## 2 Dispersion-Managed Link and WDM System Modelling  
### Dispersion-Managed Link with Random-Based RDPS  
Figure 1 shows the dispersion-managed link combined with the midway-OPC, transmitters, and receivers of WDM 24 channels of 40 Gb/s. Each half link comprises 15 optical fiber spans; thus, the total link consists of 30 fiber spans. All fiber spans include SMF and DCF for inline DM. The arrangement of the two types of optical fiber before and after the midway OPC is also important in making power-distribution symmetry in the MSSI system. As verified in the previous study of [15], this study also follows the scheme of inserting DCF before SMF in all optical fiber spans in the first half before the midway-OPC and arranging them in the opposite order in the second half. In this study, the RDPS of the optical fiber span is randomly determined to be one of 15 values from \(-\)560 ps/nm to 560 ps/nm, separated by 80 ps/nm intervals. These 15 RDPS values are determined solely by the length of the SMF or the length of the DCF in every span. We assume SMF parameters as follows: the dispersion coefficient is 16 ps/nm/km, the attenuation coefficient is 0.2 dB/km, and the nonlinear coefficient is 1.41 W\({}^{-1}\) km\({}^{-1}\). DCF is characterized as follows: the dispersion coefficient is \(-\)80 ps/nm/km, the attenuation coefficient is 0.6 dB/km, and the nonlinear coefficient is 5.06 W\({}^{-1}\) km\({}^{-1}\). These parameter values are assumed for wavelengths of 1550 nm. Each optical fiber length involved in determining the sign and magnitude of RDPS is changed by the selected RDPS based on the length that makes RDPS = 0 ps/nm. For RDPS = 0 ps/nm, the SMF length and the DCF length must be 80 km and 16 km, respectively. If the SMF length of each optical fiber span is fixed at 80 km and the RDPS is changed from \(-\)560 ps/nm to 560 ps/nm at 80 ps/nm intervals, the DCF length must be changed from 23 km to 9 km at \(-\)1 km intervals. From now on, we will call this method 'varied DCF length', as shown in Figure 1a. On the other hand, with the DCF length of each optical fiber span fixed at 16 km, the SMF length from 45 km to 115 km (5 km interval) corresponds to the RDPS from \(-\)560 ps/nm to 560 ps/nm. We call this method 'varied SMF length', which is plotted in Figure 1b. The random array scheme of RDPS considered in this paper is called 'random-inverse.' In this scheme, the RDPSs of each fiber span in the first half section are randomly selected as one of 15 values; the RDPS arrangement order of the second half section reverses the RDPS order assigned to the first half section to construct a dispersion map with antipodal symmetry. In summary, the purpose of this study is to evaluate the distortion compensation of 960 Gb/s WDM signals in cases where the factors that determine the random-based RDPS are the DCF length (Figure 1a) or the SMF length (Figure 1b) in the dispersion-managed link configured with the 'random-inverse' scheme. As the number of random cases increases, the resulting value can converge to a general value. Since the RDPS that are randomly determined in each optical fiber span of the first half section are independent of each other, if the RDPS are randomly selected for all 15 spans at the same time, the RDPS arrangement order also becomes independent. In other words, the overall arrangement order of the RDPS changes whenever the RDPS in each of the 15 spans of the first half section are selected simultaneously and randomly. We repeat 50 times to obtain 50 mutually independent RDPS array patterns under the conditions mentioned above and analyze compensation performance for all cases. Whatever the factor that determines the RDPS, the sum of the 15 RDPSs selected at random once becomes 0 ps/nm. Therefore, the accumulated dispersion of each half section shown in Figure 1 becomes 0 ps/nm. If the accumulated dispersion across all optical links is defined as net residual dispersion (NRD), the value in both Figure 1a,b is 0 ps/nm.