Steering vector modeling for polarimetric arrays of arbitrary geometry

Abstract

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.

Fast DBF for conformal arrays based on 2D Fourier decomposition

“…Consider an N ‐element antenna array of arbitrary geometry and configurations. The array steering vector is given by [9] where denotes transpose, and denote the azimuth and co‐elevation angles, respectively. In practise, it is reasonable to assume that (1≤ n ≤ N ) is in the Hilbert space of absolute‐square integrable functions defined on , i.e.…”

“…By using the array manifold decomposition technique, can be expressed as [3, 9] where denotes the sampling matrix that depends on the array characteristics only, represents the array independent spatial basis functions of the decomposition. Note that the dimension of the orthogonal basis functions is infinite for (2) to hold exactly.…”

“…There are several candidates for the basis functions such as spherical harmonics [3] and 2D Fourier basis [4–9]. In this paper, we focus on the 2D Fourier decomposition and the conventional 2D Fourier basis functions are given by [9] with where denotes Kronecker product, represents a periodic co‐elevation angle, m a and m e denote the mode indices in azimuth and elevation dimensions, respectively. The conventional 2D Fourier basis is a complete orthonormal basis on the unit torus …”

“…Array manifold decomposition technique has attracted increasing attentions in array signal processing and direction finding [3–9] due to its reliable and elegant representation of the real‐world arrays with arbitrary structures and imperfections. The technique decomposes the array steering vector (manifold) using orthogonal basis functions such as spherical harmonics [3] and two‐dimensional (2D) Fourier functions [4–9]. The 2D Fourier basis was widely used in the literatures for several reasons: (i) the 2D Fourier spectra can be obtained from the 2D discrete Fourtier transform (DFT) of the array calibration data, and hence the computational complexity is low by exploiting FFT; (ii) the Fourier basis functions have a Vandermonde structure which facilitates high‐resolution algorithms with low complexity.…”

“…The 2D Fourier basis was widely used in the literatures for several reasons: (i) the 2D Fourier spectra can be obtained from the 2D discrete Fourtier transform (DFT) of the array calibration data, and hence the computational complexity is low by exploiting FFT; (ii) the Fourier basis functions have a Vandermonde structure which facilitates high‐resolution algorithms with low complexity. However, in the conventional 2D Fourier decomposition, one has to extend the initial array steering vector in elevation dimension for the employment of 2D DFT, and the conventional 2D Fourier basis is suitable for rotating the extended function on the torus instead of the initial function on the sphere [9].…”