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A new method for the synthesis of low sidelobe beampatterns is presented, which enables beamwidth and sidelobe level to be adjusted with relative independence. Unlike existing methods for the synthesis of arbitrary beampatterns, the proposed method is based on a modification of the Dolph-Chebyshev design and requires only a few parameters to be optimized, regardless of the array size. Due to its much lower complexity, the method is implementable in wireless communications applications requiring fast and cheap, adaptive algorithms for low sidelobe arrays. The method is applicable, for instance, to the design of adaptive sector-like antennas with uniform circular arrays (UCAs), and to the design of quasi-steering-invariant beampatterns with uniform linear arrays (ULAs).