An algorithm for the computation of undesirable phase offsets in the blind phase correction method

The Reduced Constellation Decision Directed (RCDD) blind phase correction is the simple signal processing method to remove a phase offset introduced in transmission system due to the absence of carrier synchronization. This method can be used successfully for QAM signal constellations, but it can sometimes suffer convergence to a wrong phase solution. The paper presents an algorithm that allows to identify the local minimum points of the RCDD cost function for any rectangular QAM constellation in advance. The proposed algorithm bases its work on symmetric properties of both the symbol constellation and the reference points. All necessary computations leading to the final solution can be limited to the first quadrant of the complex plane. Using the developed algorithm, the undesirable phase solutions for the typical rectangular constellations are computed.