Hybrid Cramer-Rao Bound on Carrier and Sampling Frequency Offset Estimation for OFDM Systems in Rayleigh Fading Channels

Abstract

For the carrier frequency offset (CFO) and sampling (clock) frequency offset (SFO) estimation, the hybrid Cramer-Rao bound (HCRB) is developed when the CFO, SFO, information-bearing symbols are deterministic and channel coefficients are random. Both noise and channel coefficients are complex Gaussian. The HCRB is a lower bound on the mean squared estimation error for any unbiased estimator of a parameter. For the HCRB to be applicable, it is necessary for deterministic parameters to be identifiable (uniquely determined). Some necessary identifiability conditions of some deterministic parameters are found and presented. The HCRB is dependent on the initial time instant. The HCRB is used to assess the performances of some existing methods via simulation. Our results demonstrate that even the best performance is still around 10 dB higher than the HCRB. Further effort is needed to develop more accurate methods.