NCAirFL: CSI-Free Over-the-Air Federated Learning Based on Non-Coherent Detection

Over-the-air federated learning (FL), i.e., AirFL, leverages computing primitively over multiple access channels. A long-standing challenge in AirFL is to achieve coherent signal alignment without relying on expensive channel estimation and feedback. This paper proposes NCAirFL, a CSI-free AirFL scheme based on unbiased non-coherent detection at the edge server. By exploiting binary dithering and a longterm memory based error-compensation mechanism, NCAirFL achieves a convergence rate of order <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{O}(1 / \sqrt{T})$</tex> in terms of the average square norm of the gradient for general non-convex and smooth objectives, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$T$</tex> is the number of communication rounds. Experiments demonstrate the competitive performance of NCAirFL compared to vanilla FL with ideal communications and to coherent transmission-based benchmarks.