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In this paper, we present multiple techniques for phase-based narrowband backscatter tag localization in three-dimensional space with planar antenna arrays or synthetic apertures. Beamformer and MUSIC localization algorithms, known from near-field source localization and direction-of-arrival estimation, are applied to the 3D backscatter scenario and their performance in terms of localization accuracy is evaluated. We discuss the impact of different transceiver modes known from the literature, which evaluate different send and receive antenna path combinations for a single localization, as in multiple input multiple output (MIMO) systems. Furthermore, we propose a new Singledimensional-MIMO (S-MIMO) transceiver mode, which is especially suited for use with mobile robot systems. Monte-Carlo simulations based on a realistic multipath error model ensure spatial correlation of the simulated signals, and serve to critically appraise the accuracies of the different localization approaches. A synthetic uniform rectangular array created by a robotic arm is used to evaluate selected localization techniques. We use an Ultra High Frequency (UHF) Radiofrequency Identification (RFID) setup to compare measurements with the theory and simulation. The results show how a mean localization accuracy of less than 30 cm can be reached in an indoor environment. Further simulations demonstrate how the distance between aperture and tag affects the localization accuracy and how the size and grid spacing of the rectangular array need to be adapted to improve the localization accuracy down to orders of magnitude in the centimeter range, and to maximize array efficiency in terms of localization accuracy per number of elements.