# Kernel-FastICA-Based Nonlinear Blind Source Separation for Anti-Jamming Satellite Communications
## 1 Introduction
Nonlinear distortion not only causes signal deformation and spectral broadening but also generates intermodulation interference and out-of-band radiation, further degrading interference suppression capabilities [13; 14]. Faced with complex electromagnetic environments, traditional anti-jamming methods exhibit notable deficiencies in dynamic response speed, environmental adaptability, and nonlinear distortion compensation. Thus, developing efficient anti-jamming technologies with nonlinear modeling and adaptive compensation capabilities has become imperative to ensure satellite link reliability. Blind source separation (BSS) technology enables interference suppression through the exploitation of signal statistical independence, offering a novel technical pathway for anti-jamming systems [13]. The current research predominantly focuses on linear mixing scenarios, in which representative linear BSS techniques (e.g., FastICA and Infomax algorithms) [15; 16] achieve interference separation through independence maximization, with demonstrated success in mainlobe interference suppression [17; 18], spreading code estimation [19], and multi-user detection applications [20]. However, these conventional methods strictly depend on source independence assumptions and are fundamentally limited to linear mixing models, proving inadequate for addressing signal distortion caused by nonlinear components in satellite transponders. Specifically, the nonlinear compression characteristics of transponders induce strongly nonlinear superposition relationships be tween signals, resulting in drastic performance deterioration of traditional BSS approaches. Although recent advances in neural networks and Bayesian inference-based nonlinear BSS techniques have been proposed, their high computational complexity and data dependency hinder real-time implementation in resource-constrained satellite platforms [21]. Moreover, sparse component analysis [22], dictionary learning [23], and non-negative matrix factorization-based [24] nonlinear BSS methods, while promising for complex mixing scenarios, face practical limitations in satellite communication: (1) Most lack effective modeling of the physical distortion mechanisms caused by transponder nonlinearities. (2) Existing approaches fail to balance convergence speed and separation accuracy under low computational resources, limiting real-time deployment. The dual constraints of theoretical modeling accuracy and computational resource compatibility continue to impede the engineering application of nonlinear BSS in satellite communication. To address the dual challenges of nonlinear interference and onboard resource constraints, this paper proposes an efficient BSS algorithm based on kernel learning methodology. Traditional BSS methods, constrained by linear assumptions, cannot effectively handle signal distortion induced by nonlinear components (e.g., PAs and limiters) in satellite transponders. To overcome this, we construct a post-nonlinear (PNL) mixing model to precisely characterize signal distortion mechanisms and employ kernel learning to project the original nonlinear problem into a high-dimensional linear space. This preserves the fast convergence advantage of FastICA while relaxing the linear invertibility constraint. To mitigate matrix ill-conditioning caused by kernel-induced dimensionality expansion, a regularized pre-whitening strategy is introduced to enhance numerical stability. Furthermore, symmetric fixed-point iteration optimization is integrated to reduce the convergence time. The simulation results demonstrate that the proposed algorithm achieves a signal-to-interference ratio (SIR) of 15.98 dB under a 10 dB interference-to-signal ratio (ISR), with correlation coefficients of 0.846 and 0.971 between separated communication and interference signals, respectively. These results validate its superior performance in nonlinear distortion compensation and real-time processing.