A Six-Component Vector Sensor Comprising ElectricallyLongDipoles andLargeLoops— To Simultaneously Estimate Incident Sources’ Directions-of-Arrival and Polarizations

Abstract

An “electromagnetic vector sensor” (EMVS) comprises three orthogonal dipoles and three orthogonal loops, all in spatial collocation. The former triplet aims to directly measure the 3 × 1 electric-field vector e, whereas the latter triplet aims to directly measure the 3 × 1 magnetic-field vector h. Their vector cross product e × h would yield the incident source's Poynting vector, which specifies the incident wavefield's propagation direction. In reality, all these are only an idealization. Instead, a real-world dipole triad's measurement could equal the incident e, only if the dipoles were electrically short (i.e., with an electrical length of (L/λ) <; 0.1). Likewise, a practical loop triad's measurement could equal the incident h, only if the loops were electrically small (i.e., with an electrical circumference of 2π(R/λ) <; 0.1). However, such short dipoles and small loops would be electromagnetically inefficient receivers. For a practical dipole that is electrically long, its measurement equals not the incident wavefield's e but a vector dot product between: 1) the incident wave's e and 2) that dipole antenna's “effective length” vector (which depends on that dipole's (L/λ) and orientation). An analogous complexity exists for a practical loop that is electrically large. For such practical dipoles and loops, the aforementioned vector-cross-product would fail to yield the Poynting vector, hence it would inaccurately estimate the direction-of-arrival. Instead, this article will advance a new closed-form algorithm to simultaneously estimate an incident source's direction-ofarrival and polarization, despite the practical dipoles'/ loops' mathematically complicated gain/phase responses as described earlier, but without any prior knowledge of the dipoles' electric length (L/λ) nor the loops' electric radius (R/λ).