On the Cramer-Rao bound for carrier frequency estimation in the presence of phase noise

We consider the carrier frequency offset estimation in a digital burst-mode transmission affected by phase noise. The corresponding Cramer-Rao lower bound is analyzed for linear modulations under a Wiener phase noise model and in the hypothesis of knowledge of the transmitted data. Even if we resort to a Monte Carlo average, from a computational point of view the evaluation of the Cramer-Rao bound is very hard. We introduce a simple but very accurate approximation that allows to carry out this task in a very easy way. As it is shown, the presence of the phase noise produces a remarkable performance degradation of the frequency estimation accuracy. In addition, we bound and we also gain some important hints on the estimators to be used in this scenario.

[1]  Heidi Steendam,et al.  Pilot-symbol assisted iterative carrier synchronization for burst transmission , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

[2]  A. Demir,et al.  Phase noise in oscillators: a unifying theory and numerical methods for characterization , 2000 .

[3]  M.P. Fitz,et al.  Single frequency estimation with non-uniform sampling , 1996, Conference Record of The Thirtieth Asilomar Conference on Signals, Systems and Computers.

[4]  Robert Boorstyn,et al.  Single tone parameter estimation from discrete-time observations , 1974, IEEE Trans. Inf. Theory.

[5]  S. Shamai,et al.  Iterative decoding for coded noncoherent MPSK communications over phase-noisy AWGN channel , 2000 .

[6]  Marco Luise,et al.  Carrier frequency recovery in all-digital modems for burst-mode transmissions , 1995, IEEE Trans. Commun..

[7]  Umberto Mengali,et al.  The modified Cramer-Rao bound and its application to synchronization problems , 1994, IEEE Trans. Commun..

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

[9]  Heidi Steendam,et al.  The true Cramer-Rao bound for carrier frequency estimation from a PSK signal , 2004, IEEE Transactions on Communications.

[10]  Pramod K. Varshney,et al.  Spectral Dispersion of Modulated Signals Due to Oscillator Phase Instability: White and Random Walk Phase Model , 1983, IEEE Trans. Commun..

[11]  Giuseppe Caire,et al.  Joint iterative detection and decoding in the presence of phase noise and frequency offset , 2005, IEEE International Conference on Communications, 2005. ICC 2005. 2005.

[12]  Giuseppe Caire,et al.  Algorithms for iterative decoding in the presence of strong phase noise , 2005, IEEE Journal on Selected Areas in Communications.

[13]  Umberto Mengali,et al.  Feedforward frequency estimation for PSK: A tutorial review , 1998, Eur. Trans. Telecommun..

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

[15]  Roberto Garello,et al.  MHOMS: high-speed ACM modem for satellite applications , 2005, IEEE Wireless Communications.

[16]  Umberto Mengali,et al.  Data-aided frequency estimation for burst digital transmission , 1997, IEEE Trans. Commun..

[17]  Odile Macchi,et al.  A Dynamic Programming Algorithm for Phase Estimation and Data Decoding on Random Phase Channels , 1979 .

[18]  Luciano Tomba,et al.  On the effect of Wiener phase noise in OFDM systems , 1998, IEEE Trans. Commun..

[19]  Steven Kay,et al.  A Fast and Accurate Single Frequency Estimator , 2022 .