An efficient K-SCA based unerdetermined channel identification algorithm for online applications

In a sparse component analysis problem, under some non-strict conditions on sparsity of the sources, called k-SCA, we are able to estimate both mixing system (A) and sparse sources (5) uniquely. Based on k-SCA assumptions, if each column of source matrix has at most N_x-1 nonzero component, where N_x is the number of sensors, observed signal lies on a hyperplane spanned by active columns of the mixing matrix. Here, we propose an efficient algorithm to recover the mixing matrix under k-SCA assumptions. Compared to the current approaches, the proposed method has advantages in two aspects. It is able to reject the outliers within subspace estimation process also detect the number of existing subspaces automatically. Furthermore, to accelerate the process, we integrate the "subspaces clustering" and "channel clustering" stages in an online scenario to estimate the mixing matrix columns as the mixture vectors are received sequentially.