Orthogonally constrained independent component extraction: Blind MPDR beamforming

We propose a novel technique for the extraction of one independent component from an instantaneous linear complex-valued mixture of signals. The mixing model is optimized in terms of the number of parameters that are necessary to simultaneously estimate one column of the mixing matrix and one row of the de-mixing matrix, which both correspond to the desired source. The desired source is assumed to have a non-Gaussian distribution, while the other sources are modeled, for simplicity, as Gaussian-distributed, although in applications the other sources can be arbitrary. We propose an algorithm that can be interpreted as a blind self-steering Minimum-Power Distortionless Response (MPDR) beamformer. The method is compared with the popular Natural Gradient algorithm for general Independent Component Analysis. Their performances are comparable but the proposed method has a lower computational complexity; in examples, it is about four times faster.