# A Noise-Tolerant Carrier Phase Recovery Method for Inter-Satellite Coherent Optical Communications
## 5 Experimental Setup and Results  
As shown in Figure 12, a hardware system was constructed within a laboratory setting to validate the proposed CPR method. This system comprised three primary components: a digital signal processing unit, an optical modulation and demodulation unit, and a carrier Doppler shift generation unit. Additionally, a spectrometer and an optical modulation analyzer were utilized to support the experimental procedures. The digital signal processing unit included FPGA, DACs, and ADCs. The FPGA facilitated the generation and reception processing of experimental binary data. The DACs operated at a sampling rate of 10 Gsps, while the ADCs functioned at 5 Gsps. The modulation and coding methods were QPSK and RS (255, 223), consistent with the simulation parameters outlined in Section 4. The carrier Doppler shift generation unit was designed to produce a Doppler shift on the carrier, thereby simulating the effects of relative motion between satellites. The optical modulation and demodulation unit realized the modulation of the carrier by the baseband signal through the MZM. Furthermore, it included a tunable LO [31], a 90\({}^{\circ}\) optical hybrid, and a balanced detector, facilitating the coherent reception of the optical signal. The key parameters for each experimental module were summarized in Table 5. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Diff-4 th** & **Noise-Tolerant** \\ \hline Multiplication & \(11K\) & \(4K\) \\ Addition & \((N_{1}+N_{2}-1)K\) & \((N+3)K\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Computational complexity. Figure 11: BER results. Initially, the FPGA in 1 generated encoded digital signals following the RS coding format, which were then converted into I/Q analog signals through the DACs. The I/Q signals were modulated onto the carrier laser with Doppler shift, generated by 3, using the MZM in 4. The modulation quality of the optical signals was observed using the optical modulation analyzer in 5. Mismatches in the MZM bias voltage or the I/Q signal amplitudes could degrade the modulation quality, thereby affecting signal demodulation. Once the modulation was optimized, the optical signal was transmitted to the 90\({}^{\circ}\) optical bridge in 4, where it mixed with the LO signal to achieve optical down-conversion. The down-converted signals were then converted into I/Q analog electrical signals using a balanced detector. Subsequently, the ADC in 1 sampled the I/Q analog signals for conversion into digital format, enabling further processing by the FPGA. The FPGA performed matched filtering, clock recovery, channel equalization, carrier recovery, and data demodulation to achieve synchronization and demodulation of the received signals. By adjusting the received optical power, the BER and carrier phase recovery performance were evaluated under various power levels. Additionally, the spectrometer in 2 was used to calibrate the wavelengths of the carrier and LO during the setup. Figure 12: Laboratory system scenario diagram. 1 Digital signal processing unit. 2 Spectrometer (AQ6370C). 3 Carrier Doppler shift generation unit. 4 Optical modulation and demodulation unit with a tunable LO inside. 5 Optical modulation analyzer (M8290A). \begin{table}
\begin{tabular}{c l} \hline \hline
**Module** & **Description and Parameters** \\ \hline \hline
1 & FPGA (XCZU49 DR from Xilinx with integrated 10 Gsps DAC), ADC (ADC12 DJ5200 RF from TI, \\  & dual-channel, maximum sampling rate: 5.2 Gsps per channel) \\ \hline
2 & Spectrometer (AQ6370C from Yokogawa, wavelength resolution: 0.02 nm) \\
3 & Frequency adjustment interval: 1 ms, frequency offset range: \(-\)5 GHz to 5 GHz, carrier wavelength (\(\lambda\)): \\  & 1550 nm, linewidth (\(\delta_{v}\)): 10 kHz \\
4 & Local oscillator (LO) with carrier wavelength (\(\lambda\)): 1550 nm, linewidth (\(\delta_{v}\)): 10 kHz, tunable frequency range: \\  & \(-\)6 GHz to 6 GHz \\
5 & Optical modulation analyzer (M8290A from Keysight, wavelength coverage: 1260 nm to 1625 nm) \\ \hline \hline \end{tabular}
\end{table}