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A uniplanar leaky-wave antenna (LWA) suitable for operation at millimeter-wave frequencies is introduced. Both unidirectional and bidirectional versions of the antenna are presented. The proposed structure consists of a coplanar waveguide fed linear array of closely spaced capacitive transverse slots. This configuration results in a fast-wave structure in which the n=0 spatial harmonic radiates in the forward direction. Since the distance, d, between adjacent elements of the array is small d≪λo, the slot array essentially becomes a uniform LWA. A comprehensive transmission line model is developed based upon the theory of truncated periodic transmission lines to explain the operation of the antenna and provide a tool for its design. Measured and simulated radiation patterns, directivity, gain, and an associated loss budget are presented for a 32-element antenna operating at 30 GHz. The uniplanar nature of the structure makes the antenna appropriate for integration of shunt variable capacitors such as diode or micro-electromechanical system varactors for fixed frequency beam steering at low-bias voltages.