In this paper, we present a closed-form expression of a Bayesian Cramér-Rao lower bound for the estimation of a dynamical phase offset in a non-data-aided BPSK transmitting context. This kind of bound is derived considering two different scenarios: a first expression is obtained in an off-line context and then, a second expression in an on-line context logically follows. The SNR-asymptotic expressions of this bound drive us to introduce a new asymptotic bound, namely the Asymptotic Bayesian Cramér-Rao Bound. This bound is close to the classical Bayesian bound but is easier to evaluate.

Abstract-This letter deals with the Cramér-Rao bound for the estimation of a hybrid vector with both random and deterministic parameters. We point out the specificity of the case when the deterministic and the random vectors of parameters are statistically dependent. The relevance of this expression is illustrated by studying a practical phase estimation problem in a non-data-aided communication context.