Low-complexity two-stage carrier phase recovery using principal component reconstruction analysis and optimal decision maximum likelihood for PS-MQAM systems

Abstract

A low-complexity two-stage carrier phase recovery (CPR) scheme based on principal component reconstruction analysis and optimal decision maximum likelihood (PCRA-OML) is proposed for probabilistic shaping (PS)-M quadrature amplitude modulation (QAM) coherent optical communication systems. In the first stage, symbols on the QPSK-shaped ring are selected, their amplitude noise is eliminated, and their amplitudes are increased, thus completing the reconstruction of the principal component. Lastly, the carrier phase is recovered using principal component phase estimation (PCPE). In the second stage, a maximum likelihood phase estimation algorithm based on optimal decision-making is employed to further enhance the stability and robustness of the scheme. The effectiveness of the proposed scheme is validated through 28 GBaud polarization division multiplexing PS-64QAM simulations and 28 GBaud PS-16QAM experiments. The experimental results indicate that in the PS-16QAM entropy of 3 bit/symbol system, when the threshold for normalized generalized mutual information is 0.9, the proposed scheme provides a 1.7 dB optical signal-to-noise ratio (OSNR) gain compared to blind phase search (BPS), and an additional 0.9 dB OSNR gain compared to the PCPE scheme. The proposed PCRA-OML scheme exhibits versatility across various shaping strengths and is less susceptible to probabilistic influences than the BPS and PCPE schemes. Additionally, under the premise of comparable performance in the PS-64QAM system, the proposed scheme reduces over 90% of the computational complexity associated with multiplication compared to BPS. In the PS-16QAM system, the proposed scheme's real multiplication complexity is only 17.8% of BPS, achieving an overall O(N) complexity.