# 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  
D2D communication plays a pivotal role in DFL within wireless networks. By enabling direct peer-to-peer model updates without a BS, D2D communication aligns with the decentralized nature of FL, optimizing energy usage by shortening transmission distances and reducing communication costs. In densely populated mobile networks, D2D allows nearby devices to efficiently exchange model updates, thereby saving energy and eliminating the need for intermediary nodes [103]. To illustrate the different operational modes of D2D communication, Figure 6 presents two modes: (a) Standalone D2D, which operates independently of any infrastructure, and (b) Network-assisted D2D, which leverages existing network resources. Additionally, Table 2 briefly summarizes key studies on energy-efficient DFL in D2D environments, which will be discussed further in this subsection. \begin{table}
\begin{tabular}{c l l c} \hline \hline
**Reference** & **Design Variables** & **Method** & **Mode** \\ \hline
[104] & Resource allocation & Deep reinforcement learning (DRL) & (a) \\ \hline
[105] & Computing power allocation and dataset correlation into & Graph learning and DRL & (b) \\  & FL scheduling & & \\ \hline
[106] & The selection of LAs and the scheduling of devices to & A low-complexity graph-theory algorithm & (b) \\  & LAs/RRBs & & \\ \hline
[107] & Device selection, offloading ratios & Graph convolutional networks (GCN) & (b) \\ \hline
[108] & Devices participating in the training, the offloading destination, the set of sampled data points, and the transmission power level of each device at each round & Deep neural network (DNN) & (b) \\ \hline
[109] & The clustering selection, CH-device scheduling, and frequency computation allocation & FL-EOCD & (b) \\ \hline
[110] & Local training periods, consensus rounds & Two timescale hybrid FL (TT-HF) & (b) \\ \hline
[111] & Participation vector, link selection matrix & A FL framework involving a one-side matching theory-based incentive mechanism to select and encourage users to take part in the process & (b) \\ \hline
[34] & Power adjustment, wireless resource allocation, link selection, and aggregation weight adaptation mechanism & Alternating optimization algorithm, semidefinite programming (SDP), tabu search-based meta-heuristic algorithm & (a) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of key studies on energy-efficient FL in D2D environments. Figure 6: Operational modes of D2D communications. When it comes to optimizing energy-efficient DFL in D2D environments, numerous studies have proposed various methods. For example, the study in [104] optimized resource allocation using deep reinforcement learning (DRL) to maximize network capacity and minimize energy consumption, while ensuring the QoS for both cellular and D2D users. In contrast, [PERSON]. [105] combined DRL with graph learning to exploit the relationships between datasets during model aggregation, which helps improve DFL accuracy and reduce model errors within the energy constraints of edge servers. Graph-based methods have gained prominence in optimizing DFL systems, particularly in heterogeneous and energy-constrained environments. These methods are effective in modeling complex relationships between devices, data, and network attributes. For instance, [PERSON]. [106] presented a low-complexity graph-theoretic algorithm to optimize parameters such as local aggregator selection and device scheduling within a DFL system. By incorporating D2D communication for model aggregation, this approach reduces energy consumption while maintaining convergence rate, minimizing the need for central server communication and achieving substantial energy savings in resource-limited environments. Similarly, [PERSON].