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

We investigate gradient aggregation in over-the-air federated learning (OA-FL) with orthogonal frequency division multiplexing (OFDM), where the parameter server (PS) employs a combining vector to estimate the aggregated gradient. By lever-aging the block-wise linear property between the subcarriers, we propose a novel channel-estimation-free (CE-Free) gradient aggregation scheme for OFDM OA-FL. In this scheme, the combining vector at the PS is linearly approximated, avoiding the requirement to train combining vectors for subcarriersindivid-ually, and thereby significantly reducing the required number of training symbols. We analyze the aggregation performance of the proposed scheme by characterizing the aggregation mean square error (MSE). Numerical results illustrate the effectiveness of the proposed scheme.