# An All-Digital Optical Phase-Locked Loop Suitable for Satellite Downlinks +
## 4 Discussion  
In this study, we have presented the evaluation of the OPLL using two sample rates to compare the behavior of _sine_ and _atan2_ phase discriminators. The _atan2_ showed a superior performance regarding the standard deviation of the controlled frequency. The moving average filter helps eliminate the harmonics of the power moment, decreasing the phase-error variance. Consequently, the low STD results from a better phase estimation and a low phase variance since the _atan2_ output is the phase error.  
Another motivation for using the _atan2_ is a scenario under low SNR conditions. If only the imaginary part of Equation (10) is used as a phase detector, it is susceptible to amplitude variations, as shown in the simulations. Thus, the OPLL loses lock under low SNR conditions or presents a significant error. An automatic gain control circuit must be employed to compensate for these amplitude variations. Using the four-quadrant arctangent discriminator improves the sensitivity of the PLL since its error output is a relation between the I and Q signals.  
Table 1 compares previously reported optical coherent receivers using the DSP or the OPLL for signal recovery with this study's proposed method. As shown in Table 1, previous studies used the Viterbi-Viterbi (VV) algorithm in data blocks for phase estimation in the case of DSPs or an analog phase detector or exclusive or gate (XOR) for the OPLL. In contrast to previous techniques, our proposed system uses a hybrid approach where the OPLL works as a complement in a DSP correction system. Thus, the Viterbi-Viterbi algorithm is applied synchronously according to the system SR.  
Figure 12: BER variation (mean of 30 events) as a function of wind speed for the OPLL using the digital discriminator and working with an SR of 625 MSa/s and 10 GSa/s. The OPLL at an SR of 625 MSa/s shows a higher degradation due to its higher power penalty.  
Furthermore, the advent of integrated photonics [33] and higher sample rate systems would make integrating both systems (OPLL and DSP) possible. For example, the VCO could be replaced by a direct digital synthesizer (DDS) that would digitally generate the microwave carrier. An OPLL employing DDS in place of VCO was previously reported [20].  
Due to its performance, the \(atan2\) discriminator was evaluated under scenarios of atmospheric turbulence. Both discriminators were compared in three scenarios: weak, moderate, and strong turbulence. These turbulence regimes induce power fading levels on the transmitted optical signal, affecting the OPLL tracking capability. The fading effect was very pronounced on the \(sine\) discriminator since its gain depends on the signal level. Since the output of the \(atan2\) discriminator is independent of the signal level input, its performance is transparent under scintillation fading effects. Consequently, the OPLL keeps tracking the input signal in different turbulence regimes.  
Regarding the atmospheric turbulence, in the model, the independent scintillation events occur on a timescale of \(\upmu\)s to ms. Consequently, the turbulence applies independent scintillations to the OPLL, corresponding to one iteration. As a result, even though the simulation only lasts a few microseconds, every iteration represents a scintillation event. Consequently, the model illustrates an abrupt change in the SNR level of the optical signal when it passes between several scintillation events. Regardless of the decreased SNR level, the OPLL utilizing the proposed digital discriminator remains locked due to its characteristics, as previously discussed.