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A log-periodic dielectric resonator antenna for possible wideband operation is considered. The proposed design consists of seven dielectric resonators (DRs) of rectangular cross-sections using a low-cost Teflon-based dielectric material with low permittivity. It has a multilayer configuration, where the DRs and feeding line are located at different layers. For ease of fabrication, the radiators are excited by an overlaid microstrip feed line on the first layer. Different characteristics such as S-parameters, gain, input impedance and radiation patterns of the proposed design are studied. The fabricated prototype exhibits a gain of 6 dBi (or better) over a wideband of 6.5-11.3 GHz with |S11| less than - 10 dB. The results from the simulation are found to closely follow those of the fabricated prototype.