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This paper deals with the problem of estimating the position of a user equipment operating in a wireless communication network. We present a new positioning method based on the angles of arrival (AOA) measured in several radio links between that user equipment and different base stations. The proposed AOA-based method leads us to a non-iterative closed-form solution of the positioning problem, and an statistical analysis of that solution is also included. The comparison between this method and the classical AOA-based positioning technique is discussed in terms of computational load, convergence of the solution and also in terms of the bias and variance of the position estimate.