## 4 Simulation and Experimentation
### Separation of Dependent Source Signals  
This section demonstrates via simulation experiments and comparisons that the algorithm in this paper is also suitable for blind source separation of dependent source signals, while the separation effect is better and faster than the traditional blind source separation algorithm. Three source signals that are correlated with each other are generated by Python. They obey the copurn-t distribution, and their correlation matrices are as follows:  
\[R= \begin{bmatrix}1&q&q^{2}\\ q&1&q\\ q^{2}&q&1\end{bmatrix} \]  
where the value of q is a random number between 0 and 1. Firstly, \(q\) is taken as 0.625 for the experiment, and again, 1000 sample points are taken, and the generated waveform and spectrum of the dependent source signal are shown in Figure 8.  
Figure 7: Comparison of separation accuracy for independent signals. The linear mixing matrix is still A. The source signal is linearly mixed to obtain the observed signals x1, x2, and x3, whose waveforms and spectrograms are shown in Figure 9.  
The waveforms and spectra of the separated signals are shown in Figure 10 after separating the observed signals with the BAS-BCA algorithm. And obtain the separation matrix \(W=\{-1.39184926-0.11501416\) 0.02704677; 0.2524785\(-0.67398223-0.12270163; -0.04869351\) 0.01061255 \(-0.68229682\). The correlation coefficients between the separation signal \(y\) and the source signal \(s\) are shown in Table 4.  
Figure 8: The source signals. (**a**) Waveforms. (**b**) Spectra. Figure 10: The separated signals. (**a**) Waveforms. (**b**) Spectra. Figure 9: The observed signals. (**a**) Waveforms. (**b**) Spectra. From Table 4, it can be seen that the correlation coefficients of s1 and y1, s2 and y2, and s3 and y3 are all close to 1, which corresponds to Figures 8 and 10. It can be seen that the BAS-BCA algorithm successfully separates the three dependent source signals. Next, the two traditional blind source separation algorithms, FastICA and SCA, as well as the BCA algorithm from the literature [4], are used to perform blind source separation of the mixed signals. In order to objectively and quantitatively compare the performance of the three algorithms, the performance index (PI) and the running time were selected for the study, in addition to the similarity coefficients and SIR. The PI evaluation index mainly uses the difference between the mixing-separation matrix and the generalized alignment matrix to measure the blind source separation effect, as shown in Equation (23). \[PI=\frac{1}{N(N-1)}\sum\limits_{i=1}^{N}\{(\sum_{i=1}^{N}\frac{|g_{ij}|}{\underset{ i}{max}|g_{ij}|}-1)+(\sum_{j=1}^{N}\frac{|g_{ij}|}{\underset{j}{max}|g_{ji}|}-1)\} \tag{23}\]  
where \(N\) represents the number of source signals, \(\underset{i}{max}|g_{ij}|\) represents the maximum value of \(|g|\) in line \(i\) of the matrix \(G\), \(g_{ij}\) is the \((i,j)\)th element of the matrix \(G\), and \(G\) is the product of the separation matrix \(W\) and the mixing matrix \(A\), which is the global matrix. Smaller PI values indicate better separation. To more obviously demonstrate the advantages of the algorithm in this paper in terms of runtime, 500,000 sample points were taken for the algorithm comparison experiment, and other conditions were kept constant. The results are shown in Table 5. It can be seen that the signal separated by the BAS-BCA algorithm has the highest correlation coefficient with the source signal, and the SIR value is also the largest and produces the smallest PI value, so the separation effect of the BAS-BCA algorithm is the best, and the running time of the algorithm is also shorter than the BCA algorithm. Then, we conducted an experiment of highly dependent sources separation. \(q\) is taken as 0.912, and again, 1000 sample points are taken, and the generated waveform and spectrum of the dependent source signal are shown in Figure 11.