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This paper develops a class of low-complexity device scheduling algorithmsfor over-the-air federated learning via the method of matching pursuit. Theproposed scheme tracks closely the close-to-optimal performance achieved bydifference-of-convex programming, and outperforms significantly the well-knownbenchmark algorithms based on convex relaxation. Compared to thestate-of-the-art, the proposed scheme poses a drastically lower computationalload on the system: For $K$ devices and $N$ antennas at the parameter server,the benchmark complexity scales with $\left(N^2+K\right)^3 + N^6$ while thecomplexity of the proposed scheme scales with $K^p N^q$ for some $0 < p,q \leq2$. The efficiency of the proposed scheme is confirmed via numericalexperiments on the CIFAR-10 dataset.

Matching Pursuit Based Scheduling for Over-the-Air Federated Learning