# Kernel-FastICA-Based Nonlinear Blind Source Separation for Anti-Jamming Satellite Communications
## 4 Results and Discussion
Figure 6: Signal separation results of FastICA at ISR = 12 dB. To comprehensively evaluate the performance of the proposed Kernel-FastICA algorithm under varying interference intensities, a quantitative analysis of the separation results is conducted for initial interference-to-signal ratios (ISRs) ranging from 3 dB to 12 dB. As illustrated in Figure 8, the correlation coefficients between the communication and interference signals exhibit distinct trends with an increasing ISR: under low-interference conditions (ISR = 3 dB), the communication signal correlation coefficient reaches 0.981, indicating nearly complete preservation of the source signal's waveform characteristics. Simultaneously, the interference signal correlation coefficient achieves 0.920, confirming the algorithm's effective suppression of interference components. As the ISR increases to 12 dB, the communication signal correlation coefficient gradually declines to 0.872, yet it remains superior to the conventional FastICA algorithm's result of 0.357 (ISR = 12 dB). This demonstrates the decoupling capability of kernel space mapping for nonlinear hybrid structures. Notably, the interference signal correlation coefficient consistently remains above 0.9, highlighting the algorithm's robustness in separating the interference components, unaffected by variations in the initial interference intensity. Further analysis of the relationship between the initial ISR (interference-to-signal ratio) and the post-separation SIR (signal-to-interference ratio) and the interference component ISR (Figure 9) demonstrates that the proposed algorithm achieves a significant balance in comprehensive performance across a wide range of interference conditions (ISR 3-12 dB). At an initial interference level of 3 dB, the communication signal recovery quality is optimal, with a post-separation SIR reaching 30.27 dB. As the interference increases to 5 dB, the SIR drops to 13.35 dB, forming a performance inflection point. Notably, within the moderate-to-strong interference range (ISR 7-12 dB), the algorithm exhibits dynamic adaptability: the communication signal SIR steadily increases from 16.84 dB to 24.46 dB, while the suppression depth of the interference component continuously strengthens, achieving a peak suppression effect of ISR = \(-\)28.23 dB at ISR = 12 dB. This phenomenon stems from the synergistic optimization mechanism of regularized pre-whitening and kernel space mapping, which adaptively adjusts the feature extraction strategy as the interference intensities--specifically, when ISR > 5 dB, the enhanced extraction of nonlinear statistical  
Figure 7: Signal separation results of Kernel-FastICA at ISR = 10 dB. features by the kernel mapping compensates for the negative impact of the rising interference intensity, leading to a gradual recovery in signal quality. Particularly under strong interference (ISR = 12 dB), although the communication signal SIR (24.46 dB) is lower than the optimal value, the interference suppression depth (ISR = \(-\)28.23 dB) improves by 2.86 dB compared with that in the moderate interference scenario, highlighting the algorithm's robustness under extreme interference conditions. These results validate that the Kernel-FastICA algorithm, through the synergistic mechanism of feature space optimization and adaptive separation, provides an on-board, real-time processing solution for satellite communication dynamic interference scenarios, achieving both high recovery quality and deep interference suppression. Figure 10 depicts the trend of the iteration error \(\Delta\)W versus the iteration count. During the initial phase (0-20 iterations), the error exhibits significant fluctuations around \(10^{0}\). Subsequently (20-100 iterations), the error gradually decreases but still shows fluctuations. Beyond 100 iterations, the error sharply drops to \(10^{-7}\), indicating rapid convergence. Figure 11 illustrates the evolution of the correlation coefficients between the separated signals and the original signals.