Tracking of a Brownian phase with linear drift: Algorithms and performances

We study the problem of tracking a Brownian phase with linear drift at the output of a simple digital receiver. The classical Costas and Decision feedback loops are compared to the particle implementation of the optimal nonlinear filter. The study of the asymptotic performance of the loops allows to tune the loops in order to minimize the mean square error. We then show that the particle filter outperforms the loops in the acquisition step and in the behavior in front of cycle slips.