A new two-stage carrier-phase recovery scheme using a combination of an optical pilot-aided algorithm with the crossed constellation transformation algorithm for either square-framed or non-square-framed M-level-quadrature amplitude modulation (QAM) Nyquist systems is proposed. It is verified in 32- and 128-QAM systems that it can provide high linewidth tolerance with little complexity.

We propose a modified-Viterbi and Viterbi phase estimation (VVPE) carrier phase recovery scheme that shows an effective capability of reducing the frequent and accumulated cycle slips induced by inter-symbol interference (ISI) in a faster-than-Nyquist (FTN) optical coherent communications system. In a 28-Gbaud FTN polarization-division multiplexed quadrature phase-shift keying optical communication system, the comparison of the proposed modified-VVPE scheme and the conventional VVPE scheme is carried out. It is proved that the proposed modified-VVPE scheme can effectively overcome the challenge of ISI induced error carrier phase estimation, which leads to a better bit error ratio performance.