Blind identification of underdetermined mixtures based on the hexacovariance

Static linear mixtures with more sources than sensors are considered. Blind identification (BI) of underdetermined mixtures is addressed by taking advantage of sixth order (SixO) statistics and the virtual array (VA) concept. Surprisingly, identification methods solely based on the hexacovariance matrix succeed well, despite their expected high estimation variance; this is due to the inherently good conditioning of the problem. A computationally simple but efficient algorithm, named BIRTH (Blind Identification of mixtures of sources using Redundancies in the daTa Hexacovariance matrix), is proposed and enables the identification of the steering vectors of up to P=N²-N+1 sources for arrays of N sensors with space diversity only, and up to P=N² for those with angular and polarization diversities. Five numerical algorithms are compared.