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In this paper, we propose an algorithm for the classification of digital amplitude-phase modulated signals in flat fading channels with non-Gaussian noise. The additive noise is modeled by a Gaussian mixture distribution, a well-known model of man-made and natural noise that appears in most radio channels. The classifier utilizes a variant of the expectation-maximization algorithm to estimate the channel and noise parameters without the aid of training symbols. With these estimates, the signal is classified using a hybrid likelihood ratio test. Results are presented which show that the proposed classifier's performance approaches that of the ideal classifier with perfect knowledge of the channel state and noise distribution.