Hybrid Maximum Likelihood Modulation Classification for Continuous Phase Modulations

In this letter, we propose a hybrid maximum likelihood (HML) classifier for continuous phase modulation (CPM). To the best of our knowledge, the proposed likelihood function is the first one for CPM signals that is based on two of its main features: nonlinear waveform, which is represented with its principal components, and signal memory, which is modeled as a Markov mapping symbol sequence. Unknown channel parameters are estimated through the expectation-maximization (EM) algorithm. An approximation method is further proposed to ensure that the proposed classifier improves classification performance at the cost of a moderate increase in calculations. Numerical results prove the superiority of the proposed approach over the classical HML classifier and feature-based classifier in terms of classifying CPM and linear modulation.