Uniqueness study of measurements obtainable with an electromagnetic vector sensor

Abstract

We investigate the linear dependence of the steering vectors of one electromagnetic vector sensor. We show that every 3 steering vectors with distinct DOAs are linearly independent. We also show that 4 steering vectors with distinct DOAs are linearly independent if the ellipticity angles of the signals associated with any 2 of the 4 steering vectors are distinct. We then establish that 5 steering vectors are linearly independent if exactly 2 or 3 of them correspond to circularly polarized signals with the same spin direction. Finally, we demonstrate that given any 5 steering vectors, then for any DOA there exists a steering vector which is linearly dependent on the 5 steering vectors.