I'm doing pilot symbols aided channel estimation for OFDM system.
Based on estimation theory we know that maximum likelihood estimator for the channel (h_hat) is as the following:
h_hat = X^-1*R, where X is a diagonal matrix of the OFDM symbols (pilot symbols I assume) and R is the random received samples defined as R = X*h + noise, where h is the true channel.
My question is how we should come up with the channel estimation while we don't know R, I mean I know that in the real world R gonna be observed samples but what about in theory? how do we suppose to calculate h_hat while we don't know R meaning true channel and noise? I thought I may be able to estimate noise variance first, but then I saw that estimation of the noise variance also depends on estimated channel...