In array signal processing, the direction of arrivals (DOAs) of the received signals are estimated\nby measuring the relative phases among antennas; hence, the estimation performance is reduced\nby the inconsistency among antennas. In this paper, the DOA estimation problem of the uniform\nlinear array (ULA) is investigated in the scenario with phase errors among the antennas, and a\ndiagonal matrix composed of phase errors is used to formulate the system model. Then, by using the\ncompressed sensing (CS) theory, we convert the DOA estimation problem into a sparse reconstruction\nproblem. A novel reconstruction method is proposed to estimate both the DOA and the unknown\nphase errors, iteratively. The phase errors are calculated by a gradient descent method with the\ntheoretical expressions. Simulation results show that the proposed method is cost-efficient and\noutperforms state-of-the-art methods regarding the DOA estimation with unknown phase errors.
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