Joint Pre-Equalization and Receiver Combining Design for Federated Learning With Misaligned Over-the-Air Computation

With the growth of terminal devices and data traffic, privacy concerns have inspired an innovative edge learning framework, called federated learning (FL). Over-the-air computation (OAC) has been introduced to reduce communication overhead for FL, however, requires stringent time alignment. Misaligned OAC has been proposed by recent research where the symbol-timing misaligned superimposed signal can be recovered via whitening matched filtering and sampling (WMFS), followed by maximum likelihood (ML) estimation. Similarly to aligned OAC, misaligned OAC also suffers from the straggler issue, leading to FL's poor performance under low EsN0. To solve this issue, we propose a novel framework of misaligned OAC FL for accurate model aggregation on wireless networks. First, we analyze the effect of aggregation error on the convergence of FL. Then, we formulate an optimization problem to minimize the distortion of the aggregation measured by mean square error (MSE) w.r.t. the transmitter equalization and receiver combining. Finally, a successive convex approximation (SCA)-based optimization algorithm is further developed to solve the resulting quadratic constrained quadratic programming. Comprehensive experiments show that the proposed algorithm achieves substantial learning performance improvement compared to existing baseline schemes and achieves the near-optimal performance of the ideal benchmark with aligned and noiseless aggregation.