CRB of carrier frequency offset estimation with virtual subcarriers

The Cramer Rao bound (CRB) of the carrier frequency offset (CFO) estimation with virtual subcarriers in orthogonal frequency division multiplexing (OFDM) systems is derived. The obtained CRB gives a lower bound, which is much tighter than the modified CRB, for the variance of any unbiased CFO estimate. Also, the maximum likelihood estimator can achieve this tight CRB at high signal-to-noise ratio. Thus, the derived CRB is a good benchmark for evaluating whether a CFO estimator is good or not.