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A low-cost leaky-wave antenna using cylindrical surface waves propagating on a grounded dielectric slab is proposed. The excited surface waves are then perturbed into a leaky-wave regime, by the addition of annular microstrip-based (“bull-eye”) gratings. Various surface-wave modes may be considered, however, we desire to achieve radiation from the fundamental TM0 mode due to its zero cutoff frequency and possibility for efficient excitation. A comprehensive design strategy is detailed in the paper. It is based on both an accurate knowledge of the modal spectrum, obtained with the method of moments, and an analysis of the resonant modes supported by the constituent microstrip rings. To further support our methodology, numerical calculations, full-wave simulations, and antenna measurements are reported for the basic structure. Also, additional designs for enhanced gain at broadside, reduced cross-polarization levels, and improved wide-angle frequency beam scanning are presented.