The OFDM MMSE channel estimator seems to require a-priori knowledge of the channel to calculate the MMSE estimate. See equation 8 here: http://cache.freescale.com/files/dsp/doc/app_note/AN3059.pdf. The autocovariance matrix explicitly includes the actual channel H or g.
However, you presumably don't have this information, otherwise why would you be estimating it? If you are able to deal with the complexity of the MMSE estimator, how do you implement it in practice without prior knowledge of what the channel is?