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Abstract: This paper addresses the problem of joint block diagonalization (JBD) of a set of given matrices. As is known that the nonunitary JBD algorithm has some advantages over the existing orthogonal one for convolutive blind source separation (CBSS). However, the nonunitary JBD algorithm is prone to converge to some unexpected degenerate solutions (singular or ill-conditioned solutions). Especially for the matrices of large dimension or the case that the number of the diagonal blocks is relatively large, the performances of the nonunitary JBD algorithm degrade more severely. To eliminate the degenerate solutions, we optimize a penalty term based weighted least-squares criterion and thus develop a fast efficient algorithm. The performance of the proposed algorithm is evaluated by computer simulations and compared with the existing state-of-the-art nonunitary JBD algorithm. The simulation results demonstrate the robustness and performance improvement of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, we elaborate an extension of classical power iteration method to nonlinear power iteration for blind separation of multiple independent sources from observed array output signals. The present algorithm, referred to as NPI, considers the estimating of the separating matrix as a nonlinear power iteration problem. By naturally choosing the positive definite normalizer for nonlinear power term, the resulting algorithm not only yields robust convergence behavior but also guarantees the orthonormality of the separating matrix at each iteration. To circumvent the difficulty of solving the inverse square root for the normalizer, an efficient adaptive singular value decomposition (SVD) technique is also adopted to obtain a fast implementation of NPI. The estimation accuracy and convergence speed of the present algorithm are illustrated through simulation results and compared with the existing adaptive algorithms. [Copyright &y& Elsevier]