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The advent of digital signal processing (DSP) to optical coherent detection means that more phase estimation options are available, compared to the earlier generation where phase-locked loops (PLLs) were invariably deployed in synchronous coherent receivers. Several phase estimation methods are numerically modeled: the maximum a posteriori (MAP) phase estimate, decision directed estimate, power law-Wiener filter estimate and power law-PLL estimate. An asynchronous coherent detection case is also modeled. The phase estimates are evaluated with respect to their tolerance of finite laser linewidth and their suitability for implementation in a parallel digital processor. Laser phase noise causes transmission system performance to be degraded by excess bit errors and cycle slips. The optimal phase estimate is the MAP estimate, and it is also included as a baseline. The power law-Wiener filter phase estimate is found to perform only marginally worse than the MAP estimate. It must be recast using a look-ahead computation to be implemented in a parallel digital processor, and the impact is investigated of the increase in the number of computations required. Differential logical detection is often used to reduce the impact of cycle slip events, and the implications of this operation on the bit error rate are studied. It is found that by choosing the correct FEC scheme differential logical detection does not increase the Q-factor penalty.