# A Noise-Tolerant Carrier Phase Recovery Method for Inter-Satellite Coherent Optical Communications
## 5 Experimental Setup and Results

Table 5: Module parameters. The BER and the estimated phase increment variance results were presented in Figure 13. In the experimental setup, the system was unaffected by factors such as temperature and vibration, with noise primarily originating from thermal noise, which remained constant in power. By adjusting the received power, the SNR was varied--a lower received power resulted in greater noise impact and higher phase estimation errors. When the received power fell below \(-39\) dBm, the BER for the Diff-4 th method approached 0.5, with an estimated phase increment variance of \(D(\hat{\theta})>7\times 10^{-4}\), indicating ineffective CPR. Conversely, when the received power was at least \(-39\) dBm, the estimated phase increment variance \(D(\hat{\theta})\) for both methods converged. The BER prior to decoding was largely equivalent, while the BER post-decoding was recorded at less than \(1\times 10^{-6}\). The experimental results confirmed that the proposed method exhibited enhanced adaptability to SNR variations. On the other hand, one of the primary challenges in inter-satellite coherent optical communications was Doppler shift. To evaluate the Doppler adaptability of the proposed method, the optical signal suffering Doppler shift was produced by the carrier Doppler generation unit. The relative velocity between satellites at low orbital altitudes is usually greater than that between satellites at high orbital altitudes [32]. For instance, in the case of Starlink, the relative velocity among satellites in low Earth orbit generally ranges from approximately \(\pm 6\) km/s, with relative acceleration typically remaining below \(10\) m/s\({}^{2}\). The specific inter-orbital variations can be simulated using software such as the Satellite Tool Kit (STK). However, the orbit simulation capabilities of STK are beyond the scope of this paper, which, instead, establishes two simplified Doppler scenarios. Scenario A involves a uniform acceleration condition characterized by a triangular wave Doppler sweep. Under an acceleration of \(10\) m/s\({}^{2}\), the relative motion speed transitions from \(0\) to \(-6\) km/s, subsequently reversing to \(6\) km/s after reaching \(-6\) km/s. The speed then decelerates from \(6\) km/s to a relative static state. The relative motion causes the carrier frequency to become \(f_{c}^{\prime}=(1+v/c)f_{c}\), resulting in \(\Delta f\in[-3871,3871]\) MHz and a Doppler shift rate of \(6.45\) MHz/s within a \(40\) min experiment cycle. Scenario B presents a variable acceleration condition, maintaining the same \(40\)-minute Doppler sweep period as Scenario A. In this scenario, the Doppler sweep follows a sinusoidal pattern, with the Doppler shift rate fluctuating between \(-10\) MHz/s and \(10\) MHz/s throughout the cycle. In both scenarios, the BER post-decoding was observed to be better than \(1\times 10^{-7}\). The BER results remained stable throughout the sweep process and did not vary with the Doppler shift. Figure 14 shows the frequency control outcomes of the LO in the receiver. It was evident that the Doppler changes in the carrier were consistently tracked at the receiver in both Scenario A and Scenario B when compared to the Doppler shift established in the transmitter. Figure 13: Experiment results. (**a**) BER experiment results. (**b**) The results of \(D(\Delta\hat{\theta})\).