## 3 Proposed Scheme
### Network Framework  
In this paper, CNN network models are deployed at each node to perform the spectral image classification task. Note that the covariance matrix of the observed signal is firstly first obtained, and then it is converted to the spectral image. The CNN network architecture used in this paper is shown in Table 1 and Figure 2.  
This study focuses on signal covariance images with relatively few pixels and simple features. For low-pixel images, local patterns are crucial for recognition. CNN can effectively capture these local details with fewer parameters. Compared to more complex models, CNN achieves high performance within a shorter training time. In federated learning, local nodes transmit trained model parameters to a central server. Using a CNN with fewer parameters helps reduce communication overhead.  
The basic structure of auto-encoders can be divided into two categories: fully connected auto-encoder and convolutional auto-encoder. Fully connected auto-encoders consist of multiple fully connected layers and are suitable for processing structured data.  
Convolutional auto-encoders, on the other hand, use a convolutional neural network structure and are suitable for processing image data.  
The aim of this paper is to compress the model parameters, so a fully connected auto-encoder is chosen. The network architecture of the fully connected auto-encoder is shown in Table 2.  
Assume that the output size of the encoder is X. The size of the model parameter to be compressed is 18,702, and the compression ratio of the encoder is changed by setting the value of X. With X defaulting to 128, for example, the compression ratio is 146.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Layer Name** & **Parameters** \\ \hline Convolutional Layer 1 & Kernel Size: \((3,10,5,5)\) \\ Max- Pooling Layer 1 & Pool Size: \((2,2)\) \\ ReLU Activation & - \\ Convolutional Layer 2 & Kernel Size: \((10,20,5,5)\) \\ Max- Pooling Layer 2 & Pool Size: \((2,2)\) \\ Dropout Layer & Default Dropout Probability \\ Flatten Layer & - \\ Fully Connected Layer 1 & in features: \((320)\), out features: \((40)\) \\ ReLU Activation & - \\ Dropout Layer & Default Dropout Probability \\ Output Layer & in features: \((40)\), out features: \((2)\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: CNN network architecture at each node.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Layer Name** & **Input/Output Size** \\ \hline Encoder & - \\ \hline Fully Connected Layer 1 & Input: 18,702, Output: 2048 \\ Tanh Activation & Input/Output: 2048 \\ Fully Connected Layer 2 & Input: 2048, Output: 512 \\ Tanh Activation & Input/Output: 512 \\ Fully Connected Layer 3 & Input: 512, Output: 256 \\ Tanh Activation & Input/Output: 256 \\ Fully Connected Layer 4 & Input: 256, Output: X (Defaults to 128) \\ \hline Decoder & - \\ \hline Fully Connected Layer 1 & Input: X(Defaults to 128), Output: 256 \\ Tanh Activation & Input/Output: 256 \\ Fully Connected Layer 2 & Input: 256, Output: 512 \\ Tanh Activation & Input/Output: 512 \\ Fully Connected Layer 3 & Input: 512, Output: 2048 \\ Tanh Activation & Input/Output: 2048 \\ Fully Connected Layer 4 & Input: 2048, Output: 18,702 \\ Tanh Activation & Input/Output: 18,702 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The network architecture of the fully connected auto-encoder.  
Figure 2: CNN Network Structure.