An optimized principal component-based phase estimation (OPCPE) algorithm is proposed for probabilistically shaped (PS) square-quadrature amplitude modulation (QAM) systems. The optimization method is based on mirroring and partially scaling the received constellation. Numerical simulation validation shows that the proposed phase recovery algorithm outperforms the well-known blind phase search (BPS) algorithm at low signal-to-noise ratio (SNR) and solves the incompatibility between principal component-based phase estimation (PCPE) and PS at high SNR. It's worth mentioning that the proposed algorithm retains the advantages of low cycle slip rate (CSR) and low computational complexity of PCPE. Furthermore, the performance of a hybrid implementation combining the proposed algorithm and BPS is also investigated. When the shaping parameter for a PS-64QAM system is 0.05, the proposed simple and hybrid methods can achieve performance improvements around 0.34-dB and 0.61-dB respectively benchmarking the widely used two-stage BPS (2S-BPS), considering the 0.8 normalized generalized mutual information (NGMI) threshold. To the best of our knowledge, this is the first time to robustly apply PCPE algorithm to PS systems, and the proposed design has stable NGMI performance, strong cycle slip tolerance and low computational complexity, which makes it a suitable candidate for practical probabilistically-shaped transmissions.

In coherent optical communication systems, where multiple modulation formats are mixed and variable, the correct identification of signal modulation formats provides the foundation for subsequent performance improvement using digital algorithms. A modulation format identification (MFI) scheme based on signal constellation diagrams and support vector machine (SVM) is proposed. Firstly, the signal constellation diagrams are divided by the fractal dimension of the weighted linear least squares (WLS-FD) algorithm, and the fractal dimension (FD) in each region is calculated, which is regarded as one of the image features. Then, the feature values of the image in different directions are extracted by the gray-level co-occurrence matrix (GLCM), and their mean and variance are calculated, which is regarded as another feature. Finally, the two features are input into the modulation format classifier constructed by the SVM to achieve MFI in coherent optical communication systems. To verify the feasibility and superiority of the scheme, we compare it with the MFI scheme based on higher-order statistical (HOS) features, GLCM features, and FD features, respectively. Further, we built a 30 GBaud coherent optical communication system with fiber lengths of 80 km and 120 km, where the optical signal-to-noise ratio (OSNR) ranges from 0 dB to 30 dB. The proposed MFI scheme identifies seven modulation formats: QPSK, 8QAM, 16QAM, 32QAM, 64QAM, 128QAM, and 256QAM. The results show that compared with the other three schemes, our proposed scheme has a better identification accuracy at low OSNR. In addition, the identification accuracy of this scheme can reach 100% when the OSNR ≥ 10 dB.

Reducing the influence of electrical crosstalk is crucial for the development of fiber optic gyroscopes. We present a six-state modulation method that takes advantage of highly flexible modulation voltages to eliminate the correlation between the modulation voltage with a fixed phase delay and the demodulation sequence. Theoretical analysis indicates that our approach can eliminate the impact of crosstalk with a fixed phase delay at any modulation depth. Experimental measurements demonstrate that compared to the conventional four-state modulation method, the zero bias is reduced by about 0.3319°/h at the modulation depth of π/2 when our method is applied. Additionally, at the depths of π/2, 2π/3, and 7π/8, the bias instability is reduced by approximately 30%, and the angular random walk (ARW) is reduced by over 60%. The results confirm its effectiveness in decreasing electrical crosstalk, which holds profound implications for enhancing the accuracy of fiber optic gyroscopes.

In this paper, a subset-optimized eight-dimensional trellis-coded quadrature amplitude modulation (SO-8DTCM-16QAM) format for higher-order constellations in high-speed optical communications is proposed. This scheme increases the number of subsets of base 2D constellation divisions. On this basis, it is further optimized by using 2D subsets for Cartesian product combinations to obtain 4D subsets and eliminate the combinations with small Euclidean distances. Finally, the 4D subsets are utilized to construct interrelated 8D subsets for trellis coding modulation and signal transmission. The proposed scheme can effectively reduce the decoding complexity and outperforms the conventional scheme at a high signal-to-noise ratio (SNR). Simulation verification of the proposed scheme is carried out, and the results show that the SO-8DTCM-16QAM achieves signal-to-noise ratio (SNR) gains of 1.60 dB, 1.56 dB, 1.51 dB, and 1.33 dB, respectively, compared with the conventional 8D-16QAM signals when BTB and 5/20/30 km optical signal transmission are performed. The SO-8DTCM-16QAM also achieves an SNR gain of 1.86 dB, 1.75 dB, and 1.22 dB at a net transmission rate of 14/21/28 GBaud. In addition, the SO-8DTCM-16/32/64QAM achieves an SNR gain of 1.27 dB, 0.80 dB, and 1.24 dB, respectively, when compared with the unoptimized 8DTCM-16/32/64QAM. Meanwhile, the proposed eight-subset SO-8DTCM-QAM scheme reduces the complexity of the decoding computation in the subset selection part and the constellation point selection part by 93.75% and 50%, respectively, compared with the unoptimized eight-subset and four-subset 8DTCM-QAM schemes. It can be seen that the proposed scheme simultaneously optimizes the transmission performance and complexity of high-speed optical communication systems and has practical application value.