Digital versus Analog Transmissions for Federated Learning over Wireless Networks

In this paper, we quantitatively compare these two effective communication schemes, i.e., digital and analog ones, for wireless federated learning (FL) over resource-constrained networks, highlighting their essential differences as well as their respective application scenarios. We first examine both digital and analog transmission methods, together with a unified and fair comparison scheme under practical constraints. A universal convergence analysis under various imperfections is established for FL performance evaluation in wireless networks. These analytical results reveal that the fundamental difference between the two paradigms lies in whether communication and computation are jointly designed or not. The digital schemes decouple the communication design from specific FL tasks, making it difficult to support simultaneous uplink transmission of massive devices with limited bandwidth. In contrast, the analog communication allows over-the-air computation (AirComp), thus achieving efficient spectrum utilization. However, computation-oriented analog transmission reduces power efficiency, and its performance is sensitive to computational errors. Finally, numerical simulations are conducted to verify these theoretical observations.