Algorithm 2: SI-XBSS (Swarm Intelligent Blind Source Separation based on Cross-Correlation)

Input:$X\left(t\right)$ Centralize and whitening $X\left(t\right)$ Initialize the parameters of swarm intelligence algorithm. Randomly generate the initial $2\times 2$ separation matrix $W$. According to the fitness function, find separation matrix $W_{best}$ by SI algorithms. Obtain mixed signals $Y^W\left(t\right)$ $Y^W\left(t\right)={\left\{ y_1^w\left(t\right),y_2^w\left(t\right)\right\}}^T=W_{best}X\left(t\right)$ Obtain mixed signals $Y^{Minus}\left(t\right)$ $Y^{Minus}\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\end{array}\right]-\left[\begin{array}{c}{y}_1^w\left(t\right)\\ y_2^w\left(t\right)\end{array}\right]=\left[\begin{array}{c}{y}_1^{Minus}\left(t\right)\\ y_2^{Minus}\left(t\right)\end{array}\right]$ Obtain mixed signals $Y^{exMinus}\left(t\right)$ $Y^{exMinus}\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\end{array}\right]-\left[\begin{array}{c}{y}_2^w\left(t\right)\\ y_1^w\left(t\right)\end{array}\right]=\left[\begin{array}{c}{y}_1^{exMinus}\left(t\right)\\ y_2^{exMinus}\left(t\right)\end{array}\right]$ Obtain the candidate separation pool $Y^{\mathrm{pool}}\left(t\right)$ $\begin{array}{cc}{Y}^{\mathrm{pool}}(t)& ={\{y_1^{pool}(t),y_2^{pool}(t),y_3^{pool}(t),y_4^{pool}(t),y_5^{pool}(t),y_6^{pool}(t)\}}^T\hfill \\ & ={\{Y^W(t),Y^{Minus}(t),Y^{exMinus}(t)\}}^T\hfill \\ & ={\{y_1^W(t),y_2^W(t),y_1^{Minus}(t),y_2^{Minus}(t),y_1^{exMinus}(t),y_2^{exMinus}(t)\}}^T\hfill \end{array}$ Calculate Xcorr ($y_{\mathrm{i}}^{pool}(t),y_{\mathrm{j}}^{pool}(t))$ $i,j\in \left[1,\lambda \right],i\ne j,\lambda =total number of{Y}^{\mathrm{pool}}(t)$ $Y(t)=\min (\mathrm{Xcorr}(y_{\mathrm{i}}^{pool}(t),y_{\mathrm{j}}^{pool}(t)))$

Output:$W_{best}$, $Y\left(t\right)$