Maximum likelihood synchronisers with arbitrary prior symbol probabilities

The likelihood function for carrier or symbol synchronisation problems with arbitrary prior symbol probabilities is derived using a new approach. The analysis indicates that the general structure of such a maximum likelihood (MAXL) synchroniser is the same as that of the conventional one with equal prior probabilities except for biasing the tanh operator input with a transition offset value nu , nu =(1/2) ln(q/p); here p is the prior probability of symbol ´1´, and q=1-p. For the case p=1/2, the general synchroniser is reduced to a conventional MAXL synchroniser, for instance the Costas loop carrier synchroniser or MAXL symbol synchroniser. But when there are no data transitions, i.e., p=1, or 0, the general synchroniser is shown to reduce to a phase-locked loop (PLL) for carrier synchroniser, or a PLL-type symbol synchroniser.<>