Abstract: The signal direction of arrival (DOA) estimation is studied based on the sparse reconstruction of the single snapshot array output. A novel single snapshot based signal DOA estimation algorithm named as iterative implementation of MMSE (II-MMSE) algorithm is proposed based on the iterative implementation of minimum mean-square (MMSE) error criterion. The II-MMSE algorithm converts the solution procedure of sparse signal vector into iteratively solving the sparse power diagonal matrix, and then estimates the signal DOA. The detailed algorithm flow of II-MMSE is summarized. The convergence of the II-MMSE algorithm and its robustness to array modeling errors are analyzed theoretically. Simulation results demonstrate that the proposed II-MMSE algorithm performs well in direction finding accuracy and multiple targets resolution under the conditions of low signal-to-noise ratio, coherent background, limited samples, and uncalibrated sensor array.