## 4 Simulation Results and Discussion
It can be confirmed that the product characteristics of most random-based RDPS distribution patterns examined are also better than those of 'non-random fixed' DM, as shown in the results in Figure 3. More strictly speaking, the  
Figure 3: The maximum launch power of the worst channel. (**a**) resulting 1-dB EOP and (**b**) resulting 2 ps TJ. proposed 'random-inverse' schemed dispersion maps are judged to be superior in terms of flexibility as the DM link because the number of random patterns outperforms the results in the 'non-random fixed' DM is greater than in the maximum launch power characteristic of Figure 3. An additional fact that can be known from the results in Figure 4 is that the proposed 'random-inverse' schemed dispersion map is more advantageous for amplitude component compensation than for phase component compensation of distorted WDM channel signals. So far, through numerical analysis based on eye diagram evaluation of the received WDM signal, we confirmed that the proposed 'random-inverse' schemed dispersion map can improve the distortion compensation and increase the allowable launch power and residual dispersion compared to the 'non-random fixed' dispersion map, which is the most common DM link configuration method. As analyzed in a previous study [15], the reason why the 'random-inverse' dispersion map is superior to the 'non-random fixed' dispersion map for compensating for the distorted WDM channels is the large symmetry of power-dispersion with respect to the midway-OPC. That is, the random-inverse distribution can make the dispersion-power profile almost symmetrical with respect to the midway OPC; thus, it is possible to satisfy the conditions necessary for compensation of the signal distortion in the MSSI system. However, these results do not say that the 'random-inverse' schemed dispersion map is the best DM link configuration method. This is because the compensation characteristics vary depending on the arrangement of the randomly selected RDPS, and consequently, this limits the application of random arrays of RDPS in DM link design. In order to increase the usability of the 'random-inverse' dispersion map as the DM link for compensating for distorted WDM channels, it is necessary to derive general and reasonable features that can improve compensation performance without specific limitations from 50 random-based RDPS array patterns. Figure 5a,b show the top five dispersion maps, which are formed with random numbers that allow good performance for both maximum launch power and product characteristics. On the other hand, Figure 5c,d shows the bottom five dispersion maps created with random numbers that allow poor performance. The results in Figure 5 were all obtained through EOP evaluation and analysis. Meanwhile, Figure 6a-d shows dispersion maps shown through TJ evaluation and analysis. Figure 4: The product of the effective NRD and launch power. (**a**) resulting 1-dB EOP, and (**b**) resulting 2 ps TJ. What can be intuitively seen from Figures 5a,b and 6a,b is that even if the RDPS sign and magnitude of each optical fiber span are selected randomly, the compensation performance can be improved only when the shape of the cumulative dispersion profile over the entire link is close to antipodal symmetry. Furthermore, the cumulative dispersion profile of the antipodal symmetric configuration for good compensation should gradually increase and then decrease in the section before the midway OPC and have a positive value overall. Figure 5: Five dispersion maps with the best/worst compensation based on EOP evaluation. (**a**) the best compensation cases for varying DCF length, (**b**) the best compensation cases for varying SMF length, (**c**) the worst compensation cases for varying DCF length, and (**d**) the worst compensation cases for varying SMF length.