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Positioning algorithms in cellular networks has become increasingly important as a means of supporting emerging services that require a sufficiently precise estimation of the position of the mobile terminal (MT) associated with a given base station (BS). Currently, even the most sophisticated positioning algorithms require at least three BSs to achieve satisfactory precision. This paper presents a novel algorithm that makes use of a single-BS antenna array to locate MTs in cellular networks. A triangulation technique is utilized and supported by some minimal information about the environment in the BS neighborhood. This algorithm is shown to perform well when operating in a microcellular environment with perfect channel-parameter estimation. The effect of finite resolution of the input parameters is also investigated. The performance is analyzed for a universal mobile telecommunications system microcellular scenario through a three-dimensional deterministic channel model. Finally, the performance of the proposed positioning technique is compared to the well-known location method based on the time-of-arrival measurements at three different BSs.