Least-Squares Algorithms for Complex-Valued Blind Source Separation

Blind source separation (BSS), as a digital signal processing approach, focuses on estimating the underlying source signals from their linear mixtures without any prior information about the source signals and mixing matrix. Conventional methods for the BSS, however, are incapable of separating the complex-valued source signals. By leveraging the negative conjugate gradient to minimize the least mean square error reconstruction (LMSER) principle in complex domain, this paper proposes a collection of least-squares algorithms for complex-valued BSS (CBSS), including least-mean square (LMS)-type algorithms and recursive least-squares (RLS)-type algorithms. We demonstrate the availability of the proposed algorithms in both circular and non-circular source signals separation. Especially, the RLS algorithm for the CBSS without prewhitening is superior in cross-talking criterion to the others, as verified by computer simulations on artificial source signals.