## 4 Simulation and Experimentation
### Separation of Dependent Source Signals
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **y1** & **y2** & **y3** \\ \hline
**S1** & 0.95674313 & 0.39900721 & 0.04960461 \\
**S2** & 0.47858537 & 0.98699327 & 0.47763681 \\
**S3** & 0.35747411 & 0.50449069 & 0.97789969 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Correlation coefficient. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **FastICA** & **SCA** & **BCA** & **BAS-BCA** \\ \hline
**similarity** & 0.61478832 & 0.75382446 & 0.94112682 & 0.99913226 \\
**coefficient** & 0.79113256 & 0.83249712 & 0.89978596 & 0.9777913 \\
**PI** & 0.86792361 & 0.84562887 & 0.96120685 & 0.98947889 \\
**PI** & 0.37858537 & 0.33259634 & 0.18382564 & 0.09763681 \\
**SIR** & 17.78995818 & 18.58967436 & 23.98567492 & 27.52189291 \\
**Time** & 19.36 & 20.21 & 29.68 & 25.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Data of separation performance evaluation index. The linear mixing matrix is still A. The source signal is linearly mixed to obtain the observed signals x1, x2, x3, whose waveforms and spectrograms are shown in Figure 12.  
The waveforms and spectra of the separated signals are shown in Figure 13 after separating the observed signals with the BAS-BCA algorithm. And obtain the separation matrix \(W=\{-0.57989843\)\(0.27412716\)\(0.30326697\); \(0.25319743\)\(-1.08609897\)\(-0.28978132\); \(-0.15634155\)\(-0.50392014\)\(-0.71771854\)). The correlation coefficients between the separation signal \(y\) and the source signal \(s\) are shown in Table 6.  
Figure 11: The source signals. (**a**) Waveforms. (**b**) Spectra. Figure 12: The observed signals. (**a**) Waveforms. (**b**) Spectra. Figure 13: The separated signals. (**a**) Waveforms. (**b**) Spectra. From Table 6, 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 11 and 13. It can be seen that the BAS-BCA algorithm successfully separates the three dependent source signals. Comparison results with other algorithms are shown in Table 7.  
It can be seen that the BAS-BCA algorithm still performs the best compared to other algorithms. However, compared to the PI and SIR values of the experiment with q set to 0.625, the current experiment has a higher PI value and lower SIR value. It can be seen that the performance of the BAS-BCA algorithm in highly dependent source separation has decreased, but compared to other algorithms, it has a better separation effect. In order to further explore the effect of correlation between source signals on the separation effect of blind source separation algorithms, the SIR values corresponding to each algorithm are obtained by selecting 10 different \(q\)-values, as shown in Figure 14.  
As can be seen from Figure 14, the SIR values of all algorithms decrease as q increases, i.e., the higher the correlation between source signals, the lower the accuracy of the separation algorithms. The average SIRs of the BAS-BCA, BCA, SCA, and FastICA algorithms \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **y1** & **y2** & **y3** \\ \hline
**S1** & 0.99705728 & 0.86008656 & 0.66929815 \\
**S2** & 0.87889169 & 0.99727447 & 0.82707136 \\
**S3** & 0.75027519 & 0.89507997 & 0.98287344 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Correlation coefficient. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **FastICA** & **SCA** & **BCA** & **BAS-BCA** \\ \hline
**similarity** & 0.52367416 & 0.76545382 & 0.93564258 & 0.99705728 \\
**coefficient** & 0.71235987 & 0.63541287 & 0.90312354 & 0.99727447 \\
**PI** & 0.79534238 & 0.77852536 & 0.95238421 & 0.98287344 \\
**SIR** & 0.49896372 & 0.39986341 & 0.21368547 & 0.15236846 \\
**Time** & 11.6689403 & 12.9658332 & 22.6854931 & 24.6235874 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Data of separation performance evaluation index. Figure 14: Comparison of correlation signal separation accuracy. are 28.65, 25.78, 20.19, and 19.3, respectively.