Linear arrays have been well studied for their widespread applications. However, they suffer from severe limitations in their scanning capabilities due to the inherent main beam spreading. The combination of two linear arrays, radiating simultaneously, may provide the coverage of a wide angular domain by identical beams. More in general, first, we consider the radiation properties of a collection of continuous linear sources by following an inverse source approach which aims at investigating the spectral decomposition of the relevant radiation operator by discussing its Singular Value Decomposition and the Number of Degrees of Freedom of the source according to its geometry. Then a connection with the known closed form results of the single line case is established. Next, for an angle geometry, the discussion of the Point Spread Function reveals the condition to be achieved for an angle source to radiate identical beams with an angular coverage larger than the one of a single linear source with the same total length. Finally, the approach is applied to linear arrays, arranged in an angle geometry, also including the effect of the element factor. Numerical results about the synthesis of identical focused radiation patterns demonstrate the usefulness of the approach.

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.

The inverse source problem has a number of applications in antenna analysis and synthesis. The properties of the radiation operator, connecting the source current to the far zone field, depends on the source geometry and can be analyzed by its singular value decomposition. Here, first, we present useful upper bounds about the number of degrees of freedom for some 2D source geometries (i.e. for elliptical and parabolic arc sources) and examine the role of two different representation variables. These results were obtained from asymptotic arguments and allow to define the maximum number of independent sources and patterns that can be radiated by each geometry. They are verified to fit the numerically computed ones, too. Next, we examine the point source reconstructions by considering the point spread function. An approximate closed form evaluation reveals that the arc length representation variable leads to a space invariant behavior. The role of the source electrical length in determining the number of degrees of freedom is pointed out, too. Finally, the radiation properties of different source geometries are compared by means of a synthetic index and examples of radiation pattern synthesis and array diagnostics confirm the need to investigate the role of the source geometry.

The paper adopts an inverse problem approach to examine the role of some 2D geometries in the source reconstruction from far zone data. It aims at evaluating the number of independent pieces of information, i.e. the number of degrees of freedom (NDF), of the source and pointing out the set of far zone fields corresponding to stable solutions of the inverse problem. Some of the results are relevant to the synthesis problem of conformal antennas, since a general comparison of different source geometries in providing radiation pattern specifications is proposed.

<div>The paper adopts an inverse problem approach to investigate the far zone radiation of a collection of 2D linear sources. By the evaluation of the number of independent pieces of information, i.e. the number of degrees of freedom (NDF), and the analysis of the reconstruction of a focusing beam, the role of the geometry can be examined in determining the set of possible radiation patterns. The results are relevant to the radiation pattern synthesis problem, since they allow to define the optimal source geometry for the hemispherical coverage with identical radiation patterns. </div>