# A Survey on Energy-Efficient Design for Federated Learning over Wireless Networks
## 4 Wireless Network Architectures for Energy-Efficient DFL
### DFL in D2D Communication Networks
[107] utilized graph convolutional networks (GCNs) to optimize device selection and offloading ratios within a D2D-enabled DFL framework, making it particularly suitable for environments with diverse device capabilities and network topologies. This model enhances DFL accuracy and reduces data processing and energy overhead by learning complex interdependencies between devices and local data distributions, outperforming traditional sampling methods. Another energy-focused approach was introduced in [108], which proposed a D2D-assisted DFL framework that minimizes the global loss of a deep neural network (DNN) model while respecting device energy constraints and edge server bandwidth limitations. By using auxiliary graphs to solve weighted maximum matching problems, this method optimizes local model uploads, leverages the energy resources of neighboring devices, and improves communication efficiency during the training process. To further improve resource utilization, [PERSON]. [109] proposed a DFL-EOCD scheme, which integrates D2D communications and overlapped clustering for decentralized aggregation. This approach reduces the energy consumption of devices while maintaining a satisfactory convergence rate. The DFL-EOCD algorithm outperforms traditional DFL schemes by optimizing energy consumption, latency, and convergence rate, offering a promising direction for DFL in decentralized networks. The study in [110] proposed a two-timescale hybrid DFL (TT-HF) framework that combines conventional device-to-server communication with D2D communications, enabling devices to perform multiple local gradient descent iterations and participate in a cooperative D2D consensus within clusters at each global aggregation interval. The authors introduced a novel definition of gradient diversity to analyze the TT-HF's convergence behavior, establishing new bounds to minimize network resource demands during distributed learning. An incentive-driven DFL framework was proposed in [111], which integrates a one-sided matching theory-based mechanism to encourage user participation. By utilizing D2D communications and forecasting channel conditions with echo state networks at each user site, this framework optimizes the trade-off between energy consumption and convergence time, thus enhancing the DFL process in communication-challenged environments. Finally, [PERSON]. [34] proposed a decentralized learning mechanism that optimizes computing power, wireless resource allocation, link selection, and aggregation weight adaptation. Using alternating optimization, semidefinite programming, and a tabu search-based algorithm, this framework minimizes total learning costs, including latency and energy consumption, while improving energy and communication efficiency in D2D-enabled DFL systems. These methods, which leverage graph-based models, address key challenges in DFL by reducing energy use, enhancing accuracy, and improving convergence rates, demonstrating the effectiveness of graph-theoretic and D2D strategies in enhancing the performance and sustainability of DFL systems.