A CANDECOMP/PARAFAC perspective on uniqueness of DOA estimation using a vector sensor array

We address the uniqueness problem in estimating the directions-of-arrival (DOAs) of multiple narrowband and fully polarized signals impinging on a passive sensor array composed of identical vector sensors. The data recorded on such an array present the so-called multiple invariances, which can be linked to the CANDECOMP/PARAFAC (CP) model. CP refers to a family of low-rank decompositions of three-way or higher way (mutidimensional) data arrays, where each dimension is termed as a mode. A sufficient condition is derived for uniqueness of the CP decomposition of a three-way (three mode) array in the particular case where one of the three loading matrices, each associated to one mode, involved in the decomposition has full column rank. Based on this, upper bounds on the maximal number of identifiable DOAs are deduced for the two typical cases, i.e., the general case of uncorrelated or partially correlated sources and the case where the sources are coherent.