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A dielectric cover is used to enhance the gain of an aperture-coupled microstrip patch antenna. The cover is spaced off of the patch antenna by air and, as expected, is found to significantly increase antenna broadside directivity in some configurations. A parametric study on the effects of spacing height, cover size, and thickness of the cover are presented. This study uses a finite element method (FEM) based, commercial analysis tool to perform these parametric searches, and so accounts for finite size ground planes and dielectrics. The previous research work reported in literature considered infinite-area ground planes and dielectrics. The wide impedance matching bandwidth of the aperture-coupled microstrip patch also allows observation of the narrow-bandwidth effects of the added dielectric cover. Finally, a proposed design methodology is outlined, and a prototype of the antenna was fabricated and experimentally verified with a peak gain of 13.9 dBi. The measured results agree reasonably well with the simulated ones.