Tensor-based techniques for the blind separation of DS-CDMA signals
Signal Processing
4D near-field source localization using cumulant
EURASIP Journal on Applied Signal Processing
Kruskal's condition for uniqueness in Candecomp/Parafac when ranks and k-ranks coincide
Computational Statistics & Data Analysis
Blind underdetermined mixture identification by joint canonical decomposition of HO cumulants
IEEE Transactions on Signal Processing
Computing symmetric rank for symmetric tensors
Journal of Symbolic Computation
Tensor algebra and multidimensional harmonic retrieval in signal processing for MIMO radar
IEEE Transactions on Signal Processing
Novel blind carrier frequency offset estimation for OFDM system with multiple antennas
IEEE Transactions on Wireless Communications
SIAM Journal on Matrix Analysis and Applications
Multihomogeneous polynomial decomposition using moment matrices
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Space-Time Blind Multiuser Detection for Multiuser DS-CDMA and Oversampled Systems
Wireless Personal Communications: An International Journal
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
General tensor decomposition, moment matrices and applications
Journal of Symbolic Computation
Hi-index | 35.69 |
CANDECOMP/PARAFAC (CP) analysis is an extension of low-rank matrix decomposition to higher-way arrays, which are also referred to as tensors. CP extends and unifies several array signal processing tools and has found applications ranging from multidimensional harmonic retrieval and angle-carrier estimation to blind multiuser detection. The uniqueness of CP decomposition is not fully understood yet, despite its theoretical and practical significance. Toward this end, we first revisit Kruskal's permutation lemma, which is a cornerstone result in the area, using an accessible basic linear algebra and induction approach. The new proof highlights the nature and limits of the identification process. We then derive two equivalent necessary and sufficient uniqueness conditions for the case where one of the component matrices involved in the decomposition is full column rank. These new conditions explain a curious example provided recently in a previous paper by Sidiropoulos, who showed that Kruskal's condition is in general sufficient but not necessary for uniqueness and that uniqueness depends on the particular joint pattern of zeros in the (possibly pretransformed) component matrices. As another interesting application of the permutation lemma, we derive a similar necessary and sufficient condition for unique bilinear factorization under constant modulus (CM) constraints, thus providing an interesting link to (and unification with) CP.