A joint blind source separation(JBSS)algorithm based on decomposition of high-order cumulant tensors is proposed.The algorithm recovers the source signals from the observation signals of multiset data.Firstly,the higher-order cross-cumulant tensors of observation signals of multiset data are calculated.Due to the potential diagonal structures of cumulant tensors,the JBSS problem can be transformed into canonical polyadic decomposition(CPD)of a higher-order tensor.Next,by tensor train decomposition(TTD),the higher-order tensor is decomposed into a simple tensor network composed of a set of interconnected core tensors of orders not higher than 3.The CPD of a higher-order tensor thereby is transformed into a set of CPDs of order-3 tensors.Finally,according to the links between TTD and CPD,after several CPDs of order-3 tensors,the mixed matrices of multi-dataset can be obtained by reordering and rescaling the factor matrices sequentially,resulting in the separation of the source signals.Simulation results show that the proposed algorithm operated at a faster speed.
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