Analytic and Asymptotic Analysis of Bayesian Cramér-Rao Bound for Dynamical Phase Offset Estimation

Stéphanie Bay (1) , Cédric Herzet (1, 2) , Jean-Marc Brossier (3) , Jean-Pierre Barbot (1) , Benoit Geller (1, 4)

1 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie
2 LBNL - Lawrence Berkeley National Laboratory [Berkeley]
3 GIPSA-C2S - GIPSA - Communication, Signal et Sécurité
4 IS - Ingénierie Systèmes

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.

Mots clés: synchronization; Communication system performance

Domaines: Réseaux et télécommunications [cs.NI]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Stéphanie Bay, Cédric Herzet, Jean-Marc Brossier, Jean-Pierre Barbot, Benoit Geller. Analytic and Asymptotic Analysis of Bayesian Cramér-Rao Bound for Dynamical Phase Offset Estimation. IEEE Transactions on Signal Processing, 2008, 56 (1), pp.61-70. ⟨10.1109/TSP.2007.906760⟩. ⟨hal-01225814⟩