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A novel full-space scanning periodic phase-reversal leaky-wave antenna array is proposed, designed in offset parallel stripline technology, and demonstrated experimentally. This antenna radiates from its small phase-reversing cross-overs, which leads to a small leakage factor and subsequently a large directivity. The operation principle of the antenna is explained from the Brillouin diagram, which shows how single-beam scanning, using the m = -1 space harmonic, is achieved as a result of the π lateral shift of the dispersion curves due to phase reversal. One of the benefits of phase reversal is to permit this radiation performance with relatively small permittivity substrates (εe,min = 4 compared to εe,min = 9 for antennas without phase reversal). An unitcell matching technique is applied to avoid reflections, and thereby prevent the presence of an open stopband so as to permit continuous space scanning with efficient broadside radiation. An efficient array synthesis procedure, based on a transmission line modeling of the structure, is utilized for the design of the antenna following specifications in terms of frequency, scanning, directivity, radiation efficiency, and sidelobe level. A uniform-aperture antenna prototype, including a balun-transformer input transition, is presented, featuring experimental beamwidth and gain at the broadside frequency (25 GHz) of 4° and 15.7 dBi, respectively.