Carrier Phase Recovery Based on Novel Principal Component Analysis and Joint Decision

Objective With the continuous growth of global data communication demand, optical communication systems are developed toward higher bandwidth, greater spectral efficiency, and larger capacity, and are recognized as the core of modern information infrastructure. To fully exploit the capacity potential of optical fiber channels and approach the Shannon capacity limit, probabilistic shaping (PS) technology is widely applied. Through the adjustment of the non-uniform occurrence probability of constellation symbols, the signal distribution is transformed from a uniform pattern into a format characterized by concentrated low-energy symbols and sparse high-energy outer symbols. Consequently, flexible rate adaptation is achieved, and both noise tolerance and spectral efficiency are enhanced. However, the non-uniform statistical characteristics of PS signals introduce new challenges. Traditional carrier phase recovery (CPR) algorithms usually rely on high-energy outer constellation points to provide reliable phase references, but in high-order PS signals, the occurrence probability of these symbols is significantly reduced, which may degrade the accuracy of phase estimation or even cause failure. In addition, traditional CPR methods often require an increased number of test phases or higher search resolution to maintain accuracy, leading to sharply increased computational complexity and hardware bottlenecks in practical systems. Blind phase search (BPS) can effectively track the signal phase, but in high-order PS systems, it is still affected by sparse outer constellation points and channel noise. Principal component-based phase estimation (PCPE) reduces computational complexity by utilizing the second-order statistics of the signal, but the numerous low-amplitude, low-confidence inner symbols dominate the covariance matrix and bias the principal component direction, leading to phase estimation errors. To address the mismatch between PS signals and conventional phase recovery algorithms, a CPR method based on novel principal component analysis and joint decision is proposed. This approach aims to ensure stable phase estimation for high-order PS signals while maintaining a reasonable balance between computational complexity and system performance. Methods A CPR method based on a novel principal component analysis and joint decision is proposed in this paper, aiming to enhance the robustness of phase estimation under non-uniform constellation structures. In the coarse estimation stage, local amplitude scaling is applied to received symbols prior to covariance matrix estimation. Instead of directly using the original samples, an amplitude-dependent weighting factor is introduced so that symbols with higher amplitudes contribute more significantly to the covariance matrix. In this way, the dominant influence of densely distributed inner constellation points is alleviated, and the directional information carried by sparse outer symbols is preserved. As a result, the extracted principal component is better aligned with the actual phase-noise direction, which enhances the reliability and stability of the coarse phase estimate. The statistical bias caused by the non-uniform symbol distribution of PS signals is therefore mitigated at the feature extraction stage. In the fine estimation stage, a joint decision framework is established based on the coarse phase compensation results. Different decision criteria are applied to symbols with different amplitude characteristics. For low-amplitude inner symbols, the maximum a posteriori criterion is employed, where the prior probability distribution of the PS constellation is explicitly incorporated into the decision metric. This allows decision errors caused by unequal symbol probabilities to be effectively reduced. For high-amplitude outer symbols, the maximum likelihood criterion is adopted due to its lower computational complexity and sufficient reliability under higher signal-to-noise conditions. The Euclidean distance metric is used to ensure accurate symbol selection. Through this two-stage design, coarse estimation provides a statistically corrected phase direction, while fine estimation refines the residual error in a decision-aware manner. As a consequence, phase estimation accuracy and robustness are simultaneously improved without introducing excessive computational burden, making the proposed method suitable for high-order PS optical communication systems. Results and Discussions The proposed method is validated on a PS-64QAM coherent optical communication simulation platform with a symbol rate of 30 Gbaud and a transmission distance of 80km. System performance is evaluated over an optical signal-to-noise ratio (OSNR) range from 10 dB to 30 dB with a step size of 0.5 dB. Simulation results for PS-64QAM signals with a shaping factor of 0.05 show that, under low OSNR conditions, phase estimation failures caused by noise are effectively suppressed, and the performance is significantly better than that of the conventional two-stage blind phase search (2S-BPS) algorithm, with a maximum generalized mutual information (GMI) gain of approximately 2.165 bit/symbol. In the high OSNR region, the proposed method overcomes the performance degradation caused by the incompatibility between conventional principal component-based phase estimation (PCPE) and PS signals, achieving a maximum performance gain of about 0.760 bit/symbol compared with the PCPE method. Furthermore, consistent and stable performance advantages are observed for the proposed method across different shaping factors in the PS-64QAM system. Regarding computational complexity, resource consumption is significantly reduced compared to the 2S-BPS method. Specifically, the numbers of adders, multipliers, and decision elements are decreased by approximately 40.2%, 38.1%, and 50.0%, respectively. Compared to the PCPE method, the resource consumption of adders, multipliers, and decision elements is increased due to the introduction of improved steps such as local scaling and weighting. However, this increase in complexity results in a substantial GMI improvement under high-order PS signal conditions, achieving an optimal balance between performance enhancement and computational cost. Conclusions To address the insufficient phase estimation performance of conventional carrier phase recovery methods in PS coherent optical communication systems, a CPR method based on a novel principal component analysis and joint decision is proposed. The method effectively improves the compatibility between PS signals and conventional algorithms through amplitude scaling, weighted covariance, and a region-based decision mechanism. Simulation results show that the proposed method achieves significantly higher GMI performance than the 2S-BPS algorithm under low OSNR conditions and raises the upper limit of phase recovery accuracy in the high OSNR region. In addition, an optimal balance between computational complexity and system performance is achieved, providing a feasible solution for high-capacity, high-spectral-efficiency optical communication systems.