AN INVESTIGATION ON NUMBER OF SIGNALS WHOSE DIRECTIONS-OF-ARRIVAL AREUNIQUELY DETERMINABLE WITH AN ELECTROMAGNETIC VECTOR SENSOR

We first study a theorem on the relationship among linear dependence o f steering vectors, correlation among signals, and the number of signa ls 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 furt her generalize the first part of the theorem to include vector-sensor arrays receiving general signals (which can be polarized, partially po larized or unpolarized). Subsequently, we show that the DOAs of two un correlated 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 correlat ed signals. Finally, we establish a relationship between uniqueness in measurements and uniqueness in MUSIC estimates.