Closed loop carrier phase synchronization techniques motivated by likelihood functions

Motivated by the theory of MAP carrier phase estimation, the authors have developed a number of closed loop structures suitably derived from maximum-likelihood (ML) and average-likelihood (AL) functions. Several of these structures reduce to previously known closed loop carrier phase synchronizers while others appear to be new. Of particular interest is one of the ML structures which, when properly optimized, gives improved mean-square phase error performance over the other ML and AL structures. The improvement is largest at low symbol SNR and is thus quite significant in applications that involve a combination of low rate coding and antenna arraying such as the NASA/JPL Galileo mission to Jupiter. The structures proposed in the paper are not exhaustive of the ways that closed loop phase synchronizers can be derived from open loop MAP estimation theory. Rather they are given primarily to indicate the variety of different closed loop schemes that can be constructed simply from likelihood and log-likelihood functions