Gain Before Tracking: Compensating Power-Amplifier Nonlinearity and Phase Noise in AFDM Uplinks
Affine frequency division multiplexing (AFDM) is a candidate waveform for fast-moving vehicles and satellites, but real transmitters add power-amplifier (PA) compression and oscillator phase noise, and no AFDM receiver corrects both. We show that AFDM's transform treats every component equally in magnitude, so the PA's effect reduces to one gain shared by all components and phase noise to a common rotation that OFDM's standard tracker removes. The order matters: the tracker relies on symbol decisions that PA compression corrupts, so the gain should be corrected first. On a six-path, fractional-Doppler channel with 256 subcarriers and a standard-compliant PA back-off, doing so lowers the uncoded bit-error rate by 7.5-12% for AFDM and about 5% for OFDM, and saves 0.5 dB at 10% block error with a rate-3/4 code; the effect is not significant at light back-off. A closed-form gain matches a blind estimate and, without pilots, performs comparably to a pilot-based joint gain estimate that costs 6% overhead. Controls show that AFDM's edge over OFDM is mostly spreading across the channel, not Doppler robustness: single-carrier DFT-s-OFDM matches it at equal back-off.