Input-Correlated Supervision Noise Limits the Benefits of OTA Training for Learned Receivers

While learned wireless receivers are typically studied using synthetic data, the impact of over-the-air (OTA) measurements for training remains unclear. We conducted a 5.88 GHz measurement campaign with a 5G/6G-like orthogonal frequency-division multiplexing (OFDM) system across diverse environments and mobility conditions, and trained a neural channel estimator and a capacity-matched end-to-end neural receiver using mixtures of measured and synthetic data. Increasing the OTA fraction revealed a fundamental asymmetry: measured data consistently improved the end-to-end receiver, whereas the channel estimator peaked at an intermediate fraction and degraded with fully measured training. We showed that this difference arises from the supervision target: OTA channel labels are derived from noisy received signals and therefore contain supervision errors correlated with the receiver input, whereas decoded bits validated by a cyclic redundancy check (CRC) provide effectively error-free supervision. A controlled denoising experiment confirmed that this correlation, rather than limited data diversity, caused the degradation. These results provide practical guidance for training learned receivers with OTA data: end-to-end receivers benefit from fully measured training, whereas channel estimators benefit from moderate OTA fractions but require improved label quality, e.g. via denoising, to unlock further gains.