# An All-Digital Optical Phase-Locked Loop Suitable for Satellite Downlinks +
## 3 System Implementation and Analysis  
### Opl  
A co-simulation technique was used to develop and analyze the OPLL. The OPLL algorithm and SNR estimation were developed in Python, whereas the photonics circuit was implemented in VPIphotonics Design Suite. The parameters of the coherent detector are based on a commercial component with a responsivity of \(R=0.04\) A/W, and the \(G_{TIA}\) gain was set to 9 k\(\Omega\) to achieve an eightfold increase in shot noise power over the thermal noise power for a \(P_{LO}\) of 1 dBm [24]. Furthermore, \(Ps\) changed as a result of the turbulence effects. The Tx and Rx lasers have a linewidth of 1 kHz for all analyses (based on the  
Figure 5: Block diagrams of phase estimation used in the DSP and the OPLL. (**a**) Block diagram of a phase compensation algorithm in DSP [18], (**b**) Block diagram of the proposed phase estimation process used in the OPLL. availability of 1 kHz linewidth lasers--NKT Koheras BOOSTIK), and the VCO has a gain of 500 MHz/V with a center frequency of 20 GHz. The propagation delay was also addressed, given that it may affect the OPLL, making it unstable. The MAF in the control loop represents a delay, where L taps introduce a delay of L samples. Furthermore, based on the commercial components, a delay of 12 ns was considered for the ADCs, and DAC [25]. For the \(atan2\), based on the hardware implementation techniques, a delay of 15 ns was considered [26]. The OPLL sampling rate will consider two sample times to compare the behavior in the tracked signal. Firstly, the OPLL will be considered to work at a sample rate (SR) of 10 GSa/s motivated by the availability of ADCs, DACs, and even DSPs that can operate at 10 GHz, allowing the OPLL to collaborate with the DSP in a correction system. As the MAF will have 10 taps, it will introduce a delay of 1 ns. The second scenario considers a relatively slow sample rate, or 625 MSa/s, where the key idea is to simulate an undersampling situation. In this case, the output data signal from the coherent detector is sampled with a frequency below the Nyquist criteria [27]. Consequently, the system could be operated with low sample rate ADCs and DACs. This scenario has already been demonstrated for OPLs regarding optical communications [28] and free-space optical communication [20] where the atmospheric turbulence was not considered. Furthermore, the MAF will have five taps, thereby introducing a delay of 8 ns. System simulations used an SR of 80 GSa/s, where the PLL working at the desired sample rate was implemented using the multi-rate sample processing technique [27]. For example, for 10 GSa/s, the SR is divided by eight by removing 8 bits from the sequence of bits. In the case of 625 MSa/s, the system follows the same procedure in which the SR is now divided by 128. Traditionally, the LF parameters are determined by finding the optimal point through [PERSON]'s relation [29]. In this method, it is possible to find the optimal loop noise bandwidth for a determined feedback loop delay that will induce the lower power penalty for an analog LF implementation. According to this relation, by increasing the delay, the loop noise bandwidth should be increased to reduce the power penalty. Previous OPLLs used this method to find the optimal point, even using a digital approach to implement the LF where control system techniques such as lead-lag compensator were used to compensate the OPLL stability [8; 20]. However, a digital approach is used to implement the LF where the loop noise bandwidth \(B_{n}\) must be specified relative to sample time \(T_{s}\) (\(B_{n}T_{s}\) parameter where \(B_{n}T_{s}<<1\)). According to the Cramer-Rao bound limit, choosing small values of \(B_{n}T_{s}\) improves the accuracy of the phase estimation [30]. Thus, for a fixed \(T_{s}\) value, the \(B_{n}\) should be increased to reduce the discriminator phase variance according to [PERSON]'s relation in case of a long feedback loop delay.