## 3 Optimized Distributed Raman Amplification Design over Multiple Fiber Spans
The theoretically predicted nonlinear product power is shown in Figure 14 as a function of frequency separation of the two lasers using the three DRA schemes. With no OPC, the nonlinear Kerr product power for all the three DRA schemes was up to \(-\)16 dBm in the low frequency region. However, because of the poor link symmetry caused by the signal power degradation between spans, scheme 1 showed the least Kerr power reduction of only \(\sim\)17 dB with a mid-link OPC. Higher Kerr product power compensation (\(\sim\)25 dB) was achieved using the first over-pumped span. The EDF-assisted scheme generated \(\sim\)1.5 dB gain to compensate the loss between spans and therefore achieved excellent signal power symmetry simultaneously for both single-span and two-span links, which showed the highest compensation (up to 32 dB) in nonlinear Kerr product power. Figure 14: Theoretically predicated nonlinear product frequency separation without/with a mid-link OPC using different DRA schemes over 2 \(\times\) 50 km spans. Dotted lines—no OPC, solid-with OPC. (**a**) No account of loss, (**b**) accounting for loss with excess Raman gain, (**c**) accounting for loss with EDF. A numerical simulation was performed based on 2 \(\times\) 2 spans (50.4 km per span, which makes \(\sim\)200 km in total) using a 200 Gb/s DP-16 QAM (32 GBaud, 256 Gbit/s line rate, 2\({}^{16}\) PRBS length, 0.1 roll-off factor) signal centered at 194.8 THz with the three different DRA schemes (DP-16 QAM signal). The nonlinear Schrodinger equations (Manakov equations) were solved using the well-known split-step Fourier method [52; 53; 54] with a step size of 0.1 km, in which the signal power profiles shown in Figure 13 were used. The noise from each amplifier was modeled as Gaussian noise and added to the signal after each step (0.1 km) [2] to ensure that parametric noise amplification was correctly captured. The ASE noise of EDFAs at the transmitter, the OPC and the receiver were considered in the simulations (\(-\)140 dBm/Hz noise power density). More details about the simulation parameters can be found in [2]. In Figure 15, the EDF-assisted scheme 3 shows a maximum launch power improvement of 9 dB at a fixed Q\({}^{2}\) factor in the nonlinear regime, exceeding the improvement observed for the conventional DRA schemes 1 and 2 (by 4 and 2 dB), respectively. This is due to the nearly perfect signal power symmetry (>93% symmetry) from the EDF-generated gain compensating the loss between spans. However, as the overall transmission distance was \(\sim\)200 km, the noise from the Raman-amplified link was limited, and therefore the results were dominated by optical noise from EDFAs in the transmitter, OPC and receiver, which obscured the Q\({}^{2}\) factor benefit introduced by the nonlinearity compensation from the mid-link OPC and contributed to the small reduction in optimum Q\({}^{2}\) factor with mid-link OPC [2]. Figure 15: Q\({}^{2}\) factors versus signal launch power in inline transmission systems without/with OPC using the optimized dual-order DRA scheme at 200 km. Dotted lines—no OPC, solid—with OPC. (**a**) No account of loss, (**b**) accounting for loss with excess Raman gain, (**c**) accounting for loss with EDF. Figure 16 shows simulated transmission performances at 2000 km using the EDF-assisted Raman Scheme. As expected, the most symmetrical Raman scheme (Figures 13c and 15c) gives \(\sim\)8 dB Q\({}^{2}\) factor improvement (Q\({}^{2}\) factor is defined as 20 log10(sqrt(2).*erfcinv(2.*(BER)). In addition, the EDFA noise at the transmitter and receivers was deliberately removed for the EDF-assisted Raman scheme to evaluate the impact of such noise. In this case over 2000 km, the impact of the noise from EDFAs at the transmitter and receiver becomes negligible as the Q\({}^{2}\) factor differences are very small.