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A generic direction of arrival (DoA) estimation methodology is presented that is based on neural networks (NNs) and designed for a switched-beam system (SBS). The method incorporates the benefits of NNs and SBSs to achieve DoA estimation in a less complex and expensive way compared to the corresponding widely known super resolution algorithms. The proposed technique is step-by-step developed and thoroughly studied and explained, especially in terms of the beam pattern structure and the neuro-computational procedures. Emphasis is given on the direct sequence code division multiple access (DS-CDMA) applications, and particularly the Universal Mobile Telecommunication System (UMTS). Extensive simulations are realized for each step of the method, demonstrating its performance. It is shown that a properly trained NN can accurately find the signal of interest (SoI) angle of arrival at the presence of a varying number of mobile users and a varying SoI to interference ratio. The proposed NN-SBS DoA estimation method can be applied to current cellular communications base stations, promoting the wider use of smart antenna beamforming.