Blind source extraction from convolutive mixtures in ill-conditioned multi-input multi-output channels

This paper presents a new approach to blind source extraction from convolutive mixtures in multi-input multi-output (MIMO) channels. Two ill-conditioned cases are considered: the number of sensors is less than the number of sources and the number of sensors is greater than or equal to the number of sources but the system is noninvertible. Although there exist several works related to ill-conditioned dynamic MIMO channels, especially on blind channel identification, how to obtain a true source only from observable convolutive mixtures is still an open problem. In this paper, beginning with introducing two blind extraction models for blind deconvolution in ill-conditioned MIMO channels, we discuss the extractability issue. Results from our extractability analysis (a necessary and sufficient condition) show that it is possible to extract individual sources from the outputs. Furthermore, all potentially separable sources (at most equal to the number of sensors) can be extracted sequentially based on these extraction models. A cost function based on cross cumulant is discussed along with the Gauss-Newton algorithm. Finally, a simulation example is presented for illustration.