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Over-the-air federated edge learning (Air-FEEL) is a communication-efficientframework for distributed machine learning using training data distributed atedge devices. This framework enables all edge devices to transmit model updatessimultaneously over the entire available bandwidth, allowing for over-the-airaggregation. A one-bit digital over-the-air aggregation (OBDA) scheme has beenrecently proposed, featuring one-bit gradient quantization at edge devices andmajority-voting based decoding at the edge server. However, the low-resolutionone-bit gradient quantization slows down the model convergence and leads toperformance degradation. On the other hand, the aggregation errors caused byfading channels in Air-FEEL is still remained to be solved. To address theseissues, we propose the error-feedback one-bit broadband digital aggregation(EFOBDA) and an optimized power control policy. To this end, we first provide atheoretical analysis to evaluate the impact of error feedback on theconvergence of FL with EFOBDA. The analytical results show that, by setting anappropriate feedback strength, EFOBDA is comparable to the Air-FEEL withoutquantization, thus enhancing the performance of OBDA. Then, we furtherintroduce a power control policy by maximizing the convergence rate underinstantaneous power constraints. The convergence analysis and optimized powercontrol policy are verified by the experiments, which show that the proposedscheme achieves significantly faster convergence and higher test accuracy inimage classification tasks compared with the one-bit quantization schemewithout error feedback or optimized power control policy.

Over-the-Air Federated Edge Learning with Error-Feedback One-Bit Quantization and Power Control