Message faults are expected to become a major problem for next-generation 5G/6G networks, due to signal fading, high backgrounds, and high density of users. Disclosed are methods to modulate and demodulate messages to optimize noise margins, greatly enhancing reliability at negligible cost, according to some embodiments. A transmitter can modulate a message using amplitude-phase modulation, yet a receiver can conveniently receive and process the signals according to separate in-phase (I) and quad-phase (Q) branches, that is, according to QAM. The receiver can then convert the I and Q values to the original waveform amplitude and phase mathematically, and then demodulate those values using predetermined amplitude and phase levels as provided by a proximate demodulation reference. By converting the as-received QAM values to the as-transmitted amplitude-phase values, the receiver can thereby avoid many noise vulnerabilities inherent in QAM-modulated messages, and thereby obtain the full noise margins provided by amplitude-phase modulation.