Likelihood methods for MPSK modulation classification

New algorithms based on the likelihood functional (LF) and approximations thereof are proposed for the problem of classifying MPSK modulations in additive white Gaussian noise. Previously introduced classifiers for this problem are theoretically interpreted as simplified versions of the ones in here. The performance of a single-term approximation to the optimal LF classifier is evaluated analytically and is shown to be very close to that of the optimal. Furthermore, recursive algorithms for the implementation of this new quasi-log-likelihood-ratio (qLLR) classifier are derived which imply no significant increase in classifier complexity. The present method of generating classification algorithms can be generalized to arbitrary two-dimensional signal constellations.>