## 3 Simulation Method and Numerical Assessment  
The characteristics of optical signal propagating in a medium dominated by loss, dispersion and nonlinearity can be expressed by the nonlinear Schrodinger equation (NLSE). Expressing NLSE as a slowly varying envelope approximation is as follows:  
\[\frac{\partial A_{j}}{\partial z}=-\frac{\alpha}{2}A_{j}-\frac{i}{2}\beta_{2j }\frac{\partial^{2}A_{j}}{\partial T^{2}}+\frac{1}{6}\beta_{3j}\frac{\partial ^{3}A_{j}}{\partial T^{3}}+i\gamma_{j}|A_{j}|^{2}A_{j}+2i\gamma_{j}|A_{k}|^{2 }A_{j}, \tag{2}\]where \(j\), \(k\) = 1, 2,..., 24 (\(j\
eq k\)), \(A_{j}\) represents the complex amplitude of the signal of the \(j\)-th channel, \(z\) is the propagation distance, \(\beta_{2j}\) is the GVD, \(\beta_{3j}\) is third-order dispersion, \(\gamma_{j}\) is the nonlinear coefficient, and \(T\) = \(t\) - \(z/v_{j}\) is the time measured in a retarded frame. The last two terms in (2) represent Kerr nonlinear effects, which are corresponding to self-phase modulation (SPM) and cross-phase modulation (XPM), respectively. It has been reported that the effect of XPM on WDM signals decreases as the dispersion of optical fiber increases [14]. The WDM signal may be affected by XPM due to the relatively high power of WDM signals, but since SMF with large dispersion coefficient was used as the basic fiber constituting the optical link, we excluded the effect of XPM based on the inference that the effect of XPM would be lower than that of SPM. The numerical approach of (2) is completed by using the split-step Fourier method [15]. The split-step Fourier method divides the transmission medium dominated by NLSE into small steps, and processes linear calculations in the frequency domain and nonlinear calculations in the time domain separately and continuously through Fourier transform and inverse Fourier transform for each step [15]. First, each WDM channel with different PRBS in the 24 transmitters in Figure 1 is generated at 0.8 nm wavelength intervals and multiplexed. The behavior of multiplexed signals transmitted over the dispersion-managed link in Figure 1 is interpreted by the NLSE of Equation (2). To analyze this, we modeled the link in Figure 1 by applying the split-step Fourier method at 0.1 km intervals. The software tool we used for simulation is MATLAB. For the noise in the transmission link in Figure 1, only the amplified spontaneous emission (ASE) generated by the EDFA was considered. The operating wavelength range of EDFA is from 1525 nm to 1570 nm, and the noise figure is assumed to be 5.5 dB based on 0 dBm of input power. The performance evaluation of the optical fiber system is generally based on the eye diagram of the received signals. The eye-opening penalty (EOP) and bit error rate (BER) are consequently measured through the eye diagram. The BER is mainly used for signal sensitivity analysis in fiber optic communication systems, whereas EOP is considered to be more effective for performance analysis of high-power signals. Since the optical signals have the launch powers above \(-10\) dBm, we use the EOP to assess the compensated optical signals in this work. An easy way to characterize the quality of digital signals degraded by deterministic distortions is the determination of the EOP. When sampling a binary signal per bit period at a specified sample time, the eye-opening (EO) is defined as the difference between the minimum value of the \"1\" pulse and the maximum value of the \"0\" pulse. We define EO by considering the average value of the received signal as follows: \(2P_{\text{av}}/(P_{1,\text{min}}P_{0,\text{max}})\), where \(P_{\text{av}}\) is the averaged power of the optical signals, and \(P_{1,\text{min}}\) and \(P_{0,\text{max}}\) are the minimum power of the '1' pulse and the maximum power of the '0' pulse, respectively. Therefore, EOP is defined as the following Equation (3) in terms of decibels.