An EM approach to carrier phase recovery in AWGN channel

In this paper, the problem of carrier phase recovery of linearly modulated signals in the presence of unknown data symbols is studied within the expectation-maximization (EM) framework using two different approaches. First, an iterative joint maximum likelihood (ML) phase estimator and data detector is derived using conditional maximization steps. Secondly, an iterative joint ML nondata-aided (NDA) phase and power spectral density estimator is derived for uncoded and coded transmitted signals. The main difference between the approaches is that the first estimator uses hard decisions whereas the second estimator uses soft decisions about the data symbols at each iteration. Furthermore, the mean-squared performance of the second estimator is approximated by the inverse of the empirical observed Fisher information. Finally, it is shown that the recursive approximations of both estimators lead to the Costas type of loops introduced earlier in the literature.