Replying to Phijkchu_Pikachu #klombak central limit theorem just states that the statistical average of sequences of RVs approach a normal distribution
It's taking a sum of two RVs. One of is correlated across elements (the signal - because a signal hits every element) and the other is not correlated across elements (the noise) so when you sum up a large beam, the noise never increases, but the signal does. So that's the central limit theorem, the noise just goes into a gaussian.
