# A Survey on Energy-Efficient Design for Federated Learning over Wireless Networks
## 3 Wireless Network Architectures for Energy-Efficient CFL
### Terrestrial-Based Architectures
#### 3.1.2 CFL in Distributed Wireless Networks  
In this subsection, we analyze the design of distributed wireless network architectures that support CFL and present recent studies addressing the energy efficiency challenges in these networks. Cell-free massive MIMO (CFMM) system can be interpreted as a combination of massive MIMO, distributed antenna systems [61], and network MIMO, which is considered the most advanced distributed wireless network.  
CFMM is recognized as a key enabler for 6G networks, as it effectively addresses significant propagation losses and enhances the quality of service, particularly for cell-edge UEs [62]. Figure 3 illustrates a CFMM system with \(M\) access points (APs) and \(K\) UEs. These distributed APs collaborate to serve UEs without geographic limitations.  
In the context of FL, CFMM enables the accommodation of a large number of served UEs compared with other wireless architectures owing to the support of the mMIMO technique. Additionally, recent studies demonstrate that CFMM can achieve a five-fold gain in spectral efficiency and a ten-fold improvement in energy efficiency compared with small-cell and cellular massive MIMO systems [63]. Moreover, the distinctive features of CFMM systems, particularly their ability to leverage the cooperative nature of distributed APs, position them as an ideal platform for implementing CFL with energy-saving techniques.  
Recent studies have introduced several strategies to reduce energy consumption in these systems. For instance, the authors of [64] focused on minimizing energy consumption in UEs during the FL training phase by optimizing key parameters such as transmit power, frequency allocation, communication time, and computation time. They proposed an iterative algorithm based on the inner approximation method, transforming the original nonconvex optimization problem into a series of convex problems. This approach identifies at least one locally optimal solution, thereby reducing energy expenditure during training. Similarly, Ref. [65] proposed a novel uplink power allocation scheme tailored for CFL in CFMM systems. This scheme simultaneously minimizes energy consumption and latency during CFL training by optimizing users' uplink transmission powers. By utilizing the coordinate gradient descent method, the algorithm accounts for the impact of each user's power on overall energy consumption and latency experienced by other users, leading to more efficient resource allocation within the CFMM framework.  
In [66], the authors presented an over-the-air CFL scheme for CFMM systems, formulating a joint optimization problem that integrates device scheduling and power scaling while adhering to energy consumption constraints. They conducted a convergence analysis and applied the Lyapunov method to simplify the long-term problem into a manageable short-term one. An alternating optimization approach is utilized to tackle the mixed-integer nonlinear programming problem. In [67], the authors highlighted CFMM's potential for federated edge learning, offering uniform coverage and high spectral efficiency. They introduced over-the-air CFL (OTA-FL), which reduces communication overhead by allowing clients to send updates simultaneously over shared resources. The study also provided  
Figure 3: CFL over a CFMM system.  
practical implementation insights for OTA-FL in CFMM environments. Similarly, Ref. [68] focuses on energy-efficient CFL in IoT networks, proposing an optimization problem to minimize energy consumption in IoT devices. It addresses challenges like power limitations and straggler effects, demonstrating the adaptability of CFMM for diverse scenarios. Collectively, these studies underscore the CFMM's potential to enhance CFL energy efficiency. They pave the way for future research to explore advanced optimization techniques and broaden the application of CFMM in diverse network environments.