# A Survey on Energy-Efficient Design for Federated Learning over Wireless Networks
## 2 Basic Principles of FL over Wireless Networks
### Overview of FL Models  
#### 2.1.1 Overview of the CFL Strategy  
As illustrated in Figure 1a, a basic CFL system relies on a central server, such as a cloud server, serving \(K\) clients (e.g., sensor IoT devices and smartphones). In wireless communication contexts, the central server is often situated at a base station (BS), which facilitates communication with and coordination of clients over wireless links. The CFL approach involves the central server aggregating local models from \(K\) clients to construct a global model \(\mathbf{q}\), which is subsequently disseminated back to the clients for further iterations.  
This architecture is particularly well suited for traditional wireless networks, such as 4G and 5G, where the BS or cloud serves as the central hub for client communication. CFL benefits from the stability and reliability of such centralized systems, enabling efficient aggregation and low-latency synchronization of models.  
The CFL process addresses the optimization problem in (1) iteratively through three key phases: local computation, communication, and global computation. During the \(j\)-th global iteration, the following steps are performed: Step 1 (Global downlink training updates): At the start of the CFL process (\(j=0\)), the central server initializes the global model, which is typically a machine learning model, such as a deep neural network, composed of multiple layers and interconnected nodes designed to capture complex patterns in data. The initialization of the model often involves setting the model parameters (weights) to  
Figure 1: Federated learning strategies.  
random values or pretrained values, depending on the specific application and prior knowledge available. Then, the central server broadcasts the global model \(\mathbf{q}^{(j)}\) to \(K\) clients over wireless downlink channels.  
Step 2 (Local computation): During the \(j\)-th iteration, the \(k\)-th client retrieves the global model \(\mathbf{q}^{(j)}\) from the central server, and uses it as the initial local model. The \(k\)-th client then trains its local dataset \(\mathbf{q}_{k}^{(j)}\) using its dataset, \(\mathbf{D}_{k}\), by minimizing the loss function \(F_{k}(\mathbf{q})\). Optimization methods such as gradient descent (GD) and stochastic gradient descent (SGD) [21] can be used to solve this optimization problem. After completing a predetermined number of local iterations, the clients transmit their locally updated models to the server via wireless uplinks.  
Step 3 (Global uplink training updates): The central server collects the locally updated models, \(\mathbf{q}_{k}^{(j)},k=1,2,\cdots,K\), from the \(K\) clients and computes a new global model \(\mathbf{q}^{(j+1)}\), using the FedAvg algorithm:  
\[\mathbf{q}^{(j+1)}:=\quad\sum_{k=1}^{K}\frac{D_{k}}{D}\mathbf{q}_{k}^{(j)}. \tag{2}\]  
The CFL training process iterates until the global model achieves the desired level of accuracy.  
To better understand the differences between CFL and DFL, Table 1 highlights their key characteristics across multiple dimensions, such as architecture, communication overhead, scalability, fault tolerance, energy efficiency, privacy, and use case suitability. This comparison provides a clear understanding of how these two paradigms differ in terms of their operational models and practical applications.