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The Viterbi-and-Viterbi (V-V) algorithm is widely used to recover the carrier phase in optical digital coherent receivers. For simplicity, the basic V-V algorithm assumes constant carrier phase within the average duration. However, this basic assumption is probably violated by factors such as laser frequency offset and nonlinear XPM. In order to improve the basic V-V carrier phase recovery, five methods are introduced, verified, and analyzed. All these methods are compatible with parallel implementation that is mandatory for a realistic DSP circuit. The Q-improvement brought by each algorithm is analyzed together with the complexity of each. Among the five methods, the laser frequency offset compensation expands the tolerable frequency offset to 0.37 symbol rate, and the optimum weighted averaging in conjunction with normalization processing improves the Q-value by 2 dB under severe XPM condition.