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In this paper, a low computational complexity rank reduce (RARE) algorithm based on 2-D nested array is proposed for direction of arrival (DOA) estimation in massive multiple-input multiple-output system. By utilizing the difference co-array of the 2-D nested array, one can obtain O(N<sup>2</sup>) virtual sensors with only N actual sensors, which can enable us to detect more number of sources than sensors. However, the large number of sensors would lead to huge computation burden, such as 2-D spectrum searching, for DOAs estimation of user's equipment. To overcome this problem, the RARE algorithm enjoying simple implementation is derived based on 2-D nested array. Instead of finding the solutions in 2-D observation space, the proposed method can solve the problem with two 1-D functions, which would reduce computational burden dramatically. Then by extending the original manifold to a larger set in the observation space, it would be much easier to obtain the solutions. Besides, the estimated azimuth and elevation angles can be paired automatically. The simulation results demonstrate the validity of the proposed method.

A RARE Algorithm for 2D DOA Estimation Based on Nested Array in Massive MIMO System