Steering vector modeling for polarimetric arrays of arbitrary geometry

In this paper, the algebraic modeling of the steering vector for dual-polarized real-world arrays with unknown configuration is addressed. The formalism provided by the wavefield modeling theory is extended to vector-fields such as completely polarized electromagnetic waves. In particular, compact expressions for decomposing the array steering vector in different orthonormal basis functions are proposed. Such decompositions are shown to be equivalent under mild conditions that typically hold in practice. Recent results on algebraic modeling of sensor arrays are generalized to vector-fields and unified. These results allow for high-resolution direction-of-arrival and polarization estimation when array calibration measurement data is available only. We show that reduced computational complexity may be achieved by making use of the Fast Fourier Transform. Such computational savings may be obtained without compromising the performance of the estimation algorithms and irrespective of the antenna array configuration. The results in this paper contribute to array design as well by providing closed-form expressions for the array steering vector, which are useful in optimizing different array performance criteria. Simulations on direction-of-arrival and polarization estimation using a real-world polarimetric array are carried out, validating our analytical results.