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, depend 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 (NDF) for some 2-D 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 NDF 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.
Highlights
THE development of conformal antennas array [1] and the increasing interest in their applications is due to several reasons
There is a lack of general synthesis methods for conformal antennas [10], that include the synthesis of the source geometry
In [29], for the first time, we proposed to apply the Singular Value Decomposition (SVD) to the analysis of the radiation operator connecting a source with non rectilinear geometry to the far field
Summary
THE development of conformal antennas array [1] and the increasing interest in their applications is due to several reasons. Amongst the most common we might mention: approaches based on constrained least square approaches [11,12,13], methods imposing convexity constraints so leading to a convex programming problem [14,15], techniques exploiting linear programming [16], the numerical optimization of non-quadratic cost functional either by vector space projections onto convex set [17] or by stochastic methods [18,19] (sometimes applied to simplified array excitation model [20]), and ad hoc semi-analytical method [21]
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