This paper presents federated learning with over-the-air (OTA) aggregation over a noisy communication channel for human activity recognition (HAR) problem. OTA aggregation permits simultaneous transmission of model weights through waveform superposition, enabling federated computation over the air. However, noise susceptibility in the channel can degrade weight signal aggregation quality. To this end, we propose a novel PerSonalized OTA FL (PerSOTA FL), which employs QR decomposition to estimate model weight. Our PerSOTA FL leverages multiple antennas for robust OTA-based aggregation, particularly in environments with low signal-to-noise ratio (SNR). Our experiments, with two real-world HAR datasets exhibiting practical data and label heterogeneity, indicate that our PerSOTA FL approach achieves comparable performance to vanilla FL while outperforms the conventional OTA FL. Our experimental results verify the efficiency of our PerSOTA FL, demonstrating its capacity for on-device personalized training while delivering a generalized HAR model through OTA FL.
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