Abstract. Canonical Polyadic Decomposition (CPD) of a higher-order tensor is an important tool in mathematical engineering. In many applications at least one of the matrix factors is constrained to be column-wise orthonormal. We first derive a relaxed condition that guarantees uniqueness of the CPD under this constraint. Second, we give a simple proof of the existence of the optimal low-rank approximation of a tensor in the case that a factor matrix is column-wise orthonormal. Third, we derive numerical algorithms for the computation of the constrained CPD. In particular, orthogonality-constrained versions of the CPD methods based on simultaneous matrix diagonalization and alternating least squares are presented. Numerical experiments are reported.

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In this paper a blind MIMO space-time equalizer is described, dedicated to convolutive mixtures when observations have been pre-whitened. Filters preserving space-time whiteness are paraunitary; a parameterization of such filters is proposed. Theoretical developments then lead to a numerical algorithm that sweeps all pairs of delayed outputs. This algorithm involves the solution of a polynomial system, whose coefficients depend on the output cumulants. Simulations and performance of the numerical algorithm are reported.

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