# Kernel-FastICA-Based Nonlinear Blind Source Separation for Anti-Jamming Satellite Communications
## 1 Introduction  
Satellite communication, as a critical infrastructure for global information interconnection, disaster emergency response, and national security, has garnered significant attention in recent years due to its integration with 5G networks and space-ground integrated systems [1, 2, 3, 4]. It plays an irreplaceable role in modern society, with its reliability directly determining the fulfillment of essential communication demands. However, the open nature of satellite communication channels renders them highly susceptible to complex electromagnetic interference (EMI), posing severe threats to the stability of communication links. Current anti-jamming technologies primarily operate in three domains: time, frequency, and space. Time-domain hopping techniques (e.g., time-hopping spread spectrum) rely on high-precision timing synchronization between transmitters and receivers. Their fundamental mechanism involves dispersing signals across multiple time slots through rapid and unpredictable hopping, thereby preventing sustained interference from covering all the hopping points. However, this approach heavily depends on timing synchronization. Even minor timing drift can lead to signal acquisition failures at the receiver, significantlydegrading anti-jamming performance. Consequently, the effectiveness of time-hopping techniques is constrained by the system's ability to maintain strict synchronization, becoming a bottleneck in environments with strong interference or dynamic channel variations [5]. Spread spectrum techniques, such as Direct Sequence Spread Spectrum (DSSS) and Frequency Hopping Spread Spectrum (FHSS), enhance anti-jamming capability by dispersing signal energy over a wider bandwidth, thereby reducing the interference power density per unit bandwidth. Specifically, DSSS [6] employs pseudo-noise codes for spectral spreading, while FHSS [7; 8; 9] rapidly switches carrier frequencies according to predefined hopping sequences. Leveraging their processing gain, these techniques exhibit robustness against narrowband interference and certain types of wideband interference. However, in complex electromagnetic environments characterized by severe multipath fading or strong wideband interference, the provided spreading gain often proves insufficient to compensate for performance degradation induced by deteriorating channel conditions. For instance, constrained by inherent spectral efficiency, DSSS remains highly vulnerable to wideband interference covering its entire bandwidth. Conversely, FHSS faces challenges of synchronization loss and throughput degradation in dynamic scenarios with rapidly varying interference. Furthermore, both DSSS and FHSS lack inherent mechanisms to effectively suppress nonlinear distortion (e.g., distortion introduced by high-power amplifiers and limiters in satellite transponders), which significantly exacerbates signal deterioration under high-interference conditions. In contrast, the proposed Kernel-FastICA algorithm, based on kernel-based blind source separation, directly addresses such nonlinear effects and delivers superior robustness and generalization performance without relying on spectral spreading or frequency agility. Spatial-domain anti-jamming techniques, such as beamforming and spatial filtering, suppress interference by dynamically steering antenna array nulls toward interference sources while enhancing spatial diversity gains for desired signals [10; 11]. These methods excel against fixed interference sources, particularly in satellite platforms. However, in high-speed or rapidly changing aerospace scenarios, null broadening and instability in beam control weaken spatial anti-jamming performance. Additionally, the limited computational resources of onboard systems pose challenges for real-time high-precision beam control. More critically, nonlinear effects introduced by power amplifiers (PAs) and limiters in satellite communication systems have emerged as key factors impairing anti-jamming performance [12].