# Multipath Interference Impact Due to Fiber Mode Coupling in C+L+S Multiband Transmission Reach
## 4 Transmission Reach Assessment
### Transmission Reach Assessment Without MPI  
In this section, we present and validate our procedure to assess the transmission reach in a C+L+S MB scenario without the MPI's impact for the 64 GBaud scenario. To estimate the maximum reach for each transmission band--C-, L-, and S-band--without MPI, we use the following four-step procedure:  
1. In the first step, and assuming a single span, we assess the channel frequency for each band, considering a range of power channel values between \(-15\) and \(5\) dBm, which minimizes the GSNR, given by Equation (4). The channel with the lowest GSNR is selected to represent each band, so that every channel within the band can, at least, propagate the estimated distance. 2. In the second step, with the channel frequency assessed in step 1, we compute the GSNR as a function of the channel power, so that the power that maximizes the GSNR for each one of the bands can be found, which is called the optimum channel power. At the end of this step, we can show that the optimum channel power is \(1\) dBm. 3. In the third step, using the channel frequency found in step 1 and the optimum channel power found in step 2, we can compute the GSNR as a function of the number of spans. 4. Finally, in step four, we compare the required signal-to-noise ratio (RSNR) for a particular modulation format and bit error rate (BER) with the GSNR computed in step 3 and estimate the maximum reach for each transmission band and modulation format. A fixed 2 dB system margin is assumed to account for performance-degrading effects [5]. Next, we present some results for a C+L+S MB scenario. In Figure 3, we represent the GSNR as a function of the channel launch power, as described in the second step above, for the three bands studied without the MPI impact. The green line represents the L-band, the red line the C-band, and the blue line the S-band. As we can observe in Figure 3, there is an optimal power that maximizes the GSNR, which is approximately \(1\) dBm for each one of the three bands. The channel power choice is an important parameter in the GSNR computation since it influences the amplifier gain and consequently the ASE noise power. Also, from Figure 3, the GSNR for the L-band is \(1.6\) dB higher than the C-band's GSNR and \(7.2\) dB higher than the S-band's, for the \(1\) dBm channel power scenario. These differences are mainly explained by the higher amplifier noise factor in the S-band and C-band when compared to the L-band [5], as well as the ISRS effect that is responsible for the power transfer between the higher to lower frequencies. Similar results are reported in [5]. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**G.654E SMF Parameters**} \\ \hline Dispersion parameter (ps/nm/km) & 21 \\ Loss coefficient (dB/km) & 0.17 \\ Raman gain profile (W\(\cdot\)THz\(\cdot\)km)\({}^{-1}\) & 0.018 \\ Core effective area (\(\upmu\)m\({}^{2}\)) & 125 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: G.654E SMF parameters [14; 29]. Figure 4 represents the NLI noise power as a function of the channel frequency, considering a 1 dBm channel power. It can be observed that the L-band is more affected by the NLI noise power in comparison with the C- and S-bands, which is justified once again by the influence of the ISRS [5]. However, regarding the influence of ASE noise power, it can be shown that the L-band is the least affected band, and the most affected is the S-band due to higher amplifier noise factors and due to its use of channels with higher frequencies [5]. Figure 5 shows the GSNR as a function of the channel frequency for a 1 dBm channel power. It can be observed that the L-band presents the best GSNR, while the S-band gives the worst GSNR. Similar results are reported in [5]. Figure 4: NLI noise power as a function of the channel frequency. Figure 3: GSNR per band as a function of the optical channel power. In Figure 6, the GSNR is represented as a function of the number of spans for the three studied bands.