Channel-Estimation-Free Gradient Aggregation for Over-the-Air SIMO Federated Learning

We study the gradient aggregation in over-the-air federated learning (OA-FL), where the parameter server (PS) uses a combining vector to estimate the aggregated gradient. We propose a novel channel-estimation-free (CE-Free) gradient aggregation scheme for OA-FL, where the combining vector at the PS is trained based on the sample average approximation (SAA) method. We analyse the aggregation performance of the proposed scheme based on the large deviation theory (LDT). In the proposed scheme, the required number of training symbols is irrelevant to the number of devices, which significantly reduces the communication cost when the FL system consists of a large number of devices. Numerical results are presented to validate the effectiveness of the proposed scheme.