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In this paper, some applications of metamaterial superstrates for directivity enhancement of cylindrical dielectric resonator antenna (CDRA) over curved ground plane are investigated. Three different types of superstrates, viz., split ring resonator (SRR), S-shape, and cubic high dielectric resonator (CHDR) are discussed. The metamaterial structure is used as a lens to improve the directivity of CDRA with small half-power beamwidth, wide impedance bandwidth, and matched input impedance. All analysis and simulations throughout this paper were carried out using the finite element method (FEM) and compared with that calculated with finite integration technique (FIT) method.