Maximum likelihood estimation of OFDM carrier frequency offset

We develop a maximum likelihood estimate for orthogonal frequency division multiplexing (OFDM) carrier frequency offset in the presence of virtual carriers. It is found that the resulting estimate has an identical form to that of a previously proposed blind OFDM carrier frequency offset estimate by Liu and Tureli (see IEEE Commun. Lett., vol.2, p.104-106, 1998). Insights are provided as to why these two algorithms are equivalent.