## 4 Frequency Up-Conversion of QPSK Data  
Frequency mixing of QPSK data carried by the electrical subcarrier, which was injected in the optical MZMs for up-conversion simulations, was evaluated at the bit rate of 100 Gbit/s. The generation and detection module generated QPSK data at the carrier frequency of 1 GHz for channel one and 2 GHz for channel two. The quality of the frequency mixing was evaluated through the error vector magnitude (EVM) of the received symbols [40]. The EVM of the mixed symbol was obtained through the BER_El-M-QAM module. As in VPI's demo, this module was used to evaluate the EVM of the received constellation. Hence, EVM values were calculated from the bit error rate (BER). This module was relevant to the BER, and the passable limit was realized as the value that provided an amounting to BER of 0.0038, which sponsored an error-free fulfillment after executing forward error correction (FEC) methods [41]. The EVM limit of the QPSK data was 17.5% [42; 43]. The optical output power directly at the SOA-MZI output was \(-0.2\) dBm with a loss of 3 dB due to the optical losses of the OF. During the optical to electrical conversion stage at the SOA-MZI output, there are thermal and shot noise currents and the photocurrent due to the mixed signal, which were generated in the photodiode (PD). Thus, the total current produced by the PD became the combination of the mixed signal current with the noise currents. After that, the electrical signal was amplified through an LNA. As a result, the noise carried on the sampled signal after photo-detection and amplification at the SOA-MZI output should be considered in any BER calculations. As seen in Figure 14, the EVM of up-converted QPSK signals augments with the mixing frequency at 100 Gbit/s for the four conditions. The EVM ranged from 10% at \(f_{s}+f_{1}=16.6\) GHz attached to \(H_{1}\) of the sampling signal up to 33% at \(10f_{s}+f_{1}=157\) GHz relevant to \(H_{10}\) for the standard modulation in the co-direction. For the differential modulation, the EVM value improves higher at the higher mixing frequency. It reaches 13.5% at 157 GHz, which was below the EVM limit of 17.5%. The EVM at the highest mixing  
Figure 13: Conversion gains of simultaneous ten up-converted signals at \(10f_{s}+f_{m}\) related to the tenth harmonic of the sampling signal at the SOA-MZI output. frequency demeaned more than the one at the lowest mixing one due to the SOA-MZI low pass behavior. Following the higher harmonic rank of the sampling signal plays the staple function to improve mixed signals because of the differential modulation principle. In the case of the counter-direction configuration, the EVM increased an average value of 2% over the full range of mixing frequencies for both modes compared to the co-direction one. It reached 15.5% at 157 GHz, which was below the EVM limit of 17.5%. Furthermore, the EVM values of up-converted QPSK signals at 100 Gbit/s were well below the required limit of 17.5% for the differential modulation mode in both configurations, while they were above the limit at the higher mixing frequencies for the standard modulation mode in both configurations. The maximum bit rate we can achieve during up-conversion process is 100 Gbit/s. The EVMs of up-converted QPSK signals at the mixing frequencies \(nf_{s}+f_{2}\) at 100 Gbit/s for the standard and differential modulation modes in co- and counter-directions are displayed in Figure 15. The comparison of the EVM between Figures 14 and 15 shows that the EVM increased an average value of 2% over the full range of the mixing frequency for the four affairs for the channel two compared to channel one. This increase was due to the electrical power of the channel two that is lower than the one of the first channel at the SOA-MZI output as well as the SOA-MZI input. The EVM achieves good values of 15.5 and 17.5% for the differential modulation mode in both configurations, respectively, at the maximum frequency range of 158 GHz.