Inverse Source on Conformal Conic Geometries

Abstract

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.

An Efficient Conformal Stacked Antenna Array Design and 3D-Beamforming for UAV and Space Vehicle Communications

“…For UAV communications, the work done in [19] proposed conical conformal array at 9.8 GHz for point-to-point communications, while in [20], the cylindrical antenna arrays are combined with conical arrays to form "CYLCON" array using microstrip Yagi antennas to provide wide solid angle scanning. On the other hand, the recent work done in [30] discussed the radiation properties of different source geometries based on the inverse source problem. One of the most important achievements in [30] is the focused patterns for mainlobes at different angular directions, however, the tested structures have relatively high sidelobe levels.…”

“…On the other hand, the recent work done in [30] discussed the radiation properties of different source geometries based on the inverse source problem. One of the most important achievements in [30] is the focused patterns for mainlobes at different angular directions, however, the tested structures have relatively high sidelobe levels. Additionally, spherical conformal arrays were proposed in [31] to compensate for the changing spherical surfaces using patch antenna structures.…”

Synthesis of High Directivity Beams for Conformal Sources

“…It is important to point out that, as shown in [9], the NDF of a conformal 2D curve source is related only to its electrical length. Therefore, it is apparent that also the directivity is proportional to it, as well known for the linear case.…”

“…For an arc of circumference of radius , = , ( ) = , ‖ ′( )‖ = , = − , = in the integral operator (1), but, differently from the circumference case, no analytical results for the pertinent SVD are available in this case. Some asymptotic reasonings [9], [20] have led to an estimation of the NDF as…”

“…In particular, the NDF defines the dimension of the space of the far field functions that can be radiated by a finite energy source, while the PSF is usually connected to the reconstruction of point-like sources. This approach has revealed itself useful in order to establish a way to compare the general radiation properties of some conformal source [9] before undertaking the synthesis procedure of a particular antenna with defined specifications [11].…”