Compressed Sensing-Based DOA Estimation with Antenna Phase Errors

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