Blind Signal Separation via Tensor Decomposition With Vandermonde Factor: Canonical Polyadic Decomposition

Several problems in signal processing have been formulated in terms of the Canonical Polyadic Decomposition of a higher-order tensor with one or more Vandermonde constrained factor matrices. We first propose new, relaxed uniqueness conditions. We explain that, under these conditions, the number of components may simply be estimated as the rank of a matrix. We propose an efficient algorithm for the computation of the factors that only resorts to basic linear algebra. We demonstrate the use of the results for various applications in wireless communication and array processing.