Radiation of a Circular Arc Source in a Limited Angle for Nonuniform Conformal Arrays

An inverse problem approach is adopted to investigate the role of a limited observation domain in conformal source radiation both in the far and near zones. The spectral decomposition of the relevant operator drives the investigation, especially by the discussion of the singular values' behavior and the point spread function (PSF). For a circular source geometry, accurate closed-form evaluations of the PSF allow to establish its angular variant behavior for limited observation angular domains. This leads to introducing a numerical procedure, based on the widths of the PSF main lobes, able to define an optimal source discretization, that is, the spacing of the array elements whose radiated field has the same number of degrees of freedom of the continuous conformal source. A nonuniform spacing is derived and the performances of the corresponding conformal arrays are compared with the uniform case, the number of elements being equal. Numerical results of pattern synthesis and array diagnostics of faulty elements support the improvement achieved by the approach when the same number of array elements are located in a nonuniform pattern.