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Based on the rank reduction theory (RARE), a decoupled method for 2D direction of arrival (DOA) estimation in the presence of elevation-dependent mutual coupling is proposed for compact uniform circular arrays (UCAs). Using a new formulation of the beamspace array manifold in the presence of mutual coupling, the azimuth estimates are decoupled from the elevation estimates and obtained with no need for the exact knowledge of mutual coupling. For the elevation estimation, a 1D parameter search in the elevation space for every azimuth estimate is performed with the elevation-dependent mutual coupling effect compensated efficiently. Though the computational load for the elevation estimation is increased compared to that of the original UCA-RARE algorithm, the 1D parameter search in our method overcomes most of the inherent shortcomings of the UCA-RARE algorithm. This enables unambiguous and paired 2D DOA estimation with the elevation-dependent mutual coupling effect being compensated for effectively. Numerical examples are presented to demonstrate the effectiveness of the proposed method.