Does the OFDM MMSE Channel Estimator Require Prior Channel Knowledge? 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?
It's true that the MMSE channel estimator requires some a-priori channel knowledge, namely the autocovariance (or autocorrelation) matrix of the channel and the signal-to-noise ratio (SNR). Note that these are statistical quantities while the aim of channel estimation is to estimate the actual channel transfer function at a certain point in time.

The autocovariance matrix $\underline R_{HH}$ is based on some statistical channel model, e.g. the Rayleigh fading channel or AWGN channel. As you have observed correctly, the channel matrix $H$ is unknown and thus $\underline R_{HH}$ cannot be calculated from $H$. It's rather an assumption based on theroetical models or earlier measurements. 

The SNR can usually be estimated from the received signal by measuring the noise power on zero subcarriers or analyzing the received constellation diagram.