A cost function analysis of a blind phase acquisition method

The Reduced Constellation Decision Directed (RCDD) blind phase correction is the simple method to remove a phase offset introduced in transmission system due to absence of carrier synchronization. This method can be used successfully for QAM signal constellations, but it can suffer convergence to a wrong phase solution. The paper presents a method to analyze static properties of the RCDD algorithm. The proposed approach, although limited to an ideal scenario with only a phase offset, allows to draw the RCDD cost function for the number of cases of QAM constellations. The investigation of the cost function properties in the case of the 16-, 32- and 64 point QAM constellations is presented in the paper.