Satellite communication systems, as a core component of global information infrastructure, have undergone unprecedented development. However, the open nature of satellite channels renders them vulnerable to electromagnetic interference, making anti-jamming techniques a persistent research focus in this domain. Satellite transponders contain various power-sensitive components that exhibit nonlinear characteristics under interference conditions, yet conventional anti-jamming approaches typically neglect the nonlinear distortion in transponders when suppressing interference. To address this challenge, this paper proposes a kernel-method-optimized FastICA algorithm (Kernel-FastICA) that establishes a post-nonlinear mixing model to precisely characterize signal transmission and reception processes. The algorithm transforms nonlinear separation tasks into high-dimensional, linear independent-component-analysis problems through kernel learning methodology. Furthermore, we introduce a regularized pre-whitening strategy to mitigate potential ill-conditioned issues arising from dimensional expansion, thereby enhancing numerical stability and separation performance. The simulation results demonstrate that the proposed algorithm exhibits superior robustness against interference and enhanced generalization capabilities in nonlinear jamming environments compared with existing solutions.

High-power jamming may drive the radio-frequency (RF) front end of a satellite receiver into a nonlinear regime, thereby invalidating the linear superposition assumption underlying conventional excision and blanking methods. We formulate dual-receiver direct-sequence spread-spectrum (DSSS) anti-jamming as a nonlinear source-separation problem in complex baseband using stacked I/Q observations. We then propose a time-domain separator that jointly estimates the desired DSSS signal and the jammer on a designated reference receiver. The separator combines a multi-scale convolutional front end with a Transformer encoder and is pretrained on synthetic nonlinear mixtures that include multi-tone or burst jamming as well as typical satellite impairments, including Doppler/carrier-frequency offset (CFO), phase noise, multipath, and additive white Gaussian noise (AWGN). Robustness under high-jammer-to-signal-ratio (JSR) conditions is improved through high-JSR oversampling and JSR-aware loss reweighting. After Stage I supervised pretraining on labeled synthetic mixtures, an optional Stage II mixture-only adaptation step further refines the separator using nonlinear reconstruction consistency and lightweight communication-motivated priors. Across 1000 test mixtures with JSRs from −5 to 15 dB, SNRs from 15 to 25 dB, and cubic coefficients $a\in \left[\mathrm{0,0.5}\right]$, the proposed method improves the desired-signal scale-invariant signal-to-noise ratio (SI-SNR) from −4.79 dB for the mixture baseline to 13.32 dB after supervised pretraining and to 17.73 dB after mixture-only blind fine-tuning. Over the same test set, the failure rate (SI-SNR < 0 dB) decreases from 60.7% to 2.3%.