A New Approach to Blind Separation of Two Sources with Three Sensors

An exhaustive investigation of the overdetermined blind source separation (BSS) 3 times 2 problem is presented. We establish a new relationship between the column vectors of the channel matrix using second order statistics (SOS) only. This relationship is then exploited to factorize the separating matrix into a whitening term, whose expression depends on whether the observations are corrupted by noise or not, and a 2 times 2 orthogonal matrix that can be determined using high order statistics (HOS). Simulation results demonstrate that resorting to the new form of the whitening matrix, mainly in the case of noisy ill-conditioned BSS, results in improved performance compared to the common whitening-based techniques.