Simultaneous Blind Separation of Mixed Source Signals

摘要

This paper presents gradient-based methods forrnsimultaneous blind separation of mixed source signals. Wernconsider the regular case where the mixing matrices havernfull column rank as well as ill-conditioned cases. First, twornnecessary and sufficient conditions for solvability analysisrnof simultaneous blind separation are established by usingrnseparation matrix of different dimensions. According to thernsolvability conditions all source signals are separated into tworncategories: separable single sources and inseparable mixtures.rnA sufficient condition is also derived for the existence ofrnan optimal partition of the mixing matrix which leads to arnunique set of separations with maximum number of separatedrnsources. Next, two cost functions based on fourth-order cumulantsrnare introduced to simultaneously separate all separablernsingle sources and all inseparable mixtures. By minimizingrnthe cost functions, two gradient-based methods are developed.rnOur algorithms derived from gradient-based methods arernguaranteed to converge. Finally, simulation results show therneffectiveness of our methods and the advantage over thernexisting Gauss-Newton algorithm used in sequential blindrnextraction.