Robust and Low-Complexity Principal Component-Based Phase Estimation Algorithm for Probabilistically Shaped Square-QAM Systems

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 0.03, by using the proposed simple and hybrid methods, the SNR required to reach the 0.8 normalized generalized mutual information (NGMI) threshold can be reduced by about 0.74 dB and 0.98 dB, respectively, benchmarking the widely used two-stage BPS (2S-BPS) algorithm. 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 GMI performance, strong cycle slip tolerance and low computational complexity, which makes it a suitable candidate for practical probabilistically-shaped transmissions.