The problem of parameter estimation of coherent signals impinging on an array with vector sensors is considered from a new perspective by means of the decomposition of tensors. Signal parameters to be estimated include the direction of arrival (DOA) and the state of polarization. In this paper, mild deterministic conditions are used for canonical polyadic decomposition (CPD) of the tensor-based signal model; i.e., the factor matrices can be recovered, as long as the matrices satisfy the requirement that at least one is full column rank. In conjoint with the estimation of signal parameters via the algebraic method, the DOAs and polarization parameters of coherent signals can be resolved by virtue of the first and second factor matrices. Hereinto, the key innovation of the proposed approach is that the proposed approach can effectively estimate the coherent signal parameters without sacrificing the array aperture. The superiority of the proposed algorithm is shown by comparing with the algorithms based on higher order singular value decomposition (HOSVD) and Toeplitz matrix. Theoretical and numerical simulations demonstrate the effectiveness of the proposed approach.
Double coupled canonical polyadic decomposition of third-order tensors: Algebraic algorithm and relaxed uniqueness conditions