Wireless federated learning (FL) relies on efficient uplink communications to aggregate model updates across distributed edge devices. Over-the-air computation (a.k.a. AirComp) has emerged as a promising approach for addressing the scalability challenge of FL over wireless links with limited communication resources. Unlike conventional methods, AirComp allows multiple edge devices to transmit uplink signals simultaneously, enabling the parameter server to directly decode the average global model. However, existing AirComp solutions are intrinsically analog, while modern wireless systems predominantly adopt digital modulations. Consequently, careful constellation designs are necessary to accurately decode the sum model updates without ambiguity. In this paper, we propose an end-to-end communication system supporting AirComp with digital modulation, aiming to overcome the challenges associated with accurate decoding of the sum signal with constellation designs. We leverage autoencoder network structures and explore the joint optimization of transmitter and receiver components. Our approach fills an important gap in the context of accurately decoding the sum signal in digital modulation-based AirComp, which can advance the deployment of FL in contemporary wireless systems.

We propose a privacy-preserving uplink over-the-air computation (AirComp) method, termed FLORAS, for single-input single-output (SISO) wireless federated learning (FL) systems. From the perspective of communication designs, FLORAS eliminates the requirement of channel state information at the transmitters (CSIT) by leveraging the properties of orthogonal sequences. From the privacy perspective, we prove that FLORAS offers both item-level and client-level differential privacy (DP) guarantees. Moreover, by properly adjusting the system parameters, FLORAS can flexibly achieve different DP levels at no additional cost. A new FL convergence bound is derived which, combined with the privacy guarantees, allows for a smooth tradeoff between the achieved convergence rate and differential privacy levels. Experimental results demonstrate the advantages of FLORAS compared with the baseline AirComp method, and validate that the analytical results can guide the design of privacy-preserving FL with different tradeoff requirements on the model convergence and privacy levels. A preliminary version of this work was presented at the 2023 IEEE International Conference on Communications [1]. Xizixiang Wei and Cong Shen are with the Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, USA. Tianhao Wang is with the Department of Computer Science, University of Virginia, USA. Ruiquan Huang and Jing Yang are with The Department of Electrical Engineering, The Pennsylvania State University, USA.