Coherent optical communication technology possesses a significantly higher communication rate and receiver sensitivity, which has been applied in fiber optic networks and space optical communication by researchers. Compared with the optical fiber channel, the space atmospheric channel possesses significant randomness and fluctuation, and the relative motion between the terminals will introduce an additional Doppler frequency shift. Thus, the frequency offset and phase noise of the space optical communication systems are characterized by a large fluctuation range and a fast-changing rate. Traditional coherent optical communication systems realize carrier synchronization mainly by reference light method, optical phase-locked loop method, and digital signal processor (DSP) open-loop carrier synchronization method. However, it is difficult to implement the reference light method in space atmospheric channels with a large dynamic range. The tuning rate of the optical phase-locked loop method is slow, leading to poor performance. Besides, these two methods will lead to a more complex system. An open-loop synchronization scheme is recommended by researchers, although there is phase ambiguity when an open-loop synchronization scheme is used in large dynamic link conditions. Therefore, the optimization of open-loop synchronization schemes is of great significance for meeting the needs of different space optical communication applications. We aim to develop a carrier synchronization algorithm to solve the phase ambiguity problem of coherent optical communication systems with a large frequency offset and large phase noise and to provide a competitive carrier synchronization method for space coherent optical communication systems. We believe that this will be helpful for the development and application of space coherent optical communication technology.

Considering the simple implementation and small computation of the Mth power carrier synchronization algorithm, we realize the carrier synchronization algorithm by optimizing the Mth power carrier synchronization algorithm. The principle of the Mth power carrier synchronization algorithm is analyzed, and the regular phase ambiguity is found, namely that the phase ambiguity can be treated as one of the M situations. It should be noted that both the actual frequency offset ambiguity and phase noise ambiguity are randomly distributed in the M situations. The adopted enumeration method is simple and effective. To decrease the computation of the procedure as much as possible, the unwrapping phase ambiguity procedure is combined with the frame synchronization process. In the unwrapping phase ambiguity procedure, different combinations of frequency offset ambiguity and phase noise ambiguity are tried until the frame synchronization is successful. The different combinations can be tried in parallel to improve signal processing speed. The carrier synchronization algorithm is applied in free-space dual polarization-quadrature phase shift keying (DP-QPSK) coherent optical communication systems to verify the effectiveness.

A DP-QPSK free-space coherent optical communication simulation system is built in OptiSystem, and frequency offset and phase noise are characterized by changing laser frequency and linewidth. Also, a DP-QPSK free-space coherent optical communication experimental system is built between two buildings 600 m apart. The simulation and experimental results show that our carrier synchronization algorithm is effective for DP-QPSK coherent optical communication systems, and the error vector magnitude (EVM) value of the carrier synchronization constellation is always less than 15% (Figs. 7, 10, and 11). Besides, the quality of demodulation constellation is independent of frequency offset, phase noise, and modulation parameters, and the bit error rate is 0% (Fig. 8). In the experimental system, comparative analysis of our carrier synchronization algorithm and Mth power carrier synchronization algorithm is carried out. Although it is a fact that the demodulation constellation EVM values using the Mth power carrier synchronization algorithm are almost the same as our carrier synchronization algorithm, but the bit error rate will be up to 37.5% or 25% when the Mth power carrier synchronization algorithm is applied directly. Thus, it is essential to unwrap phase ambiguity for space coherent optical communication applications.

We propose an unwrapping phase ambiguity carrier synchronization algorithm for the free-space coherent optical communication system. To verify the effectiveness of the carrier synchronization algorithm, we build a free-space DP-QPSK coherent optical communication simulation system and experimental system with different frequency offsets and phase noises. Our carrier synchronization algorithm requires correlation operations of the frame synchronization process to be implemented multiple times, whose mathematical expectation is M2/2. However, once the modulation format of the system is determined, the operational logic of the unwrapping phase ambiguity process is fixed. Thus, the unwrapping phase ambiguity process can be operated in parallel to improve signal processing speed. Besides, the frequency offset and phase noise compensation range of the proposed carrier synchronization algorithm are not constrained by the modulation rate and modulation order of the coherent optical communication system. A higher modulation order system needs to increase the implement times of correlation operations in the frame synchronization process, while the carrier synchronization effect is almost not influenced. The carrier synchronization algorithm may be applied to future coherent optical communication systems with a higher communication rate and modulation format.