## 5 Experimental Frequency Mixing Performance  
In order to compare with the simulation results, we built an experimental setup [22], which was the same as the one used in the simulation setup. Besides, the operating point was similar for both setups. The maximum frequency range reached in the experimental work is limited to \(4f_{s}+f_{10}=64.4\) GHz due to limited bandwidth of the ESA. So, the comparison between the real and simulated work will be for frequency mixing of the ten channels (10 IF signals) in the range of the mixing frequencies from \(f_{s}+f_{1}=\)15.6 + 0.2 = 15.8 GHz, which is the lowest mixing frequency, to \(4f_{s}+f_{10}=4\) (15.6) + 2 = 64.4 GHz, which is the highest one. We only compared the real and simulated up-converted signals of the ten channels based on the SOA-MZI in the co- and counter-direction schemas for the differential modulation at \(4f_{s}+f_{m}\) related to the fourth harmonic of the sampling signal. As a result, for the experimental study, ten channels are up-converted simultaneously, which are the same as the second part of the simulations. The conversion gain of the simultaneous ten up-converted signals was measured at \(4f_{s}+f_{m}\) as shown in Table 3, where \(m\) ranges from one to ten. In addition, it increased with the channel order \(m\) due to rise the electrical power of the mixed signal with \(m\). The measured conversion gain was lower than the simulated one due to the noise that is generated at the receiver, such as shot and thermal noise in addition to optical losses to the optical fiber for both co- and counter-direction schemas. The experimental work confirmed the behavior of the counter-direction, which exhibited a lower conversion gain of 2 dB in comparison with the co-direction schema. In order to measure the quality of the optical transmission system, the EVM of the ten QPSK up-converted signals were measured in the co- and counter-directions and compared with the simulation results at the bit rate of 100 Gbit/s, as displayed in Table 4. The real EVMs were higher than the simulated ones for both the co- and counter-directions due to the unexpected noise and the thermal noise in the experimental setup. In the counter-direction, for both the real and simulated works, the EVM degraded 2% for all the channels in comparison with the co-direction. This confirmed that the co-direction system was better than the counter-direction one in terms of its quality. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Conversion Gain (dB)**} \\ \cline{2-7} \(4f_{s}+f_{m}\) & \multicolumn{3}{c}{**Co-Direction**} & \multicolumn{3}{c}{**Counter-Direction**} \\ \cline{2-7}  & **Real** & **Stimulated** & **Difference** & **Real** & **Stimulated** & **Difference** \\ \hline Channel One \(4f_{s}+f_{1}\) & 31 & 33 & 2 & 28.9 & 31 & 2.1 \\ Channel Two \(4f_{s}+f_{2}\) & 30.8 & 32.9 & 2.1 & 28.6 & 30.9 & 2.3 \\ Channel Three \(4f_{s}+f_{3}\) & 30.6 & 32.8 & 2.2 & 28.3 & 30.8 & 2.5 \\ Channel Four \(4f_{s}+f_{4}\) & 30.4 & 32.7 & 2.3 & 27.8 & 30.7 & 2.9 \\ Channel Five \(4f_{s}+f_{5}\) & 30 & 32.6 & 2.6 & 27.4 & 30.6 & 3.2 \\ Channel Six \(4f_{s}+f_{6}\) & 29.6 & 32.5 & 2.9 & 27 & 30.5 & 3.5 \\ Channel Seven \(4f_{s}+f_{7}\) & 29.2 & 32.4 & 3.2 & 26.6 & 30.4 & 3.8 \\ Channel Eight \(4f_{s}+f_{8}\) & 28.8 & 32.2 & 3.4 & 26.2 & 30.2 & 4 \\ Channel Nine \(4f_{s}+f_{9}\) & 28.4 & 32 & 3.6 & 25.8 & 30 & 4.2 \\ Channel Ten \(4f_{s}+f_{10}\) & 28 & 31.8 & 3.8 & 25.5 & 29.8 & 4.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Real and stimulated conversion gains of the ten up-converted signals in co- and counter-direction schemas at \(4f_{s}+f_{m}\). The eye diagram is another way to study the quality of the system simultaneous ten QPSK up-conversion. It visualizes the effect of noise and signal distortion as a result of transmission over a channel.