Abstract
The Direction of Arrival (DOA) estimations of systematic errors are caused by diffraction distortions of the measured spatial structure of a electromagnetic field. These distortions result from scattering of incident waves on the antenna system and nearby scatterers (mobile carrier body, antenna mast, underlying surface, etc.) in wide frequency band, including the resonant frequencies of nearby objects. This article proposes a method for minimizing the DOA estimation systematic error by forming an additional virtual receiving channel—a Virtual Antenna Array (VAA). The VAAs were formed by use of classical apparatus of electrodynamics—the Huygens-Kirchhoff principle, the method of equivalent fields and sources, and the quasistatic approximation of the field based on the theory of analytical functions of the complex variable (Cauchy integral, Laurent series). The proposed method does not require calibration of the antenna system or a priori information about the geometry and material properties of the scatterers (dry or wet soil, opened or closed vehicle doors, etc.). Therefore, it gives good results in cases of mobile and stationary arrays, or changing carrier body geometry.
Highlights
The term “Virtual Antenna Array” (VAA) denotes a set of spatial samples of electric or magnetic field components approximated in the vicinity of the elements of a Real Antenna Array (RAA)and nearby scatterers—the carrier body, underlying surface, and other objects
We study two methods for extracting information about electromagnetic field from signals at the elements of antenna system: (1) a method based on the basic principles of electrodynamics [21] (Huygens-Kirchhoff principle, Lorentz lemma, Kirchhoff integral, equivalent fields principle, and equivalent currents principle); (2) a method based on the theory of analytic functions of a complex variable [22] (Cauchy integral, Poisson integral, and Laurent series), which can be used because the scattered field can be analyzed in the quasistatic approximation
When the diameter of RAA is shorter than the wavelength (2rr < λ0 ), we can form a VAA by another method, based on measured values of the fields and their analytical continuation using the theory of analytical functions of a complex variable z = x + iy; in particular, the Cauchy integral [25,26]
Summary
The term “Virtual Antenna Array” (VAA) denotes a set of spatial samples of electric or magnetic field components approximated in the vicinity of the elements of a Real Antenna Array (RAA). Friedlander [1] studied a modification of the ROOT-MUSIC method based on the use of the signal subspace of VAA instead of the spatial correlation matrix, and the procedure for selecting the polynomial roots corresponding to the true DOA. Based on dividing the virtual array into many subarrays, and forming a new array covariance matrix, the proposed algorithm is suitable for estimating both the uncorrelated and correlated signal sources These approaches [16,17,18,19,20], based on interpolation of the field at points lying between the antenna array elements, do not increase the dimensions (do not reduce an influence of the distortions caused by nearby scatterers) of the VAA more than that of the RAA.
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