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A method for quadrature amplitude modulation (QAM) constellation classification is proposed by exploiting the phase information of noisy characteristic functions. This method of classification is theoretically and asymptotically invariant to the presence of additive white Gaussian noise, thus allowing for lower classification error. A simple yet effective method for extracting phase information from the characteristic function is presented. This QAM classifier, tested against a known fourth order cumulant method, is shown to be very effective at moderate SNR. It also shows some desirable traits that enable it to be complementary to the cumulant algorithm.