  In Federated edge learning (FEEL), energy-constrained devices at the network
edge consume significant energy when training and uploading their local machine
learning models, leading to a decrease in their lifetime. This work proposes
novel solutions for energy-efficient FEEL by jointly considering local training
data, available computation, and communications resources, and deadline
constraints of FEEL rounds to reduce energy consumption. This paper considers a
system model where the edge server is equipped with multiple antennas employing
beamforming techniques to communicate with the local users through orthogonal
channels. Specifically, we consider a problem that aims to find the optimal
user's resources, including the fine-grained selection of relevant training
samples, bandwidth, transmission power, beamforming weights, and processing
speed with the goal of minimizing the total energy consumption given a deadline
constraint on the communication rounds of FEEL. Then, we devise tractable
solutions by first proposing a novel fine-grained training algorithm that
excludes less relevant training samples and effectively chooses only the
samples that improve the model's performance. After that, we derive closed-form
solutions, followed by a Golden-Section-based iterative algorithm to find the
optimal computation and communication resources that minimize energy
consumption. Experiments using MNIST and CIFAR-10 datasets demonstrate that our
proposed algorithms considerably outperform the state-of-the-art solutions as
energy consumption decreases by 79% for MNIST and 73% for CIFAR-10 datasets.
