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A new blind carrier phase reconstruction method that can be applied to both square- and cross-suppressed-carrier L-ary quadrature amplitude modulations (QAMs) is proposed. This method is based on a special phase metric that performs an absolute minimum for the carrier phase offset. In particular, it does not require any modification of the modulation structure. As a result, the non-coherent detection process is easy even for modulations with large QAM constellations. Simulation results will demonstrate the good performance of the estimator described, which is superior to that of conventional blind phase estimation methods.