The paper addresses the challenges of low-latency and privacy in emerging high-stake applications, such as drones and smart vehicles, by proposing a novel over-the-air computation (AirComp) approach for fast global model aggregation in federated learning. Federated learning, which trains machine learning models on mobile devices without centralizing data, is hindered by limited communication bandwidth. The proposed method leverages the superposition property of a wireless multiple-access channel to compute the weighted average of locally updated models from multiple devices, reducing the number of communication rounds. This is achieved through joint device selection and beamforming design, formulated as a sparse and low-rank optimization problem. A difference-of-convex-functions (DC) approach is developed to enhance sparsity and accurately detect rank-one constraints, leading to efficient algorithms. The DC algorithm is shown to converge globally, and its performance is superior to state-of-the-art methods, as demonstrated through numerical results. The paper contributes to improving the statistical learning performance and convergence rate in on-device distributed federated learning systems.The paper addresses the challenges of low-latency and privacy in emerging high-stake applications, such as drones and smart vehicles, by proposing a novel over-the-air computation (AirComp) approach for fast global model aggregation in federated learning. Federated learning, which trains machine learning models on mobile devices without centralizing data, is hindered by limited communication bandwidth. The proposed method leverages the superposition property of a wireless multiple-access channel to compute the weighted average of locally updated models from multiple devices, reducing the number of communication rounds. This is achieved through joint device selection and beamforming design, formulated as a sparse and low-rank optimization problem. A difference-of-convex-functions (DC) approach is developed to enhance sparsity and accurately detect rank-one constraints, leading to efficient algorithms. The DC algorithm is shown to converge globally, and its performance is superior to state-of-the-art methods, as demonstrated through numerical results. The paper contributes to improving the statistical learning performance and convergence rate in on-device distributed federated learning systems.