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We investigate the capabilities of reduced-size integrated lens antennas to produce flat-top radiation patterns for broadband wireless communication systems at millimeter waves. The main challenge consists in controlling accurately the lens radiation performance over a broad frequency band while reducing its size; this constitutes a difficult task since producing highly shaped beams usually leads to oversized lens antennas. The design procedure is based on the geometrical optics/physical optics method (GO/PO), and the antenna characteristics are confirmed by full-wave simulations since the antenna size is only a few wavelengths. Our numerical results demonstrate that one anti-reflection coating is necessary even if the lens is made in a low-permittivity material (Rexolite). The resulting double-shell dielectric lens antenna has been fabricated and measured. The experimental results are in very good agreement with the simulations, and the radiation characteristics are stable over a 14% relative bandwidth, which is enough for broadband communications at millimeter waves.