CRB for Carrier Frequency Offset Estimation with Pilot and Virtual Subcarriers

The Cramer Rao bound (CRB) for the carrier frequency offset (CFO) estimation with OFDM blocks consisting of virtual, pilot and data subcarriers is derived in this paper. From the CRB derived in the general case that all the three kinds of subcarriers exist, the CRB for the special cases that one or two kinds of the subcarriers are absent can be easily deduced. Further more, the derived CRB is a tight lower bound as well designed estimators, e.g. the maximum likelihood (ML) estimator, can achieve it at high signal to noise ratio (SNR). Thus, the derived CRB is a good benchmark for evaluating many different CFO estimators.