# Periodic Monitoring and Filtering Suppression of Signal Interference in Mine 5G Communication
## 3 Materials and Methods
### Blind Source Separation  
Blind source separation is a technique that recovers or extracts independent source signals from mixed signals without knowing the distribution or the mixing model of the source signals [19; 20]. The schematic diagram is shown in Figure 2.  
Figure 1: Process flow of the interference-suppression scheme.  
It is assumed that \(N\) sets of observation signals \(x_{i}(t)\) are obtained from \(N\) different channels, and each signal is a linear mixture of \(M\) independent source signals \(s_{i}(t)\); that is, \(x=As\), where \(x=[x_{1},\,x_{2},\,\ldots,\,x_{N}]^{\mathrm{T}}\) and \(s=[s_{1},\,s_{2},\,\ldots,\,s_{M}]^{\mathrm{T}}\) are the observation signal vector and the independent source signal vector, respectively. The purpose of blind source separation is to use the observed signal vector x to recover the source signal vector \(s\); that is \(s\approx y=Wx\), since both the source signal vector \(x\) and the mixing matrix \(A\) are unknown, solving the separation matrix \(W\) is called blind source separation. The basic idea of blind source separation is to first establish a cost function according to the separation principle, and then optimize the cost function to obtain a separation matrix or a mixture matrix. The blind source-separation problem can be transformed into an optimization problem of a cost function, where the cost function is generally a function of the separation matrix or the mixing matrix. The separation or extraction of the source signal can be achieved by using the optimization theory to solve the separation matrix or the mixing matrix under extreme conditions.  
Independent component analysis is a common blind source-separation algorithm [21]. It can be known from the central limit theorem that the Gaussian property of the mixed signal is higher than that of the independent source signal. Independent component analysis is a cost function constructed according to the principle of signal independence to separate or extract source signals from a linear mixture of independent source signals. The implementation of independent component analysis needs to satisfy three conditions: the source signals are statistically independent of each other, the source signals satisfy the non-Gaussian distribution, and the mixing matrix is full-rank. For 5G communication signals and interference signals in coal mines, the first two conditions are naturally satisfied, and the third requires the number of observation channels to not be less than the number of source signals; that is, \(N\geq M\), which can be achieved by diversity sampling.  
The algorithm flow of blind source separation based on independent component analysis is shown in Figure 3.  
Figure 3: Algorithm flow of blind source separation.  
Figure 2: Schematic diagram of blind source separation.  
First, whitening pre-processing is performed on the received mixed signal to decorrelate the data to facilitate the fast convergence of the algorithm. Whitening refers to the fact that the covariance matrix of the vector is a unit matrix, which is generally realized by the eigenvalue decomposition of the covariance matrix. Then, the initial separation point \(W_{0}\) is selected for the initial output, i.e., \(Y_{0}=W_{0}x\). The next step is to update the separation matrix by iteratively updating the rule:  
\[W_{n+1}=W_{n}+\mu(I+f(x)x^{\mathrm{H}})W_{n} \tag{1}\]  
where \(\mu\) is the learning factor, \(I\) is the unit matrix, and \(f(x)\) is the activation function, which can be \(f(x)=-\mid x\mid^{3}\mathrm{sgn}(x)\). Finally, judge whether \(W\) converges; that is, judge whether \(\mid(W_{n+1})^{\mathrm{H}}W_{n}\mid\) is close to 1. If it does not converge, \(n=n+1\), go back to the third step. If it converges successfully, the separation matrix \(W\) will be output.