## 8 Simulations
### Simulation Results  
Figure 4 presents the impact curves of different resource allocation methods on the global model across three datasets in a heterogeneous client scenario. Among these methods, Method 3 performs the worst. This method fixes the selected clients during the asynchronous aggregation phase, preventing other clients from participating. As a result, only updates from high-computing-capability clients are received during each aggregation, which harms collaboration fairness and hinders global model updates. Method 2, which employs random selection for aggregation, performs moderately as it can gather information from different clients during the asynchronous aggregation phase. Method 1, which uses a full aggregation strategy, shows better results. Although it gathers more client information, it fails to distinguish the contribution levels of each client, and the number of training iterations per client is lower compared to strategies that involve client selection. Consequently, while Method 1 leads in accuracy, the total energy consumption of the clients remains high. Method 4 measures contribution based on each client's loss value. This method performs well in later stages, achieving higher global model accuracy. Method 5, designed for client selection in homogeneous client scenarios, saves bandwidth resources, allowing some clients more training opportunities. It also achieves high global model accuracy in later stages. However, since it does not account for heterogeneous computing capability and only relies on SV and model similarity for selection, it loses some truly high-quality clients, leading to delays and higher energy consumption in the early stages, failing to outperform other algorithms. The algorithm proposed in this paper combines the advantages of the above baselines, achieving convergence to a high-performance global model while also ensuring low delay and energy consumption for short-term goals. We also compared it with another federated learning strategy, namely Method 6. Although this approach adopts a multi-criteria client selection scheme, its bandwidth allocation is static, the aggregation strategy relies on the standard FedAvg algorithm, and the fault-tolerance mechanism is based on a fixed participation threshold. As a result, its performance is inferior to the method proposed in this paper. Specific experimental data can be found in Table 2.  
The IoT wireless resource allocation scheme proposed in this paper comprehensively considers the heterogeneous computing capabilities of clients and the contribution of their models, avoiding the neglect of truly high-contribution clients in simple selection methods. From the perspective of energy consumption, the system delay and energy consumption required to achieve the specified accuracy are significantly reduced, with up to 70% of the time saved in reaching the target and up to 60% of client energy consumption conserved. Figure 4: The accuracy curves of the global model across different training rounds under various resource allocation schemes in a heterogeneous client scenario based on the following datasets: (a) MNIST; (b) CIFAR10; (c) FashionMNIST. In terms of accuracy, under the same 100 rounds of global communication, this algorithm can further improve the maximum accuracy of the global model by approximately 0.06% to 0.39% compared to not performing client selection (i.e., Method 1). We continue to conduct ablation experiments on two aspects of the proposed scheme: pairing optimization and contribution weight reward-penalty factors. The experiments focus on the performance of the global model in FL, specifically the maximum accuracy within 100 communication rounds and the number of global rounds required to reach the specified accuracy.