## 4 Simulations and Discussions
### Simulation Results  
Firstly, we evaluate the performance of the auto-encoder without considering noise. The comparison of test accuracy at no compression and compression ratio of 143 is shown in Figure 5. The results show that after 30 rounds of training with a compression ratio of 143, the performance of the model compression scheme is similar to the performance of the scheme without compression. This indicates that our scheme reduces the communication overhead while maintaining the learning accuracy.  
Further, Furthermore, to evaluate the denoising performance of the proposed scheme, we consider the case where the model parameter transmission is contaminated by noise. Gaussian noise with a mean of 0 and standard deviation of 0.1 is superimposed on the model parameters transmitted by each node. First, we train the denoising auto-encoder using model parameters contaminated with noise and model parameters without noise. The trained denoising aotuauto-encoder is then applied to the FL framework.  
In Figures 6 and 7, the accuracy of applying the denoised auto-encoder is significantly higher than the undenoised case. The results show that under a compression ratio of 143, our auto-encoder achieves a terrific denoising effect, although it cannot completely eliminate the noise.  
Moreover, we evaluate the performance of the denoising auto-encoder under different compression ratios. The test accuracy and average accuracy are shown in Figures 8 and 9. The results show a decrease in performance as the compression ratio increases. This may be due to the fact that as the compression ratio increases, the more information is lost after encoding and decoding.  
In the communication process, Gaussian white noise, channel fading, and various other interference factors coexist. The combined effects of these factors lead to variations in the bit error rate (BER) of data received by the central server, resulting in discrepancies between the data sent by local nodes and the data received in the cloud.  
Figure 5: Test accuracy at no compression and compression ratio of 143.  
To simplify the network architecture and enhance the feasibility of the study, an equivalent simulation approach is adopted. Specifically, Gaussian white noise of varying intensities is superimposed to simulate cloud-received data under different BER conditions. This equivalent experiment enables a simulation-based analysis of system performance under different levels of communication interference. The results are shown in Figure 10. As the level of communication interference increases, the accuracy of federated learning exhibits a significant downward trend.  
To evaluate the denoising performance of the proposed denoising auto-encoder, we use median filtering as a baseline and compare both methods under the same noise conditions. Median filtering is a classical denoising algorithm that operates by sorting all data points within a local neighborhood and replacing the central value with the median of the sorted values. This method effectively removes isolated noise points while preserving edge information, ensuring minimal distortion to the original data structure and features.  
The results are shown in Figure 11. The blue curve represents accuracy under noise-free conditions, the green curve corresponds to accuracy with median filtering, the black curve represents accuracy without any noise processing, and the red curve indicates accuracy with the proposed denoising auto-encoder. The results demonstrate that the proposed auto-encoder significantly reduces the impact of noise and outperforms the median filtering approach.  
Figure 6: Test accuracy under noise, denoising, and without noise.  
Figure 8: Test accuracy under different denoising compression ratios.  
Figure 7: Average accuracy under noise, denoising, and without noise.  
Figure 10: Performance under different levels of communication interference.  
Figure 9: Average test accuracy under different denoising compression ratios.