Satellite array receivers must suppress interference whose spatial, spectral, and temporal characteristics vary across operating conditions, often with limited known symbols for adaptation. This paper studies when learned subspace augmentation is useful under finite pilot support. The receiver retains the instantaneous complex-linear receive subspace and adds a low-dimensional orthogonal complement generated from temporal and spectral features, with all basis coefficients estimated jointly from known symbols. A finite-sample analysis separates oracle representation gain from the additional pilot-to-payload estimation error caused by basis enlargement. Across 720 seen-family conditions, the proposed receiver achieves mean uncoded bit error rate (BER) 0.06521, versus 0.06572 for the receive-span ablation and 0.06719 for minimum-variance distortionless response; the 0.78% reduction relative to receive-span is modest and concentrated in spatially loaded narrowband regimes. A same-frame trained-versus-untrained comparison shows an average benefit from parameter optimization in the reference realization. Independent retraining from three initializations yields closely clustered held-out performance, while the selected model order varies between $L=1$ and $L=2$. For three unseen interference families, mean net augmentation gain is negative and aggregate MSE does not improve over receive-span. The results therefore identify a condition-dependent regime in which subspace augmentation is useful when representation gain exceeds finite-pilot estimation cost, rather than a broadly transferable advantage across interference types.

To address the issues of suboptimal sparsity and the tendency of clustering algorithms to converge to local optima in the estimation of the mixing matrix within underdetermined blind source separation (UBSS) systems, a novel mixing matrix estimation algorithm based on source signal sparsity is proposed. Firstly, the principle of underdetermined mixing matrix estimation leveraging source sparsity is derived. Building upon this foundation, improvements are made from enhancement of signal sparsity and optimization of the clustering algorithm. To overcome the limited sparse representation capability of conventional time–frequency (TF) transformation methods, a source signal sparsity enhancement algorithm based on the Local Maximum Synchroextracting Transform (LMSET) is proposed. This method rearranges the TF coefficients by detecting local maxima in the frequency direction, thereby achieving a more desirable TF resolution and enhanced signal sparsity. Furthermore, to mitigate the sensitivity of the Fuzzy C-Means (FCM) algorithm to initial cluster centers and its propensity for local optima, a robust FCM algorithm optimized by the PID(Proportional-integral-Derivative)-based Search Algorithm (PSA) is adopted. Simulation results demonstrate that the proposed algorithm achieves a superior TF representation and enhances the sparsity of source signals across various environments. Compared to traditional algorithms, the estimation accuracy of the mixing matrix is increased by 19.8%, effectively improving the performance of mixing matrix estimation in underdetermined blind source separation systems.