This article investigates energy-ecient federated learning (FL) in multiple-input–multiple-output (MIMO) edgeenabled Internet of Things (IoT) networks, where user equipment (UE) is enabled with simultaneous wireless information and power transfer (SWIPT) capabilities. To jointly optimize communication and computation resources, a hierarchical optimization framework is proposed to minimize the total e ective energy consumption per global FL round, while satisfying latency, power, frequency, power-splitting (PS), and local accuracy constraints. By exploiting the time-scale separation between wireless resource allocation and learning accuracy adaptation, the resulting nonconvex problem is decomposed into a short-term convexified subproblem for communication and computation resource optimization, solved via successive convex approximation (SCA), and a long-term subproblem for local accuracy updates, addressed using coordinate descent (CD). The proposed algorithm ensures convergence to a stationary solution with polynomial complexity, achieving significant computational savings compared to exhaustive search. Simulation results verify that the proposed framework achieves substantial energy consumption reduction and faster convergence compared with the benchmark schemes. Furthermore, results demonstrate that increasing the base station (BS) antenna array or the energy harvesting eciency enhances the network sustainability and scalability of FL for energyconstrained IoT devices.
