## 2 Dispersion-Managed Link and WDM System Modeling  
### Dispersion-Managed Link  
The dispersion-managed link with the embedded midway OPC for transmitting WDM 24-channels of 40 Gb/s is illustrated in Figure 1. Each half link comprises 27 fiber spans; thus, total link consists of 54 fiber spans. All fiber spans include the SSMF and DCF, and the length of the SSMF is fixed to 80 km. The previous studies have shown that the deployment of fibers in the fiber span affects the compensation of each distorted channel [13; 14; 15]. The compensation is further increased when the arrangements of the SSMF and DCF are opposite with respect to the OPC. In this study, the DCF preceded the SSMF in every fiber span of the former half link; the DCF, on the other hand, was placed after the SSMF in the latter half link. In this study, the RDPS of fiber span was randomly selected as 1 of 27 values from \(-1300\) to \(1300\) ps/nm, which were distinguished with intervals of 100 ps/nm. Each RDPS was determined by the length of the DCF because the length of the SSMF and the dispersion coefficients of the SSMF and DCF are fixed. We assumed the SSMF parameters as follows: the dispersion coefficient was 17 ps/nm/km, the attenuation coefficient was 0.2 dB/km, and the nonlinear coefficient was 1.41 W\({}^{-1}\) km\({}^{-1}\). The DCF was characterized as follows: the dispersion coefficient was \(-100\) ps/nm/km, the attenuation coefficient was 0.6 dB/km, and the nonlinear coefficient was 5.06 W\({}^{-1}\) km\({}^{-1}\). These parameter values were assumed for wavelength of 1550 nm. The completed random distribution of RDPSs means the arrangement order of random-value RDPS is not fixed in both halves. However, as mentioned earlier, the MSSI-based DM link configured with completed random distribution does not sufficiently compensate for the distorted WDM channels because it is difficult to establish the symmetry of local dispersion with respect to the OPC. Therefore, in this work, the RDPS distribution in the former half link is only essentially random, while the distribution in the latter half link is two cases with artificially arranged RDPSs as follows. The first case is expressed as \"random-inverse\", in which the RDPS of each fiber span in the former half link is randomly and independently determined as 1 of 27 values, while the arrangement of RDPSs for each fiber span in latter half is opposite to that of the former half. For the second case, in the latter half, the arrangement of the RDPSs of the fiber span is the same as the randomly aligned RDPSs in the former half; this case is called \"random-follow\". We also considered \"all-random\" distribution, in which the RDPS of each fiber span is simultaneously randomly arranged in both halves to compare the compensation performance. In considering three cases, we investigated 50 different distribution patterns. However, for a reasonable analysis of the compensation performance, the RDPS arrangement of the former half link was kept the same in all three cases. In summary, after randomly arranging 27 RDPSs for each fiber span of the former half, the RDPS for each fiber span in latter half was allocated in the same order as the arrangement in the former half (random-follow distribution), or the arrangement order of RDPS in the latter half was reversed with the former half (random-inverse distribution). Dispersion-managed links with completely different random arrangement of RDPS in the former half and latter half were also considered. These processes were independently repeated 50 times. It is well known that the best compensation occurs when the net residual dispersion (NRD) is sustained near but not 0 ps/nm in \"pseudolinear\" systems [16]. Our investigated  
Figure 1: The 960 Gb/s WDM transmission system through the dispersion-managed link and the midway OPC. system is also included the pseudolinear system. Thus, the arbitrary fiber span should control the NRD to optimal value.