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Damian Marek

You could make a 4 QAM Demodulator to get back the primary signal. The demodulator should be made so that it does not care about the detailed parts in each quadrant, but simply detects which quadrant the symbol is in. That would give back the first signal.

For the second it would also be a 4 QAM demodulator but with its constellation shifted into one of the quadrants. Just make a user defined IQ map.