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A system to measure the direction of arrival (DOA) of a signal within a 45-degree conical sector is demonstrated. The system is compact and uses only four circularly polarized patch elements. A printed beamforming network is used to create a set of partially overlapping beams allowing DOA estimation without ambiguity. Neural networks are used to first classify the antenna signals and then estimate the DOA. The proposed system was validated experimentally in C band and, in spite of the highly disturbed beams caused by the finite size of the antenna platform, it was shown that DOA estimation errors in the order of one degree were achievable under signal-to-noise ratios of 10 dB.