An average Cramer-Rao bound for frequency offset estimation in frequency-selective fading channels

Several variations of Cramer-Rao bounds for carrier frequency offset (CFO) estimation in frequency-selective fading channels have been used to benchmark practical estimators' performance or to design training signals for CFO estimation. Among them, the extended Miller-Chang bound (EMCB) provides a tighter bound than the CRB for locally unbiased estimators. However, there is no closed-form expression of the EMCB for the CFO estimation in frequency-selective fading channels with an arbitrary training signal. In this letter, we derive a closed-form exact average CRB (the EMCB) valid for any training signal and any signal structure for the CFO estimation over frequency-selective Rayleigh fading channels with uncorrelated or arbitrarily correlated taps. The accuracy and generality of the proposed average CRB expression, and its advantages over the existing expressions are corroborated by numerical and simulation results.

[1]  P. Bianchi,et al.  Joint frequency offset and channel estimation in the OFDMA uplink: Cramer-Rao bounds and training sequence design , 2005, IEEE 6th Workshop on Signal Processing Advances in Wireless Communications, 2005..

[2]  Georgios B. Giannakis,et al.  Cyclic prefixing or zero padding for wireless multicarrier transmissions? , 2002, IEEE Trans. Commun..

[3]  Hlaing Minn,et al.  Two novel iterative joint frequency-offset and channel estimation methods for OFDMA uplink , 2006, IEEE Transactions on Communications.

[4]  A. Robert Calderbank,et al.  Pilot Designs for Consistent Frequency-Offset Estimation in OFDM Systems , 2007, IEEE Transactions on Communications.

[5]  A. M. Mathai,et al.  Quadratic forms in random variables : theory and applications , 1992 .

[6]  Petre Stoica,et al.  Training sequence design for frequency offset and frequency-selective channel estimation , 2003, IEEE Trans. Commun..

[7]  Umberto Mengali,et al.  An improved frequency offset estimator for OFDM applications , 1999, IEEE Communications Letters.

[8]  Moisés Simões Piedade,et al.  On the Miller-Chang lower bound for NDA carrier phase estimation , 2004, IEEE Transactions on Communications.

[9]  Hlaing Minn,et al.  An optimal training signal structure for frequency-offset estimation , 2005, IEEE Transactions on Communications.

[10]  Khaled Ben Letaief,et al.  Carrier frequency offset estimation for OFDM systems using null subcarriers , 2006, IEEE Transactions on Communications.

[11]  Vijay K. Bhargava,et al.  Optimal periodic training signal for frequency offset estimation in frequency selective fading channels , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

[12]  Tariq S. Durrani,et al.  Frequency estimation in the presence of Doppler spread: performance analysis , 2001, IEEE Trans. Signal Process..

[13]  Vijay K. Bhargava,et al.  OFDM frequency offset estimation based on BLUE principle , 2002, Proceedings IEEE 56th Vehicular Technology Conference.

[14]  Umberto Mengali,et al.  The modified Cramer-Rao bound in vector parameter estimation , 1998, IEEE Trans. Commun..

[15]  Fulvio Gini,et al.  On the use of Cramer-Rao-like bounds in the presence of random nuisance parameters , 2000, IEEE Trans. Commun..

[16]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[17]  I. Miller.  Probability, Random Variables, and Stochastic Processes , 1966 .

[18]  Heidi Steendam,et al.  Synchronization sensitivity of multicarrier systems , 2004, Eur. Trans. Telecommun..

[19]  Marc Moeneclaey,et al.  BER sensitivity of OFDM systems to carrier frequency offset and Wiener phase noise , 1995, IEEE Trans. Commun..

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

[21]  Umberto Mengali,et al.  Carrier-frequency estimation for transmissions over selective channels , 2000, IEEE Trans. Commun..

[22]  M. Ghogho,et al.  Training Design for Multipath Channel and Frequency-Offset Estimation in MIMO Systems , 2006, IEEE Transactions on Signal Processing.