# Analysis of Available Components and Performance Estimation of Optical Multi-Band Systems
## 3 Quantifying the Capacity and Transparent Reach of an OMB System
### Results  
In this section, we employ the physical layer formalism presented in the previous section to investigate the attainable transparent reach and capacity for an OMB system with S, C, and L-bands. Using the power allocation method of Equation (6), the computed optimal power for the middle channel of each band is \(-0.2\), \(-1.4\), \(-8.3\), and \(-9\) dBm for S\({}_{1}\), S\({}_{2}\), C, and L-bands, respectively. From these power levels, it is evident that the S-band requires a significantly higher power compared with C and L in order to compensate for the power depletion due to SRS. Moreover, the power of C and L-bands stresses them to operate in a deeply linear regime, where ASE noise is the dominant effect. Furthermore, three modulation formats are examined, namely PM-QPSK, PM-16 QAM, and PM-64 QAM, where each one requires a different OSNIR value in order to attain the same BER, as it is obvious from Equation (2). In particular, we target a BER of \(10^{-3}\) for which, from Equation (2), the required OSNIR is 9.8, 16.55, and 22.5 dB for PM-QPSK, PM-16 QAM, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter/Band** & \(\mathbf{S_{1}}\) & \(\mathbf{S_{2}}\) & \(\mathbf{C}\) & \(\mathbf{L}\) \\ \hline \(\lambda\) (nm) & 1467.5 & 1497.5 & 1547.5 & 1592.5 \\ \(a\) (dB/km) & 0.246 & 0.23 & 0.211 & 0.209 \\ \(D\) (ps/nm/km) & 12.1 & 14 & 16.9 & 19.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Operational parameters for each amplification band (extracted from [20]). and PM-64 QAM, respectively. Finally, the baud rate is set to 32 Gbaud, and the channel spacing equals 37.5 GHz. The OSNIR when the signal traverses a different number of optical nodes is illustrated in Figure 3. The inter-node distance is set to 150 km, and this link comprises three fiber spans of 50 km. The target OSNIR, which leads to a BER equal to \(10^{-3}\) for the three modulation formats, is also plotted with dashed lines. As it is evident, the C and L-bands, which are favored due to SRS, show a higher OSNIR performance compared with S\({}_{1}\) and S\({}_{2}\)-bands. In particular, the OSNIR of the S\({}_{1}\)-band is up to 3.4 dB lower compared with the other three bands, which in turn leads to a smaller attainable transparent reach. Evidently, when PM-QPSK is employed, a transparent reach of more than 2250 km can be attained in all bands. Next, when PM-16 QAM is considered, the attainable reach varies significantly between bands, from 600 km for the S\({}_{1}\)-band to 1350 km in the C-band. Finally, the PM-64 QAM can be employed to interconnect only adjacent nodes, as the OSNIR can hardly clear the threshold of 22.5 dB after 150 km in S\({}_{1}\) and S\({}_{2}\)-bands. As Figure 3 shows only an instance of OSNIR for the central channel of each band, Figure 4 illustrates the OSNIR for various channels per band. We calculate the OSNIR every 5 nm after 5, 10, and 15 optical nodes. A guard band of 5 nm is also considered between S\({}_{1}\) and S\({}_{2}\)-bands and between C and L-bands, whilst a larger guard band of 20 nm is set between the S\({}_{2}\) and C-bands. The latter guard band is set as the commercially available DFAs fail to provide sufficient gain in this spectral region. We can observe that even within the same band, there is a significant OSNIR difference of up to 4 dB between the channels located at the band edges. This clearly indicates that Equation (6) is needed to incorporate a greater number of channels from each band, and not only the central one if a flatter OSNIR over the entire band is the target. Another observation is that in order to increase further the number of channels, the unexploited 20 nm guard band between the S and C-bands has to be filled. For this purpose, the existence of a commercially available amplifier for this amplification range is mandated. Finally, we tabulate the overall attainable capacity and transmission reach when different modulation formats are employed (Table 7). In this table, we show the transmission reach for the channel with the lowest OSNIR in each band.