CANDECOMP/PARAFAC decomposition based multi-dimensional nonuniform harmonic retrieval

Two CANDECOMP/PARAFAC decomposition based multi-dimensional nonuniform harmonic retrieval algorithms are derived, which are referred to as search efficient Tensor-MUSIC (SE-T-MUSIC) and generalized Tensor-ESPRIT (G-T-ESPRIT). Comparing with the conventional Tensor-MUSIC algorithm, SE-T-MUSIC reduces the computational complexity significantly in terms of the number of searching grids. On the other hand, G-T-ESPRIT is a search-free polynomial rooting based algorithm. It is a R-dimensional generalization of the conventional generalized ESPRIT approach and multidimensional optimization is not required. Furthermore, a CP decomposition based combinatorial search method is proposed to associate the estimated frequencies over R dimensions.