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In this letter, the problem of non-coherent direction of arrival (DOA) estimation is investigated exploiting the sign of the measurements in order to resolve the inherent ambiguity of the problem. Although the phase values are inaccurate, the sign of real and imaginary parts of the measurements will most likely remain correct under limited phase errors. Furthermore, a new approach for solving the problem is proposed employing a modified version of the Majorization-Minimization (MM) technique, without any prior information about the number of incident signals. Some theoretical analyses of our proposed algorithm are also provided in the paper. Finally, the simulation results are presented, demonstrating the efficiency of the proposed algorithm in comparison to some state-of-the-art methods in the literature. [ABSTRACT FROM AUTHOR]