a better-quality LO laser, which has a narrower linewidth and leads to a smaller EEPN, can significantly save the bandwidth and the computational effort in the operation of MC-DBP. Figure 4 shows the simulation results of the 9-channel 32-Gbaud Nyquist-spaced DP-16 QAM system at different scenarios of MC-DBP with and without the application of EEPN. The transmission distance is 2000 km. It can be seen from Figure 4a that the optimum launch powers for the use of EDC, single-channel, partial-channel, and full-field DBP are \(-2.0\) dBm, \(-2.0\) dBm, \(-1.0\) dBm, \(3.0\) dBm, respectively, when there is no EEPN. Corresponding optimal BERs are \(6.56\times 10^{-3}\), \(5.11\times 10^{-3}\), \(2.35\times 10^{-3}\), and \(2.36\times 10^{-3}\), respectively. When the EEPN is applied with an LO laser linewidth of 1 MHz, the optimum launch powers keep the same for the cases of EDC, single-channel, and 5-channel DBP, but decrease to 1.0 dBm for the case of FF-DBP. Meanwhile, the optimal BERs rise to \(1.67\times 10^{-2}\), \(1.51\times 10^{-2}\), \(1.51\times 10^{-2}\), and \(5.51\times 10^{-3}\), respectively. Due to the EEPN with an LO laser linewidth of 1 MHz, the best BER for the FF-DBP increases by two and a half orders of magnitude, similar as the optimal BERs. Figure 3: Simulation results of the DP-QPSK system with (w/) and without (w/o) equalization-enhanced phase noise (EEPN) at different multi-channel digital backpropagation (MC-DBP) bandwidths. (**a**) Bit-error-rate (BER) versus optical launch power, (**b**) achievable information rate (AIR) versus optical launch power. the DP-QPSK system. Apparently, the DP-16 QAM system is more sensitive to the EEPN than the DP-QPSK system. Because the transmission distance in the DP-16 QAM system is only a quarter of that in the DP-QPSK system, this will lead to the reduction of EEPN variance (to a quarter) according to Equation (1). The AIRs versus optical launch powers in the 9-channel 32-Gbaud Nyquist-spaced DP-16 QAM transmission system are shown in Figure 4b. It is found from Figure 4b that, similar to the DP-QPSK system, the EEPN with an LO laser linewidth of 100 kHz poses marginal degradation on AIRs in all EDC and MC-DBP schemes compared to the scenario without any EEPN. However, the EEPN with an LO laser linewidth of 1 MHz will cause a significant degradation to the AIRs. For the FF-DBP, the best AIR drops from 2.30 Tbit/s to 2.19 Tbit/s and the optimum launch power decreases from 3.0 dBm to 1.0 dBm compared to the scenario without any EEPN.