## 4 Simulation Results and Discussion  
Figure 2 shows the eye diagrams of the worst channel launched with 9 dBm power into the 'random-inverse' schemed dispersion-managed link configured by the specific random distribution (random pattern numbers 24 and 39). Among the 50 random pattern numbers, the 24 th and 39 th random patterns of RDPS are selected because they clearly showed the difference in compensation for changes in DCF length and SMF length, which are ultimately factors that determine RDPS. The results in Figure 2 are all obtained from the DM link with NRD set to 8 ps/nm. The EOP in Figure 2a,b are obtained as 5.71 dB and 0.81 dB, respectively, and the TJ in Figure 2c,d are obtained as 4.09 ps and 7.48 ps, respectively. When comparing the compensation of the distorted WDM channel depending on the length of the DCF or SMF length that determines the RDPS, it is reasonable to apply the same arrangement of RDPS in each case. Thus, the eye diagrams in Figure 2a,b and Figure 2c,d are results obtained from the dispersion-managed link with the same RDPS random arrangement applied, respectively. Figure 2: The eye diagrams. (**a**) random pattern number 24; varied DCF length, (**b**) random pattern number 24; varied SMF length, (**c**) random pattern number 39; varied DCF length and (**d**) random pattern number 39; varied SMF length. The reason the authors show Figure 2 is to inform that even for the same RDPS random arrangement, EOP and TJ should vary depending on the factors contributing to each RDPS. In other words, we confirmed from Figure 2 that the amplitude and phase component compensation for the distorted WDM signal depends on the RDPS random array and the specific method of creating it. From now on, the evaluation and analysis of the compensated WDM will be based on the comparison of each method of creating the RDPS random array. Figure 3a,b show the maximum launch power values corresponding to 1-dB EOP and 2 ps TJ, respectively. In Figure 3, \"descending order number\" means that the resulting maximum launch power is sorted from the largest value to the smallest value to facilitate comparative analysis. The values of 5.33 dB and 2.5 dB shown in Figure 3a,b represent the maximum launch power at which the worst channel received through the 'non-random fixed' DM would result in 1-dB EOP and 2 ps TJ, respectively. It can be confirmed from Figure 3a,b that the EOP and TJ characteristics through compensation in more than 45 RDPS array patterns out of 50 randomly generated in this study are superior to 'non-random fixed' scheme. In particular, the results in Figure 3 show that even if the same RDPS random arrangement is applied, the method of determining the RDPS by the DCF length can achieve improved performance in more random cases than the method of determining the RDPS by the SMF length. Figure 3a,b show the results when the NRD of individual DM link is set to 8 ps/nm, but as mentioned in previous research [15], there are several NRDs other than this value of the DM link that can obtain EOP of 1 dB or TJ of 2 ps. As in the previous study [15], the minimum and maximum NRD can be obtained for the launch powers of the WDM channel in the considered 102 types of DM links, which are classified according to the random pattern of RDPS and the method for determining it. Of course, the minimum and maximum NRD are the lower and upper limits that meet EOP of 1 dB or TJ of 2 ps. The width from this minimum NRD to the maximum NRD is defined as the effective NRD range, and the trajectory of the effective NRD range for the launch power becomes a closed curve. The effectiveness of applying the 'random-inverse' schemed dispersion map into the DM link increases as the area of the corresponding closed curve increases. We have defined the area of this closed surface in reference [15] as the product of the effective NRD and the launch power. Figure 4 shows the product of the effective NRD and launch power for all 'random-inverse' schemed dispersion maps.