## 4 Results  
The system shown in Figure 1 was simulated for the depicted SCM/SSB and OSCM/SSB frequency plans. Pseudo random binary sequences (PRBS) of \(2^{10}-1\) bits were generated in each baseband source. Each PRBS was delayed by a random integer number of bits to ensure a degree of decorrelation between subchannels. In the baseband receivers, the digital signals were sampled in the middle of the bit period before performing a binary decision. It is important to note that the BER was calculated emulating a real system, in contrast with other approaches that estimate BER according to statistical distributions of noise. For different values of OMI, the attenuation of the VOA in the receiver was increased until a BER of 3.8 \(\times\)\(10^{-3}\) was achieved, which is the typical BER threshold for hard-decision forward error correction (HD-FEC) codes with a 7% overhead. With this procedure, the optical receiver sensitivities were obtained as a function of OMI. The simulated results, obtained with the VPI software, are illustrated in Figure 2, where they are also compared with the theoretical calculations obtained with the mathematical model presented in Section 3. Note that the results are shown as a function of overall rms OMI with respect to \(V_{\pi}\):  
\[M_{\%}=m\frac{2}{\pi}\sqrt{\frac{N}{2}}\cdot 100=\frac{v_{\text{rms}}\sqrt{N}}{V _{\pi}}\cdot 100=\frac{V_{\text{RMS}}}{V_{\pi}}\cdot 100, \tag{3}\]  
where \(v_{\text{rms}}\) is the rms voltage per subchannel and \(V_{\text{RMS}}\) is the overall rms voltage. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Frequency Plan**} & \multicolumn{2}{c}{**SCM (Subcarrier Multiplexing)**} & \multicolumn{2}{c}{**OSCM (Orthogonal Subcarrier Multiplexing)**} \\  & \multicolumn{2}{c}{**(Figure 1a)**} & \multicolumn{2}{c}{**(Figure 1b)**} \\ \hline IMP Count & \(N_{IM3}\) & \(N_{CTB}\) & \(N_{IM3}\) & \(N_{CTB}\) \\ Subchannel 1 & 2 & 0 & 1 & 0 \\ Subchannel 2 & 0 & 1 & 0 & 1 \\ Subchannel 3 & 1 & 0 & 1 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: IMP (intermodulation products) count for each subchannel in the photocurrent. Focusing on the SCM/SSB case, from Figure 2a, it can be deduced that the mathematical model estimates the sensitivities with an error \(\leq\)2 dB when the optical noise is dominant over nonlinearities (\(M_{\%}\leq 35\%\)). When nonlinearities are dominant, especially triple-beat for Subchannel 2, the error can be higher. This effect occurs because the Gaussian approximation is more accurate to model the ASE noise than the IMD. In reality, the effect of IMD is also related to the phase alignment of subchannels and can vary for different sampling points. Apart from that, the IMD count in this particular case is small, and Gaussian approximations tend to be more accurate when a higher number of intermodulation products take place. However, and despite the inaccuracies of the model, it can be observed that the optimum OMI that gives rise to the best achievable optical sensitivity for each subchannel is accurately predicted by the mathematical model (\(M_{\%}\approx 30\%\)). The mathematical model was developed for the non-overlapping SCM case. However, as the OSCM eye diagrams also present an ideal sampling point in the middle of the bit period [13], which is impaired only by noise and distortion, the mathematical model can also be applied to OSCM. A perfect compatibility of the model with OSCM is expected when the optical noise is completely dominant over IMD and determines the final sensitivity. In other cases, as any intermodulation product also distorts the adjacent subchannels, higher deviations between the VPI simulation and theory are expected. This effect can be observed in Figure 2b. In this case, even for low values of OMI (\(M_{\%}\leq 35\%\)), the error is higher than in the previous case, \(\leq\)4 dB. However, similarly to the previous case, the optimum OMI for each subchannel is predicted with a negligible error (\(M_{\%}\approx 25\%\) for Subchannel 2 and \(M_{\%}\approx 35\%\) for Subchannels 1 and 3).