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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?

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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.

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  • $\begingroup$ Thank you for the response, Deve. I want to upvote, but I don't have enough reputation points yet. I will come back when I do. $\endgroup$ – miker Feb 5 '15 at 17:40
  • $\begingroup$ What I could not find in the literature on the subject was: what is the error penalty for picking the wrong channel model to fit to the MMSE estimator? e.g. if you make errors trying to track a fast fading channel, or you pick the wrong power delay profile to fit $\endgroup$ – miker Feb 5 '15 at 18:04
  • $\begingroup$ @miker Unfortunately, I don't know. Maybe this thesis discusses it: inue.uni-stuttgart.de/forschung/dissertationen/… $\endgroup$ – Deve Feb 6 '15 at 8:49

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