# Effect of Phase Noise on the Optical Millimeter-Wave Signal in the DWDM-RoF System
## 4 Results and Discussion
Figure 7: The constellation diagram of phase noise at different phase imbalances (**a**) at \(\pi/12\)(**b**) at \(\pi/6\) (**c**) at \(\pi/4\) (**d**) at \(\pi/3\) and (**e**) at \(5\pi/12\). For further investigation of phase imbalance effects and phase noise, we compared the input and output mm-wave signal at the MZM, as shown in Figure 8. In this figure, the blue refers to the input signal and the red refers to the output signal. A 2 dB power difference was found between the input signal and the output signal, and this was due to the imbalanced splitting ratio (\(\gamma\)) of the two branches of the MZM, which caused a higher phase imbalance in the output signal. The phase imbalance has a strong influence on the output of the mm-wave signal, as proven in Equations (5) and (6). Additionally, the output signal included the phase noise resulting from the phase imbalance that occurred at the MZM modulator. By controlling phase imbalance, the phase noise could be reduced. In this study, we analyzed additional parameters to show the performance of the mm-wave signal in the DWDM-RoF system. Figure 9 shows the OSNR values of the mm-wave signal in the DWDM-RoF system. At a BER of \(10^{-9}\), the OSNR values were 15.3, 15.5, 16, 17, and 17.9 dB for the phases of \(\pi\)/12, \(\pi\)/6, \(\pi\)/4, \(\pi\)/3, and \(5\pi\)/12, respectively. The mm-wave signal was improved at the phase of \(5\pi\)/12 based on the OSNR value of about 18 dB. This is proof that controlling phase imbalance enhanced the mm-wave signal with regard to the OSNR factor. Therefore, we demonstrated that adjusting the phases to control the phase imbalance can improve the performance of the mm-wave signal and lower the phase noise. The phase noise is affected by the SNR according to Equation (8), where the phase noise is a function of the SNR. Therefore, calculating the SNR for the mm-wave signal provides additional information about the effect of phase noise on the mm-wave signal. Figure 10 shows the SNRs for the mm-wave signal in the DWDM-RoF system. At a BER of \(10^{-9}\), the SNRs were 13.2, 13.5, 14, 15, and 16 dB for the phases of \(\pi\)/12, \(\pi\)/6, \(\pi\)/4, \(\pi\)/3, and \(5\pi\)/12, respectively. A difference of 2.8 dB was observed between the SNRs at the phases of \(\pi\)/12 and \(5\pi\)/12. Thus, the SNR for the mm-wave signal is better at the phase of \(5\pi\)/12 due to minimal phase imbalance at that phase. To achieve a reliable system, the signal level must be significantly greater than the noise level. The higher SNR values are considered excellent, whereas an SNR below 15 dB may result in a slow, unreliable connection [30; 37]. Figure 8: The optical mm-wave signal, the input signal, and the output signal. To examine the phase noise of the mm-wave signal, it was important to examine the EVM at different phases applied to the DWDM-RoF system. According to Equation (9), phase noise and phase imbalance are functions of the EVM. The EVM is expressed in percent by multiplying the ratio by 100%. Figure 11 shows the EVM versus the phase noise. The EVM of the mm-wave signal at the phase of 5\(\pi\)/12 ranges from 20% to 30%. In general, the EVM is the difference between received symbols and ideal symbols or the difference between the ideal constellation points and the received constellation points [38]. The EVM values for the mm-wave signal demonstrated that the phase of 5\(\pi\)/12 had a lower EVM, and therefore a lower difference between the transmitted constellation points and the received constellation points in the system, than other phases. Figure 10: BER vs. SNR of the mm-wave signal in the DWDM-RoF system. Figure 9: BER vs. OSNR of the mm-wave signal in the DWDM-RoF system. To lower the phase noise in the mm-wave signal, the phase imbalance was controlled and decreased using the PS. Figure 12 shows the phase noise before and after controlling the phase imbalance of the mm-wave signal. Both phase imbalance and phase noise were estimated in degrees. The phase imbalance ranged from 0.44 to 0.1 degrees.