## 2 Dispersion-Managed Link and WDM System Modelling
### Dispersion-Managed Link
The remaining three cases are structures that determine the magnitude of the residual dispersion allocated to each fiber span in relation to the number of fiber spans of the four FSGs arranged in each half-link. More specifically, based on the magnitude of the residual dispersion allocated to one fiber span in the FSG with the smallest number of fiber spans (this is called'reference residual dispersion' (abbreviated as 'rRD')), the magnitude of the residual dispersion allocated to each fiber span constituting the other three FSGs is obtained  
Figure 2: The proposed dispersion maps. by artificially changing the rRD magnitude depending on the number of fiber spans of the corresponding FSG. In the dispersion map shown in Figure 2c, the residual dispersion magnitudes of each fiber span of the FSG with 4 fiber spans, with 8 fiber spans, and with 16 fiber spans in each half-link are obtained by multiplying the magnitude of the rRD by 2, 4, and 8 times, respectively. In this dispersion map, if the increase/decrease rate of cumulative dispersion in FSG with 2 fiber spans is \(\pm\)100 (ps/nm)/span, then the increase/decrease rate of cumulative dispersion in FSGs with 4, 8, and 16 fiber spans has values of \(\pm\)200 (ps/nm)/span, \(\pm\)400 (ps/nm)/span and \(\pm\)800 (ps/nm)/span, respectively. For this reason, we will call the dispersion map in Figure 2c,d the'squared' scheme. In the dispersion map shown in Figure 2e,f, the residual dispersion magnitudes of each fiber span of the FSG with 4 fiber spans, with 8 fiber spans, and with 16 fiber spans in each half-link are obtained by multiplying the magnitude of the rRD by 2, 3, and 4 times, respectively. In this case, because the increase/decrease rate of the cumulative dispersion in each FSG is 2, 3, and 4 times of FSG with 2 fiber spans, respectively, these will be called to the 'linear' scheme. The last dispersion map considered in this study is the 'flatted' scheme shown in Figure 2g,h, because the maximum and minimum cumulative dispersion of each FSG are constant, unlike other dispersion maps. This dispersion map can be obtained by allocating the values corresponding to 1/2, 1/4, and 1/8 times of the magnitude of the rRD as the residual dispersion magnitude of each fiber span of FSGs with 4, 8, and 16 fiber spans, respectively. In summary, there are 16 types of dispersion maps proposed in this paper for compensation of distorted WDM channel signals according to the detailed configuration methods described so far. For the convenience of analyzing the simulation results, we classify and express the 16 dispersion maps in Figure 2 as \"the variation rate of rRD for each FSG--the deployment pattern of zero-crossing places: shape of unit dispersion map\", for example, \"fixed-DG: AD\", \"linear-GD: AD\", \"flatted-DG: DA\", etc. The shape of the 16 dispersion maps shown in Figure 2 is determined by appropriate selection of the lengths and dispersion coefficients of the SMF and DCF constituting the transmission link. In this paper, the length and the dispersion coefficient of SMF (\(l_{\text{SMF}}\) and \(D_{\text{SMF}}\)) are assumed to be 80 km and 17 ps/nm/km, respectively, and the dispersion coefficient of DCF (\(D_{\text{DCF}}\)) is assumed to be \(-\)100 ps/nm/km in all fiber spans. However, to adjust the cumulative dispersion and the shape of the specific dispersion map, only the DCF length of each fiber span (\(l_{\text{DCF}}\)) is varied by the equation below. \[l_{\text{DCF}}=\frac{(l_{SMF}\times D_{SMF})-RD}{|D_{DCF}|}, \tag{1}\]  
where \(RD\) means the residual dispersion of each fiber span. Other characteristics of SMF and DCF assumed in this paper are as follows: the attenuation coefficient of SMF is 0.2 dB/km, the nonlinear coefficient of SMF is 1.35 W\({}^{-1}\)km\({}^{-1}\) at 1550 nm, the attenuation coefficient of DCF is 0.6 dB/km, and nonlinear coefficient of DCF is 5.06 W\({}^{-1}\)km\({}^{-1}\) at 1550 nm.