A system for carrier phase recovery, including a receiver for receiving one or more frames of L symbols. A phase estimator performs carrier phase estimation for the received frames of L symbols, and the resulting carrier phase estimates are stored in a non-transitory computer-readable storage medium. One or more rotators de-rotates the received frames of L symbols by one or more of the carrier phase estimates, and a data processor calculates a sum of the outputs of the L de-rotated signals raised to an nth power, and determines a real part of the sum. A minimum determination device determines a minimum of the real part of the sum with respect to the carrier phase estimates, and phase unwrapping and multiplier removal is performed if a minimum has been determined.