On-Line Hybrid CrameR-Rao Bound for Oversampled Dynamical Phase and Frequency Offset Estimation

This paper deals with the on-line estimation of a dynamical carrier phase and a frequency offset in a digital receiver. We consider a Brownian phase evolution with a linear drift in a Data Aided scenario. The proposed study is relative to the use of an oversampled signal model after matched filtering, leading to a coloured reception noise and a non-stationary power signal. We derive a closed-form expression of the Hybrid Cramer-Rao Bound (HCRB) for this estimation problem. We use a Binary Offset Carrier (BOC) function as shaping pulse. Our numerical results show the potential gain of using the oversampled signal for estimating the dynamical phase and frequency offset, obtaining better performances than using a classical synchronizer.

[1]  M. Melamed.  Detection , 2021, SETI: Astronomy as a Contact Sport.

[2]  Sailes K. Sengijpta.  Fundamentals of Statistical Signal Processing: Estimation Theory , 1995 .

[3]  H. V. Trees.  Detection, Estimation, And Modulation Theory , 2001 .

[4]  J. Barbot,et al.  Analytic and Asymptotic Analysis of Bayesian CramÉr–Rao Bound for Dynamical Phase Offset Estimation , 2008, IEEE Transactions on Signal Processing.

[5]  William G. Cowley,et al.  Phase and frequency estimation for PSK packets: bounds and algorithms , 1996, IEEE Trans. Commun..

[6]  L. Ros,et al.  On-line Bayesian CraméR-Rao bound for oversampled dynamical phase offset estimation , 2008, 2008 3rd International Symposium on Communications, Control and Signal Processing.

[7]  A. Gualtierotti.  H. L. Van Trees, Detection, Estimation, and Modulation Theory, , 1976 .

[8]  William Moran,et al.  Cramer-Rao lower bounds for QAM phase and frequency estimation , 2001, IEEE Trans. Commun..

[9]  Pierre-Olivier Amblard,et al.  Phase tracking: what do we gain from optimality? Particle filtering versus phase-locked loops , 2003, Signal Process..

[10]  Benoit Geller,et al.  On the Hybrid Cramér Rao Bound and Its Application to Dynamical Phase Estimation , 2008, IEEE Signal Processing Letters.

[11]  Carlos H. Muravchik,et al.  Posterior Cramer-Rao bounds for discrete-time nonlinear filtering , 1998, IEEE Trans. Signal Process..

[12]  Benoit Geller,et al.  Bayesian CramÉr-Rao bound for dynamical phase offset estimation , 2007, 2007 IEEE 8th Workshop on Signal Processing Advances in Wireless Communications.