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In this paper, a convex-optimization based design method is proposed to solve the near-field beamformer design problem for improving the performance of an MRI system. The aim is to find the minimum number of antennas required for a uniform circular array which is capable of forming a beam with a pre-defined sidelobe attenuation level for an arbitrary focal point within a given circular scanning area. The minimax criterian (minimizing the maximum response at the sidelobe region) is employed in the design. Design examples have shown that the proposed method can solve the problem successfully.