## 4 Simulation Experiment and Result Analysis
### Correlation Coefficient Analysis  
The selection of the source signal, experimental conditions and parameter settings are the same as described previously. Then, the blind observation signal after chaotic masking are processed at the receiver to achieve the extraction of source signal. In this paper, the Fast IVA algorithm is proposed to use it to perform FD-CbSS for the blind observation signal, and the waveforms of the separation result are shown in Figure 5.  
In Figure 5, it can be seen that the waveform shapes of the separated signals obtained using the Fast IVA algorithm are almost identical when compared with the source signal graphical information, both in time domain waveform and spectrogram. Therefore, from a subjective point of view, it can be considered that the algorithm realizes the blind extraction of the source speech signal. However, it is not enough to rely on visual judgment only. Here we use the correlation coefficient as the objective evaluation criterion of the separated signal, and the data in Table 1 are the average of 20 experiments. In Table 1, s1 and s2 represent the source speech signals, while y1, y2 and y3 represent the separated signals obtained by the Fast IVA algorithm. As you can see, the correlation coefficient between the separated signal y1 and the chaotic signal is as high as 0.9991, which is close to 1. In addition, the correlation coefficients between the separated signals y2 and y3 and the corresponding source speech signals s2 and s1 are 0.9932 and 0.9278, respectively, which proves that the algorithm achieves the recovery of speech signals. The algorithm not only achieved the estimation of source speech signal, but also enabled a better recovery of the wide-spectrum chaotic signal. Thus, a high degree of reduction in the separated signal is illustrated from an objective point of view, and the blind extraction effect of the noise-like signal is guaranteed. This paper proposes using the Fast IVA algorithm, which exploits both the statistical independence between multi-source signals and the internal dependence of each signal. The algorithm is not only fast and effective but also solves the permutation ambiguity problem in the FD-CbSS process and eliminates the permutation design in the standard ICA frequency-domain algorithm. To verify the superiority of this algorithm for convolutional blind signal separation and extraction, it is compared with two algorithms from the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Correlation Coefficient** & **s1** & **s2** & **Chaotic Signal** \\ \hline y1 & 0.0018 & 0.0016 & 0.9971 \\ y2 & 0.0027 & 0.9632 & 0.0120 \\ y3 & 0.9278 & 0.0137 & 0.0163 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Correlation coefficient between each separated signal and the source signal. Figure 5: The separated signal graphic information is obtained by using the Fast IVA algorithm. (**a**) Time–domain waveform of separated signals; (**b**) Spectrogram of separated signals. literature [38; 39]. To this end, we conducted a large number of repeated experiments to reduce the randomness and improve the reliability of the results. To assess the stability of these algorithms, this experiment controlled for the consistency of the input signals and parameters, and 20 Monte Carlo experiments were conducted with each separation algorithm as a single variable only. The three blind separation algorithms are compared in terms of separation accuracy (average correlation coefficient). Table 2 shows the average values of the above indicators obtained after 20 trials. From the comparative analysis of the experimental results, it can be seen that the Fast IVA algorithm has the highest correlation coefficient and has better separation accuracy. By comparing with EFICA algorithm and IF algorithm, it is proved that the algorithm has better convergence speed and separation performance.