I thought you were being handwave-y about the signal being returned because that's an obscenely small amount of power, but you're right. Hardware that is probably 50 years old at this stage, in the cold of (interstellar)space, and we're still able to talk to it despite the signal after its long journey back being ~0.000000000000000001w.
Essentially averaging. To put it simply, noise is random while the signal is not. So if you average 2x the noise reduces but sqrt(2) but the signal remains. Keep doing that and you have the signal appear out of the noise.
GPS operates at a negative SNR. That also uses code division multiple access to allow multiple transmitters to operate on the same frequency and the signals do not interfere.
Imagine you're watching a trail of animal footprints in the snow, but the snow has covered parts of the trail (noise), so some prints are unclear. You're trying to figure out exactly which path the animal took. The Viterbi algorithm is like a detective method for doing just that, but instead of animal tracks, it's used for decoding messages or signals that got partially scrambled during transmission.
This is fascinating. It sounds like viterbi builds probabilities from known data, is that right? Is it essentially looking at the faint signal now and comparing it to data from when the signal was stronger and extrapolating?
That’s how I understand it. I think it uses knowledge of the state changes, what they should be like, and selects the most likely one from a table of options. Based on what it knows about the signal, it guessed whether it’s more likely to be a or b.
I use it with ham radio, where the software I use sends signals well under the noise floor (-23db) that can still get across call signs, signal reports, and maybe a thank you. The naked ear would not hear a thing at the low end of received signal.
