## 4 Simulations and Discussions
### Parameter Setting  
Orthogonal Frequency Division Multiplexing (OFDM) is a multi multi-carrier modulation technique. It divides a broadband signal into multiple orthogonal sub-carriers, each of which transmits an independent data stream, and ultimately superimposes the signals of all sub-carriers for transmission. It has strong resistance to multi-path fading, high spectrum utilization, strong resistance to inter inter-symbol interference, and can flexibly allocate resources. As a result, the signal type considered in this paper is the OFDM signal due to its universality and versatility.  
To verify the performance of our proposed scheme, an SS dataset is designed first, and the theory of the designed dataset is introduced as follows. An initial training and test dataset is created, where the OFDM signal is treated as the primary user's signal, and the transmission medium is characterized by a Rayleigh fading channel. Noise is introduced to the OFDM signal after it passes through the Rayleigh fading channel. The signal-to-noise ratio (SNR) varies from a certain value to another, with a specified increment. For the multi-antenna system employed in the experiment, the number of antennas is fixed at 10, and the number of sampling points is determined as 10. The sampling covariance matrix is computed based on the real and imaginary components of the received signals, leading to a covariance matrix of a particular size of \(10\times 10\times 2\). For the true color plot, there are three channels, with the first two representing the real and imaginary parts of the sampling covariance matrix, and the third being a matrix of zeros. The dimensions of this matrix are dictated by the number of antennas in the system. Subsequently, the true color plot is resized to a specified dimension.  
During the dataset creation, two scenarios are taken into account: one with the signal noise and the other with noise alone. Consequently, each dataset is split into two sections, with 3000 samples for each scenario. The entire dataset comprises 45,000 samples, of which 30,000 are allocated for training, and the remaining 15,000 samples form the test set. The dataset contains a total of 30,000 images, where the ratio of the training set to the test set is 2:1. The training and test sets are evenly distributed across 10 nodes. In addition, we consider different auto-encoder compression ratios and noise scenarios.  
The number of training rounds is set to 100 to ensure sufficient learning. There are 10 participating nodes. The batch size is 1, allowing fine-grained parameter updates and reducing memory usage, but it may increase training time. Each node has 2000 training samples and 1000 test samples. The Adam optimizer is used. It adaptively adjusts the learning rate and speeds up convergence. The learning rate is set to 0.001. This value ensures stable updates while enabling efficient optimization. The comprehensive parameters of the proposed algorithm is shown in Table 3.  
In establishing the CNN framework, this study explores different configurations of convolutional and linear layers. The results are shown in Figure 3. The left figure compares the performance of 2-layer and 3-layer convolutional networks. In the early training stages, the 2-layer model shows a clear advantage. As the models approach convergence, the difference becomes negligible. Additionally, the 2-layer model has fewer parameters, which helps reduce communication overhead in federated learning. The right figure compares 2-layer and 3-layer linear networks, where the 2-layer model demonstrates superior performance.