To leverage massive distributed data and computation resources in the Internet-of-Things (IoT) networks, federated learning (FL) is considered to be a promising technique with benefits of improved data privacy and communication efficiency. Meanwhile, cell-free massive multiple-input multiple-output (cell-free massive MIMO) is a promising technology to enable the IoT networks to support FL. By deploying the access points (APs) closer to the IoT devices, path loss attenuation can be reduced. However, the performance of FL is still constrained by the limited power resources of IoT devices. To address this issue, we design an energy-efficient FL scheme over cell-free IoT networks by formulating an optimization problem to minimize the total energy consumption of the IoT devices participating in the FL process. To solve the intractable problem in hand, by exploiting its unique structure, we decompose it into three sub-problems that facilitate the development of the proposed scheme. First, we derive the optimal central processing unit (CPU) operating frequency for IoT devices. Then, we design an optimal power allocation scheme to mitigate the straggler effect. Next, nonlinear programming method is adopted to obtain a sub-optimal solution for the reformulated problem. Finally, a three-stage algorithm is proposed for energy consumption minimization by considering these sub-problems. Simulation results demonstrate the close-to-optimal performance of the proposed algorithm for energy savings compared with three baseline algorithms and the capability to support large numbers of IoT device access by mitigating the straggler effect.

High quality triangular Cu_2−xSe nanocrystals were successfully synthesized through a green phosphine free route by the non-injection one-pot colloidal approach with Se–octadecene (ODE) as a precursor. CuSt₂ was used as reactant and oleylamine (OAM) was used as reaction solvent. By using this new non-injection method, triangle shaped Cu_2−xSe nanocrystals with sizes ranging from 2.8 to 12 nm were achieved by simply controlling the reaction time. Transmission electron microscopy (TEM) and high resolution TEM (HRTEM), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), and energy dispersive X-ray (EDX) measurements were used to characterize as-synthesized nanocrystals. Cubic berzelianite crystal phase and narrow size distributions were demonstrated by the results. Additionally, the narrow size distribution promoted as-synthesized Cu_2−xSe nanocrystals self-assembled into ordered superstructures with the assistance of OAM.

Cell-free massive Multi-input Multi-output (MIMO) can offer higher spectral efficiency compared with cellular massive MIMO by providing services to users through the collaboration of distributed APs, and cell-free massive MIMO systems with distributed operations are attracting a great deal of industry attention due to their simplicity and ease of deployment. This paper aims to find an optimal solution for energy efficiency in the downlink operation in the Industrial Internet based on cell-free massive MIMO systems with distributed operations. A system model is proposed, and a theoretical analysis on energy efficiency is presented. The optimization problem of efficient downlink operation is formulated as a mixed-integer nonlinear programming (MINLP) problem, which is further decomposed into two sub-problems, i.e., maximizing the sum-rate of the downlink transmission and optimizing the total energy consumption. The two sub-problems are addressed via AP selection and power allocation, respectively. The simulation results demonstrate that our algorithms can significantly improve the energy efficiency with low computational complexity in comparison with traditional distributed cell-free massive MIMO. Even in the presence of pilot contamination, the proposed algorithms can still provide significant energy efficiency when a large number of IoTDs are connected.