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A recent paper  has introduced a new class of dielectric resonator antennas (DRAs), the so-called supershaped DRAs (S-DRAs). This class of radiators took its name from the mathematical formula, known in literature as superformula (see  and references therein), that defines the geometry of the base of the dielectric prism acting as dielectric resonator (DR). S-DRAs feature wideband matching characteristics (with relative bandwidths exceeding 50%) and broadside radiation. Moreover, the radiation pattern of this family of DRAs can be varied by changing the DR shape such to become broad and rather stable over large frequency ranges. All these features, combined with the possibility of manufacturing S-DRAs in an inexpensive manner, suggest a possible application of these components in the realm of indoor communication. More specifically, such antennas could be used as access points for wireless local area networks supporting ultra wide band application. However, a closer look at the radiation properties of the S-DRAs has put in evidence the fact that some components of the radiated fields experience sharp notches along specific directions. This could cause severe fading effects in the radio channel in the case of using inexpensive receiving devices (e.g. mobile hand-held terminals). To mitigate this problem an improved version of a specific sub-set of S-DRAs is hereafter presented. The selection of DR cross-shapes having two symmetry planes allows for the excitation of two orthogonal and degenerate radiation modes that, combined, ensure circularly polarized radiated fields. A dual-point feed strategy (see , Ch. 7) is adopted to ensure broadband operation. Naturally, as means to ensure circularly polarized radiation, the two degenerate and orthogonal radiating modes are fed with synchronous time-harmonic signals of equal amplitude having an initial phase difference of 90°.