Hi Marcus,
I completely agree to the statement. But take a look at this simple model:
y(t) = h(t) * x(t) + n(t).
'y' is the received signal, 'h' is the channel response (here I assumed that the channel is linear as a filter), 'x' is the desired signal and 'n' is noise and the sign '*' is the convolution. Hence, if we try to find signal (x) power to noise (n), it implies that the 'h' is somehow estimated. Again, consider that noise and channel are different both statistically and in nature.
take look at the "Tom Rondeau"s website:
He said:
" In the case of an SNR estimator, though, I thought about this and had to come to the conclusion that the only way to handle this is to have an estimator that you can plug in variables for your channel model, which of course assumes that you have or can estimate these parameters."
So we need acquire 'h'.
Best,
Mostafa