Abstract
The solution of inverse source problems by numerical procedures requires the investigation of the number of independent pieces of information that can be reconstructed stably. To this end, the mathematical properties of the relevant operators are to be examined in connection with the source shape. The aim of this work is to investigate the effect of the source shape on the eigendecomposition of the radiation operator in a 2D geometry, when the radiated field is observed over a semi-circumference in the far zone. We examine both the behavior of the eigenvalues and the effect of the choice of the representation variables on the point spread function (PSF). In particular, the effect of the choice of the representation variables is considered since operator properties may depend on it. We analyze different source shapes evolving from a line to a semi-ellipse and, finally, to a semi-circumference, in order to understand how the increase of the source aspect ratio affects the results. The main conclusions concern an estimate of the number of degrees of freedom in connection with the source geometry and the fact that the PSF exhibits the same variant behavior along the considered domain, independently of the observation variable. The practical relevance of the result is illustrated by two numerical examples. The first one deals with the conformal array diagnostics for the reliable reconstruction of the excitation of the array elements. The second one concerns the array synthesis problem, and a comparison between the radiating performances of the source geometries is presented.
Highlights
Conformal antennas [1] are attracting increasing interest in several applications in radar and mobile communication systems
Together with the interest in new array designs, interest is growing in the problems that typically need to be addressed in this area, such as array diagnostics, which deals with determining the presence of possible faulty elements, negatively affecting both gain and sidelobe levels
The role of the geometry in the inverse source reconstruction problem for far zone data has been examined by referring to a semi-elliptic source when the observation domain is a semi-circumference
Summary
Conformal antennas [1] are attracting increasing interest in several applications in radar and mobile communication systems. Array antennas, whose elements are located on a curved surface, may exhibit several advantages from the aerodynamical point of view, since they can follow the surface of vessels or aircrafts, and from the electrical one [2]. Together with the interest in new array designs, interest is growing in the problems that typically need to be addressed in this area, such as array diagnostics, which deals with determining the presence of possible faulty elements, negatively affecting both gain and sidelobe levels. The array diagnostics problem has been treated in different ways in literature [4,5,6,7,8,9,10]. In [11], a neural network is exploited to localize a maximum of three faulty elements in a 16-element array, while in [12], a Moore-Penrose pseudoinverse is used to retrieve the current distribution of a planar array of parallel dipoles with faulty elements, and in [13,14], compressed sensing/sparse recovering techniques have been introduced in order to deal with a large amount of data, which is the case of large arrays
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