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Machine learning (ML) is a widely accepted means for supporting customized services for mobile devices and applications. Federated Learning (FL), which is a promising approach to implement machine learning while addressing data privacy concerns, typically involves a large number of wireless mobile devices to collect model training data. Under such circumstances, FL is expected to meet stringent training latency requirements in the face of limited resources such as demand for wireless bandwidth, power consumption, and computation constraints of participating devices. Due to practical considerations, FL selects a portion of devices to participate in the model training process at each iteration. Therefore, the tasks of efficient resource management and device selection will have a significant impact on the practical uses of FL. In this paper, we propose a spectrum allocation optimization mechanism for enhancing FL over a wireless mobile network. Specifically, the proposed spectrum allocation optimization mechanism minimizes the time delay of FL while considering the energy consumption of individual participating devices; thus ensuring that all the participating devices have sufficient resources to train their local models. In this connection, to ensure fast convergence of FL, a robust device selection is also proposed to help FL reach convergence swiftly, especially when the local datasets of the devices are not independent and identically distributed (non-iid). Experimental results show that (1) the proposed spectrum allocation optimization method optimizes time delay while satisfying the individual energy constraints; (2) the proposed device selection method enables FL to achieve the fastest convergence on non-iid datasets.