## 3 Simulation Results  
In this section, numerical simulations based on the above analyses will be conducted. Firstly, the back-to-back (BtB) performance is investigated to evaluate the benchmark quality of considered transmission systems. Figure 2 shows the BtB performance of the measured BER versus the optical signal-to-noise-ratio (OSNR) for the 9-channel 32-Gbaud Nyquist-spaced DP-QPSK, DP-16 QAM, and DP-64 QAM systems. It is found that, to achieve a BER target of \(10^{-3}\), the required OSNRs in the DP-QPSK, the DP-16 QAM, and the DP-64 QAM transmission systems are 14.0 dB, 20.6 dB, and 27.0 dB, respectively. Figure 2: Back-to-back (BtB) performance of 9-channel 32-Gbaud Nyquist-spaced dual-polarization quadrature phase shift keying (DP-QPSK), dual-polarization 16-ary quadrature amplitude modulation (DP-16 QAM), and dual-polarization 64-ary quadrature amplitude modulation (DP-64 QAM) transmission systems. With and without taking EEPN into account, the BERs and AIRs of the 9-channel Nyquist-spaced transmission systems using EDC and MC-DBP are studied. Modulation formats of DP-QPSK, DP-16 QAM, and DP-64 QAM were applied. The linewidths of the transmitter laser and the LO laser were both set as 0 Hz to remove the EEPN. To include the EEPN, both the transmitter and LO laser linewidths were set to be equal, and two sets of values were considered: 100 kHz (for common ECL lasers) and 1 MHz (for common DFB lasers), respectively. Single-channel, partial-bandwidth, and full-field DBP were applied to perform nonlinearity compensation in the DSP-based receiver. The case of CD compensation only was also analyzed as reference results. In all following simulations, the MC-DBP was operated with 800 steps per span and a nonlinear coefficient of 1.2 /W/km to ensure its optimal performance. Simulation results of the 9-channel 32-Gbaud Nyquist-spaced DP-QPSK transmission system with and without the application of EEPN are shown in Figure 3, where the total distance of fiber link is 8000 km. The results are obtained under the use of EDC or MC-DBP with different back-propagated bandwidths. Figure 3a shows the BER versus optical launch power in DP-QPSK transmission system, the system BER using MC-DBP is obviously reduced compared with the EDC-only scheme under different LO linewidths. The compensation effect of FF-DBP is the most obvious because the intra-channel and inter-channel nonlinear interactions in the transmission channels were fully mitigated. When there is no EEPN, the optimum launch powers of \(-2.0\) dBm, \(-2.0\) dBm, \(-1.0\) dBm, and \(1.0\) dBm with the best BERs of \(3.43\times 10^{-3}\), \(2.10\times 10^{-3}\), \(1.09\times 10^{-3}\), and \(1.70\times 10^{-3}\) are achieved for the scenarios of EDC, single-channel, 5-channel, and full-field DBP, respectively. However, when EEPN is applied with an LO laser linewidth of 100 kHz, the optimum launch powers for EDC, signal-channel, and 5-channel DBP are still \(-2.0\) dBm, \(-2.0\) dBm, and \(-1.0\) dBm, respectively. However, the optimum launch powers for full-field DBP is changed to 0.0 dBm. Corresponding BERs rise to \(4.25\times 10^{-3}\), \(2.54\times 10^{-3}\), \(1.45\times 10^{-3}\), and \(1.46\times 10^{-3}\) compared to the scenario of no EEPN. When the LO laser linewidth rises to 1 MHz, the distortions from EEPN will become greater according to Equation (1). Simulation results in Figure 3a show that the optimum launch powers for EDC, signal-channel, and 5-channel DBP remain constant, respectively, but for FF-DBP, it drops to \(-1.0\) dBm. The system BERs increase further to \(1.41\times 10^{-2}\), \(1.07\times 10^{-2}\), \(8.75\times 10^{-3}\), and \(6.95\times 10^{-3}\) for EDC, signal-channel, 5-channel, and full-field DBP, respectively. It can be clearly seen that the performance of FF-DBP is the most susceptible to EEPN compared to EDC, single-channel, and 5-channel DBP.