Analytic and Asymptotic Analysis of Bayesian CramÉr–Rao Bound for Dynamical Phase Offset Estimation

In this paper, we present a closed-form expression of a Bayesian Cramer-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 offline context, and then a second expression in an online context logically follows. The SNR-asymptotic expressions of this bound drive us to introduce a new asymptotic bound, namely the asymptotic Bayesian Cramer-Rao Bound. This bound is close to the classical Bayesian bound but is easier to evaluate.