# An All-Digital Optical Phase-Locked Loop Suitable for Satellite Downlinks +
## 3 System Implementation and Analysis
### Results  
The previously performed analyses lay the groundwork for the turbulence analyses conducted in this section. The OPLL was evaluated through variations of the turbulence  
Figure 8: OPLL phase error and the induced power penalty for several \(B_{n}T_{s}\) at both sample rates and MAF coefficients number. (**a**) Phase error and power penalty for several \(B_{n}T_{s}\) values at 10 GSa/s, (**b**) Phase error and power penalty for several \(B_{n}T_{s}\) values at 625 MSa/s. channel where the two proposed SRs were evaluated. The proposed digital discriminator was also compared with the imaginary part of the fourth-power moment for each SR. In an OPLL, the phase error variance will reflect on the phase noise of the controlled frequency. Thus, one measure of comparison would be to compare the variances of the two discriminators. However, since they have different gains, the variance calculation is impaired. Therefore, the STD of the controlled frequency will be used as a metric for comparing the performance of the two discriminators. Figure 9 shows the VCO output frequency behavior for a strong turbulence regime and a wind speed of 60 m/s for the OPLL working with an SR of 10 GSa/s. Figure 10 shows the VCO output frequency behavior for the same atmospheric turbulence conditions, however for the OPLL working with an SR of 625 MSa/s. Each color represents the fade values where the system is analyzed for thirty different values or thirty iterations. These values were the random fluctuations determined by the turbulence model, resulting in the estimated SNR level shown in Figure 11.  
Figure 10: VCO output frequency behavior under strong turbulence and wind speed of 60 m/s for the OPLL working with SR of 625 MSa/s. (**a**) OPLL using the proposed digital phase detector, (**b**) OPLL using the sinusoidal discriminator. Figure 9: VCO output frequency behavior under strong turbulence and wind speed of 60 m/s for the OPLL working with SR of 10 GSa/s. (**a**) OPLL using the proposed digital phase detector, (**b**) OPLL using the sinusoidal discriminator. The VCO output frequency behavior using the digital discriminator (\(atan2\)) and the imaginary part (\(sine\)) is shown in Figures 9a and 9b, respectively, for an SR of 10 GSa/s. For an SR of 625 MSA/s, the VCO output frequency behavior is shown in Figure 10a,b. For an SR of 10 GSa/s, the OPLL with the \(atan2\) discriminator was studied with a total delay of 30 ns, whereas the \(sine\) phase detector was analyzed with a total delay of 6 ns, as it became unstable with delays longer than that. For an SR of 625 MSA/s, as the \(B_{n}\) value decreased, both discriminators were analyzed under a total delay of 35 ns. The MAF has five taps, representing a delay of 8 ns. The \(sine\) discriminator presents a higher oscillatory characteristic and an STD of the controlled frequency. The STD variation is related to the gain of the \(sine\) discriminator since its gain, as shown previously, depends on the system parameters. As the input power level changes due to turbulence, the gain also changes, reflecting the OPLL phase error variance and the controlled frequency STD. Also, as indicated by the variation of the central frequency, the OPLL loses the lock during higher fading and cannot recover the track signal. For all turbulence scenarios, the proposed digital discriminator had the same gain of 1 in both SRs. As the phase error is computed using the \(I/Q\) signals, the \(atan2\) has the advantage of being independent of system parameters. As a result, without modifying the OPLL project, it was possible to analyze the system under various turbulence scenarios. It also has a low STD of the controlled frequency, as shown in Figures 9a and 10a. For example, comparing the STD of both SRs for an SNR of approximately 8 dB (third event in Figure 11), the OPLL at 10 GSa/s shows an STD of \(\pm 6.5\) kHz while the OPLL at 625 MSA/s shows an STD of \(\pm 34\) kHz. This is due to its higher phase error variance, as previously discussed.