Linear dependence of steering vectors associated with tripole arrays

We are concerned with the linear independence of steering vectors associate d with tripoles, each of which provides measurements of the three component s of electric field induced by electromagnetic signals. We first establish that for a single tripole, any steering vector is linearly dependent on at least one other steering vector corresponding to a different direction-of-a rrival (DOA) for a general problem where signals may arrive from anywhere i n a three-dimensional (3-D) space, but every two steering vectors with dist inct DOA's are linearly independent if the signals are nonlinearly polarize d and arrive from a strictly hemispherical space. We then obtain a series o f upper hounds for the number of linearly independent steering vectors asso ciated with a tripole array with general sensor configurations, We also sho w that for applications where signals are known to be linearly polarized in the same direction, the ability to estimate DOA's using a tripole array is identical to that using a scalar-sensor array if both of them have identic al sensor configurations.