# Periodic Monitoring and Filtering Suppression of Signal Interference in Mine 5G Communication
## 3 Materials and Methods
### Interference Monitoring Based on Deep Complex Network  
The convolutional neural network is essentially an input-to-output mapping that can learn a large number of mapping relationships between an input and output without any precise mathematical expression between the input and output, as long as the values are known [22; 23; 24]. The deep complex network is considered as an extension of the convolutional neural network, which has a richer representation ability and stronger robustness to noise. The input signals, weights, and activation functions of deep complex networks are all complex numbers, and a special network structure needs to be designed for complex numbers, including complex convolution, complex activation function, and complex batch normalization. Complex convolution: A complex vector \(h=a+ib\) is the input to the convolutional layer, where \(a\) and \(b\) are real vectors. The complex number matrix \(M=X+iY\) is the convolution kernel, and the convolution operation is:  
\[M\times h=(X\times a-Y\times b)+i(Y\times a+X\times b) \tag{2}\]  
Written in matrix form:  
\[ \begin{bmatrix}Re(M\times h)\\ Im(M\times h)\end{bmatrix} = \begin{bmatrix}X&-Y\\ Y&X\end{bmatrix} \times \begin{bmatrix}a\\ b\end{bmatrix}  \tag{3}\]  
where \(Re(M\times h)\) and \(Im(M\times h)\) are the real and imaginary parts of the feature map after convolution, respectively. Complex activation function: The activation function is a nonlinear function that exists between the layers of the neural network, which can enhance the expressive ability of the deep neural network, making the network serve as almost any function. The Rectified Linear Unit (ReLU) activation function is the most commonly used activation function in convolutional neural networks. The function expression is as follows:  
\[\mathrm{ReLU(z)=max(0,z)} \tag{4}\]  
For deep complex networks, complex ReLU can be selected as the activation function, and its expression is as follows:  
\[\mathrm{CreLU(z)=ReLU(Re(z))+iReLU(Im(z))} \tag{5}\]  
Complex batch normalization: Usually, convolutional neural networks rely on batch normalization to speed up learning. First, normalize the input data:  
\[\widetilde{x}=\frac{x-E(x)}{\sqrt{V}} \tag{6}\]\[V= \begin{bmatrix}Cov(Re(x),Re(x))&Cov(Re(x),Im(x))\\ Cov(Im(x),Re(x))&Cov(Im(x),Im(x))\end{bmatrix}  \tag{7}\]  
For deep complex networks, batch normalization is as follows:  
\[BN(\widetilde{x})=\gamma\cdot\widetilde{x}+\beta \tag{8}\]  
where \(\gamma\) and \(\beta\) are the complex domain scaling parameter matrix and the complex domain offset parameter vector, respectively, and their initial values are as follows:  
\[\gamma= \begin{bmatrix}1/\sqrt{2}&0\\ 0&1/\sqrt{2}\end{bmatrix} ,\ \beta=0 \tag{9}\]  
The processing flow of interference monitoring based on the deep complex network is shown in Figure 4.  
Data acquisition: As shown in Figure 1, \(W\) is a static matrix that is the result of the most recent run of the blind source-separation module, and \(x\) is the mixed signal containing the interferer and source signals. Once the interference conditions change, the composition of \(x\) will change, \(y=Wx\) cannot achieve a good interference separation effect, and the data \(y\) must contain certain interference. Feature monitoring: This step is repeated five times for the three layers of complex convolution, complex excitation function, and complex pooling, learning to monitor different features each time. Classification identification: The target signal is classified and identified using machine learning algorithms, and the classification output is provided using the softmax function. The output of the softmax function is 0 to 1, and the sum of the output values is 1, which represents the relative probability between different categories. For the different categories here, including signals and different kinds of noise, according to the output of the softmax function, the proportion of all interference can be obtained and used as the output of the interference-monitoring module.