Techniques for blind source separation using higher-order statistics

The blind source separation (BSS) problem consists of the recovery of a set of statistically independent source signals from a set of measurements that are mixtures of the sources when nothing is known about the sources and the mixture structure. This paper considers the separation and estimation of independent sources from their instantaneous linear mixed observed data. The concept of higher-order moment and higher-order time-frequency distribution matrices are also introduced. In practice, separation can be achieved by using suitable second-order statistics (SOS) and/or higher-order statistics (HOS). Computationally feasible implementations are presented based on joint diagonalisation of the moment matrices and matrices of the principal slices of the time-multifrequency domain of support of the moment-based Wigner trispectra. The latter approach allows separation of the sources with nonstationarity properties. Simulation results are given to demonstrate the effectiveness of the proposed approaches