[tonyarkles]

The sibling post did a good job at outlining some techniques. I’m going to give you a simple example that might help with “ahhh you can get stuff under the noise”

Let’s say you have a noise source made up of random numbers from -1 to 1 (mean 0). And a signal that represents a binary 1 as 0.1 and a binary 0 as -0.1. Our binary signal gets added to the noise.

With one bit and one noise sample, we don’t really get much out of it. 0.567 - 0.1 = 0.467 and 0.567 + 0.1 = 0.667. Looking at 0.467 and 0.667, we can’t really make any judgement of whether either of those samples is a 1 or a 0.

If you extend your bits out though so that, say, one bit gets transmitted 100 times, then you can take 100 samples on the receive end and take the mean of those. Because the noise source has mean zero, the noise component of the (noise+sample) mean should come out around zero. So you get a mean of maybe -0.075, or a mean of 0.083. At that point, it’s reasonable to say “it was likely a -0.1 or 0.1” that was transmitted.

All of the fancy techniques enhance this process, but at its core that’s fundamentally what’s happening. Some of the techniques spread things out over different frequencies, some spread out over time, but it’s all roughly the same idea.