An investigation on number of signals whose directions-of-arrival are uniquely determinable with an electromagnetic vector sensor

We first study a theorem on the relationship among linear dependence of steering vectors, correlation among signals, and the number of signals whose DOAs are uniquely determinable, which was derived by Wax and Ziskind (1989) and Nehorai et al. (1991) for a class of scalar-sensor arrays. We then extend the theorem to include all scalar-sensor arrays, as well as vector-sensor arrays receiving polarized signals. We further generalize the first part of the theorem to include vector-sensor arrays receiving general signals (which can be polarized, partially polarized or unpolarized). Subsequently, we show that the DOAs of two uncorrelated signals can be uniquely determined with one electromagnetic vector sensor, regardless of the states of polarization. However, it may be impossible to determine uniquely the DOAs of two fully correlated signals. Finally, we establish a relationship between uniqueness in measurements and uniqueness in MUSIC estimates.