Joint Client Selection and Receive Beamforming for Over-the-Air Federated Learning With Energy Harvesting

Federated learning (FL) is a well-regarded distributed machine learning technology that leverages local computing resources while protecting privacy. The over-the-air (OTA) computation has been adopted for FL to prevent excessive consumption of communication resources by employing the superposition nature of wireless waveform. Meanwhile, energy harvesting technology can relieve the energy constraint of clients and enable durable computation for FL. However, few of the existing works on OTA FL have considered jointly performing client selection and receive beamforming optimization with energy harvesting clients. The objective of this work is to address this issue to improve the learning performance of OTA FL. Specifically, we first derive the expression of the optimality gap regarding client selection and receive beamforming design. Then, to minimize the optimality gap, a mixed-integer nonlinear programming (MINLP) problem is formulated and decomposed into two sub-problems. Next, the semidefinite relaxation method and the channel-energy-data (CED)-based method are developed to optimize the receive beamforming sub-problem and client selection sub-problem iteratively. One alternative optimization method is proposed to deal with the decoupled sub-problems for obtaining the solutions to the original MINLP problem. Our simulation results demonstrate that the proposed solution is superior to the other comparison schemes in various parameter settings.