Blind Source Separation Based on Cumulants With Time and Frequency Non-Properties

This paper presents new results on blind separation of instantaneously mixed independent sources based on high-order statistics together with their time and frequency non-properties (i.e., the non-stationarity and non-whiteness of sources). Separation criteria of mixtures are established on a set of cumulants at different time instants using the non-stationarity of sources and/or time-delayed cumulants using the non-whiteness of sources. It is shown that cumulants at different time instants and time-delayed cumulants can be used as criteria for blind source separation (BSS). Furthermore, it is proved that the cumulant-based separation criteria are directly related to the separability conditions. Batch-data and online learning rules are developed based on the joint diagonalization of symmetric fourth-order cumulant matrices, and the learning rules are further simplified to correlation-based BSS algorithms. In addition, an initialization strategy is proposed for improving the convergence of the learning rules. Simulation results are given to demonstrate the validity and performance of the algorithms.