Blind Instantaneous Noisy Mixture Separation with Best Interference-Plus-Noise Rejection

In this paper, a variant of the well known algorithm FastICA is proposed to be used for blind source separation in off-line (block processing) setup and a noisy environment. The algorithm combines a symmetric FastICA with test of saddle points to achieve fast global convergence and a one-unit refinement to obtain high noise rejection ability. A novel test of saddle points is designed for separation of complex-valued signals. The bias of the proposed algorithm due to additive noise can be shown to be asymptotically proportional to σ for small σ, where σ is the variance of the additive noise. Since the bias of the other methods (namely the bias of all methods using the orthogonality constraint, and even of recently proposed algorithm EFICA) is asymptotically proportional to σ, the proposed method has usually a lower bias, and consequently it exhibits a lower symbol-error rate, when applied to blind separation of finite alphabet signals, typical for communication systems.