Maximum likelihood synchronization of burst-mode CPM

In this paper, we derive a joint maximum likelihood (ML) algorithm for the estimation of frequency offset, carrier phase and symbol timing for continuous phase modulations (CPMs). We have considered a burst-mode scenario over additive white Gaussian noise (AWGN) channels in which an optimized training sequence is embedded within each burst in order to assist the synchronization task. The proposed data-aided (DA) approach takes advantage of the optimum training sequence structure which can be applied to the entire CPM family. The simulation results show that the estimator performs quite close to the theoretical Cramér-Rao bound (CRB) for all synchronization parameters in terms of their estimation error variances even at low signal-to-noise ratios (SNRs).