I'll consider a 20 MHz bandwidth between 1.99-2.01 GHz. The carrier has been modulated by an OFDM signal (I/Q modulation) and is passed through a narrowband filter at the receiver.
The noise that is actually received after the input filter is narrowband. So, it is not white anymore. The noise looks like a sinewave of 2 GHz with varying amplitude and phase, which has a Rayleigh distribution. In time domain, something like this:
This is something like the aliasing measured when undersampling a signal, but it has a Rayleigh distribution.
BER is expressed in the simplest case for an AWGN channel. I've seen that the procedure is to add AWGN of a certain SNR to the signal. The representation of this in time domain is not how the signal measured after the filter would appear, in my understanding.
An example of AWGN addition is this (https://www.mathworks.com/help/comm/ug/analog-passband-modulation.html)
Looking at the picture above, considering that the signal is sampled at the Nyquist rate, we can observe that there is an uncertainty in the values that are sampled. Could the same uncertainty appear with a bandlimited gaussian noise of the same power? Is that the baseband received signal that is represented above? Are there cases when the white gaussian noise is not equivalent to the real bandlimited gaussian noise?
BER in AWGN appears to be the most common metric of noise performance, so there must be an explanation for this method. What is it?