## 5 Conclusions  
We review the application of distributed Raman amplifiers with different designs for nonlinearity compensation in mid-link OPC systems. We demonstrate for single-span system with mid-link OPC that a dual-order backward-pumped Raman scheme can efficiently compensate the nonlinearity given that the pump powers are optimized to maximize the signal power profile symmetry. We show that using optimized pump powers can achieve up to 97% symmetry and 39 dB nonlinear product power reduction using a mid-link OPC. For longer span length, bidirectional Raman pumping is required to maintain a similar level of symmetry. We demonstrate that a random fiber laser amplifier is the most suitable solution for mid-link OPC WDM systems using span lengths between 60 and 100 km with the best performance at the distance of 62 km, demonstrating the Kerr product reduction up to 37.6 dB.  
For multiple span systems, the optimized configurations (utilizing a 25 cm EDF) improve signal power profile symmetry and consequently enhance fiber nonlinearity compensation efficiency. This technique can compensate the loss of passive components between the spans and therefore maximize the overall signal power symmetry up to 93% in realistic multi-fiber-span link in a cost-effective manner. We demonstrate that, in the multi-span link with a mid-link OPC, using this scheme shows ~32 dB nonlinear product compensation that is at least 7 dB higher than conventional dual-order Raman schemes. We also show that, for nearly symmetrical signal power profiles, the Raman schemes in both the single-span and two-span systems give a 9 dB enhancement of the nonlinear threshold in the 200 Gb/s DP-16 QAM transmission system using a mid-link OPC.  
[PERSON] and [PERSON] proposed the concept and initiated the study. [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] carried out numerical simulations. [PERSON], [PERSON] and [PERSON] performed the experiments. [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] conducted analytical calculations. [PERSON] and [PERSON] supervised the studies. The paper was written by [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the UK Engineering and Physical Sciences Research Council (EPSRC) Grant EP/S003436/1 (PHOS), EP/V000969/1 (ARGON), EP/S016171/1(EEMC), the Polish Ministry of Science and Higher Education Grant 12300051, EU Horizon 2020 Project 101008280, RTI2018-097957-B-C33 (ECOSYSTEM) funded by Spanish MCN/AEI/10.13039/501100011033, Research and innovation Programme SINROTON2-CM (S2018/NMT-4326) co-financed by ESF funds, and the National Natural Science Foundation of China Grant 61975027.  
Not applicable.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Span Lengths** & **Raman Pumping Schemes** & **Optimum Signal Power Profile Symmetry** \\ \hline
25 km & First-order bidirectional pumping & 97\% [12] \\
50 km & Dual-order backward pumping & 97\% [23] \\
62 km & Second-order bidirectional pumping with random fiber laser & 97\% [29] \\
100 km & Second-order bidirectional pumping with random fiber laser & 72\% [29] \\
2 \(\times\) 50 km & Dual-order backward pumping with EDF in the first span, no & 93\% [2] \\  & EDF in the second span & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of the best span symmetry with corresponding Raman schemes at different span lengths.  
Data Availability Statement: Original data are available at Aston Research Explorer ([[https://doi.org/10.17036/researchdata.aston.ac.uk.00000534](https://doi.org/10.17036/researchdata.aston.ac.uk.00000534)]([https://doi.org/10.17036/researchdata.aston.ac.uk.00000534](https://doi.org/10.17036/researchdata.aston.ac.uk.00000534)) (accessed on 16 December 2021)).  
The authors would like to thank [PERSON] and [PERSON] for insightful discussions and Sterlite Technologies and Finisar for industrial support.  
The authors declare no conflict of interest.