Rank-1 ambiguity of steering vector of an array with five co-localized and orthogonally oriented sensors

The rank-1 ambiguity problem involved in the Polarization-Angular Coherence Structure (PACS) of a 5-D co-localized vector antenna whose elements are orthogonally oriented is addressed in this paper. Two kinds of equivalent relations are defined, under which several typical and easy-analyzed 5-D PACSs are studied. It is further shown in the paper that with only one 5-D vector antenna, DOA and polarization of one signal except for the case of horizontally polarized signal could be uniquely identified, as is done by the well-known 6-D ElectroMagnetic (EM) vector sensor. Some representative examples are also given to validate the present analyses.