Computationally-efficient blind source extraction under extremely low SNR conditions based on principal component analysis

Signal extraction under extremely low signal-to-noise ratio (SNR) conditions remains a challenging task in signal processing. Conventional separation and extraction algorithms can achieve satisfactory performance but the computational burden is heavy since they usually involve complicated update rules and require a sufficient number of iterations. In this paper, we prove that, under extremely low SNR conditions, principal component analysis (PCA) can be used as an engineering approximation of the optimal solution for independent vector extraction (IVE). Based on this conclusion, two computationally-efficient methods are proposed to obtain the demixing vector. Both methods involve only a few simple operations and thus require much less computational resources. Numerical experiments across various scenarios demonstrate that the proposed algorithms can achieve comparable performance to conventional algorithms with light computational burden. • Signal extraction under extremely low signal-to-noise ratio (SNR) conditions is rarely explored. • Traditional algorithms are effective but computationally-intensive. • Principal component analysis (PCA) is an approximate solution in low SNR scenarios. • Two PCA-based algorithms are proposed to solve for the demixing vector. • The proposed methods demonstrate effectiveness and efficiency in various scenarios.