A novel, soft-decision-aided, maximum likelihood (SDA-ML) phase estimator is derived for carrier phase estimation in coherent optical communication. For estimating the carrier phase of the current symbol, SDA-ML uses both the feedback of earlier soft data decisions and the feedforward of later soft data decisions. The estimator is applicable to arbitrary 2-D modulations, where the symbols can have unequal energies and unequal a priori probabilities, and the constellation can be asymmetrical. An iterative SDA-ML algorithm and a simplified DA-SDA-ML algorithm with a reduced computational complexity are proposed. Both algorithms have no phase ambiguity. The data detector does not require to estimate the phase explicitly. Simulations show that SDA-ML and DA-SDA-ML outperform the $M$th power and DA-ML in the presence of strong linear laser phase noise.
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