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@potto216, I'm opening this thread to continue your discussion from #18.
ADS-B uses binary pulse position modulation (PPM), see this ADS-B Presentation.
The reason I use a non-coherent demod (the mag^2 before the ADS-B framer) is to avoid needing frequency synchronization. Since the modulation is through amplitude (and not phase), computing the power is a "cheap" matched filter. A true matched filter would need to be aligned with the baseband frequency offset of the signal, caused by the receiver's frequency offset and the signal's Doppler shift.
While you are correct that non-coherent demod has worse performance over coherent demod, non-coherent demod is less computationally complex. And in this case, I think that's a win.
I'm open to new ideas, improvements, and implementations, though. 😄