## 3 Conversion Gain Results
Moreover, for differential modulation in co- and counter-directions, the conversion gain improved 10 dB at the highest mixing frequency compared to the standard modulation in both directions. Figure 11: Up-conversion gain at different mixing frequencies for the standard and differential modulation modes in the co- and counter-directions. The IF1 signal at \(f_{1}=1\) GHz is up-converted at \(nf_{s}+f_{1}\). Figure 12: Up-conversion gain at different mixing frequencies for the standard and differential modulation modes in the co- and counter-directions. The IF2 signal at \(f_{2}=2\) GHz is up-converted at \(nf_{s}+f_{2}\). As a result, we could obtain an up-conversion process in co- and counter-directions with very close simulation results through the conversion gain. Besides, positive conversion gain was achieved at the high mixing frequencies. Moreover, the maximum frequency range up to 158 GHz was achieved for both directions. It is crucial to notice that SOA-MZI low pass behavior degraded the mixed signal for about 35 dB at 158 GHz at any carrier frequency. However, the modulation principle played a significant role in amplifying the electrical power of the sampled signal compared to the switching principle [22; 35]. This resulted in higher conversion gains. Table 2 can be considered as another view of the conversion gains of up-converted signals, as shown in Figures 11 and 12. To clarify the figures, three conversion gains at the first, fifth, and tenth mixing frequencies have only been selected with respect to the first and second channels. The best up-conversion gains of mixed signals were shown for the standard modulation in the co-direction. Besides, the conversion gains related to channel two exhibited slightly lower values compared to the ones related to channel one under the four considered scenarios. In order to make the conversion scheme utilizing a SOA-MZI useful for the implementation of RoF, mm-wave or microwave systems, many IF signals at the UP or LP can be simultaneously up-converted at the SOA-MZI output. This is due to the wavelength of the sampled signal at the SOA-MZI output that is different to that of the optical input signal carrying data. Hence, for the second part of the simulation work, ten optical data signals injected at the UP for the standard modulation in co- and counter-directions were up-converted at the SOA-MZI output at mixing frequencies \(nf_{s}+f_{m}\), where \(m\) ranged from 1 to 10. On the other hand, five IF signals injected at the UP and other five ones were injected at the LP for the differential modulation in both directions are up-converted at the SOA-MZI output at \(nf_{s}+f_{m}\). \(f_{m}\) ranged from 0.2 GHz at \(m=1\) to 2 GHz at \(m=10\). For example, the IF1 signal (channel one) was at \(f_{1}=\)0.2 GHz, the IF5 signal (channel five) was at \(f_{5}=1\) GHz, which corresponded to the channel one in the first part of simulations, and the IF10 signal (channel ten) was at \(f_{10}=2\) GHz that corresponds to the channel two of the first part of simulations. Up-conversion gains were achieved for the simultaneous up-converted signals at \(nf_{s}+f_{m}\). They were only presented at \(10f_{s}+f_{m}\) related to \(H_{10}=10f_{s}\) of the sampling signal, as exhibited in Figure 13 for the four scenarios. Besides, the up-conversion gain slightly decreased with the channel rank for the four scenarios. For the differential modulation mode, the conversion gain improved 10 dB over the entire channel range compared to the standard modulation mode in both direction schemas. In the counter-direction schema, the conversion gain declined 2 dB for all channels compared to the one in the co-direction for both modes.