# A Novel Complex-Valued Blind Source Separation and Its Applications in Integrated Reception
## 6 Simulation Analysis
### Separation Performance Analysis  
Figure 4 shows the time and time-frequency plots of the source signal, observed signal (first four channels), and separated signal at SNR = 10 dB and JSR = 20 dB. The waveform plots of 40-60 us are taken for a clear display. From the source signal time-frequency diagram, it can be seen that the source signals overlap each other in the time-frequency domain, which is difficult to be separated by the traditional filtering method. Since the jamming is relatively large, the observed signal has been basically covered by the jamming signal, and only the time-frequency points of the jamming model can be seen. Figure 4: _Cont._  
The separated signal waveforms clearly show that each algorithm produces different distortions. Due to its high jamming power, the jamming signal separated by each algorithm is the most distinct. Among the six algorithms, the proposed algorithm achieves the highest separation accuracy. It closely resembles the source signal with minimal distortion. After applying amplitude and phase correction, the resulting signal matches the source signal in terms of both amplitude and phase. Table 1 presents the similarity coefficient, performance index, and iteration times for the different algorithms. This algorithm yields the highest similarity coefficients for all signals except the jamming signal. Moreover, the average similarity coefficient exceeds 0.9, indicating a high level of separation accuracy. Additionally, this algorithm exhibits the smallest performance index, suggesting the highest estimation accuracy for the mixing matrix. Compared to cFastICA, RobustICA, and FAGD, it requires the fewest iterations and achieves a faster convergence speed. Figure 5 is the objective function curve of Equation (26) obtained by 30 times Monte Carlo with different algorithms. The CGWO [35], IGWO [36], WOA [38], SOA [39], NGO [40], PSO [41; 42], SSA [43], and DBO [44] are all excellent swarm intelligence optimizers proposed in recent years. The above optimizers all have the problems of prematurity and low accuracy in different degrees. Compared with GWO, IGWO, and CGWO, NCGWO demonstrates higher convergence speeds and solution accuracy by incorporating improved strategies such as a nonlinear convergence factor and chaotic disturbance strategy. The integration of these strategies enables the NCGWO to generate more dominant solutions, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithm** & **JADE** & **cFastICA** & **Sobi** & **RobustICA** & **FAGD** & **Proposed** \\ \hline \multirow{4}{*}{Similarity coefficient} & 0.7694 & 0.4318 & 0.5435 & 0.5173 & 0.8384 & 0.8680 \\  & 0.9908 & 0.9701 & 0.9679 & 0.9907 & 0.9796 & 0.9888 \\  & 0.5669 & 0.2867 & 0.2965 & 0.3210 & 0.7079 & 0.8860 \\  & 0.7784 & 0.5428 & 0.4567 & 0.7001 & 0.8311 & 0.9260 \\ \hline Average & 0.7768 & 0.5630 & 0.5662 & 0.6323 & 0.8392 & 0.9160 \\ \hline Performance index & 0.0175 & 0.1281 & 0.1301 & 0.0886 & 0.0086 & 0.0054 \\ \hline Iteration & \(\backslash\) & 55 & \(\backslash\) & 114 & 94 & 38 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Similarity coefficient, performance index, and iterations. Figure 4: Time domain and time–frequency domain plots of the source signal, observed signal (first four channels), and separated signal at SNR = 10 dB and JSR = 20 dB. (**a**) Source signal waveform (0–500 us), (**b**) source signal waveform (40–60 us), (**c**) source signal time–frequency diagram, (**d**) observed signal time–frequency diagram, (**e**) observed signal waveform, (**f**) separated signal waveform (JADE), (**g**) separated signal waveform (cFastICA), (**h**) separated signal waveform (SOBI), (**i**) separated signal waveform (RobustICA), (**j**) separated signal waveform (FAGD), (**k**) separated signal waveform (proposed), (**l**) separated signal after amplitude phase correction (proposed). surpassing the performance of the aforementioned optimizers.