Asynchronous hybrid maximum likelihood classification of linear modulations

In this paper, we consider the problem of linear modulation classification in the presence of unknown time offset, phase offset and received signal amplitude. We develop a novel hybrid maximum likelihood (HML) approach based on a Generalized Expectation Maximization (GEM) algorithm [1]. Our approach is applicable to all QAM and PSK modulations, and it does not require any assumptions on the received signal-to-noise ratio (SNR). The GEM algorithm provides a tractable procedure to obtain maximum likelihood (ML) estimates which are extremely hard to obtain otherwise. Moreover, our approach employs only a small number of samples (in the order of hundreds) to perform both time and phase synchronization, signal power estimation, followed by modulation classification. The proposed approach also enables maximum a posteriori (MAP) decoding of the unknown constellation symbol sequence as a by-product of the GEM algorithm. We provide simulation results that show that the proposed approach provides excellent classification performance.