A simple but important observation for the July.
Let us consider two sinusoidal signals of opposite phases during the time : and Obviously, the signals cancel each other completely and the mean power of the additive signal is just 0:
I we were a bit silly, we could try to add the powers of the signals separately together:
let us assume that and are some random variables of mean 0 (or deterministic variables, as a deterministic variable just is a random variable with a degenerate distribution). We have that
The uncorrelatedness assumption holds for Gaussian noises – and furthermore – we can often consider that all distinct signals in the same communication system are essentially uncorrelated.