Trivial ambiguity of polarization-angular coherence structure of a tripole antenna

The paper shows how to simplify the discussion of the trivial ambiguity (a. k. a. rank-1 ambiguity) problem associated with the polarization-angular coherence structure (PACS) of a tripole antenna by defining a new coordinate system where the two signals of concern both lie in the same coordinate plane, along with a theoretical demonstration indicating that the involved coordinate rotation has no effect on the study of the problem under consideration. The identified situations suffer from the trivial ambiguity are found to be well coincident with that of the performance degradation formerly observed for an adaptive tripole antenna based on the least-mean-square (LMS) criterion. Some representative examples are also given to validate the given analyses.