Turbo Source Extraction Algorithm and Noncancellation Source Separation Algorithms by Kurtosis Maximization

The kurtosis maximization criterion has been effectively used for blind spatial extraction of one source from an instantaneous mixture of multiple non-Gaussian sources, such as the kurtosis maximization algorithm by Ding and Nguyen, and the fast kurtosis maximization algorithm (FKMA) by Chi and Chen. By empirical studies, we found that the smaller the normalized kurtosis magnitude of the extracted source signal, the worse the performance of these algorithms. In this paper, with the assumption that each source is a non-Gaussian linear process, a novel blind source extraction algorithm, called turbo source extraction algorithm (TSEA), is proposed. The ideas of the TSEA are to exploit signal temporal properties for increasing the normalized kurtosis magnitude, and to apply spatial and temporal processing in a cyclic fashion to improve the signal extraction performance. The proposed TSEA not only outperforms the FKMA, but also shares the convergence and computation advantages enjoyed by the latter. This paper also considers the extraction of multiple sources, also known as source separation, by incorporating the proposed TSEA into the widely used multistage successive cancellation (MSC) procedure. A problem with the MSC procedure is its susceptibility to error propagation accumulated at each stage. We propose two noncancellation multistage (NCMS) algorithms, referred to as NCMS-FKMA and NCMS-TSEA, that are free from the error propagation effects. Simulation results are presented to show that the NCMS-TSEA yields substantial performance gain compared with some existing blind separation algorithms, together with a computational complexity comparison. Finally, we draw some conclusions