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Grid Evolution: An Iterative Reweighted Algorithm for Off-grid DOA Estimation with Gain/Phase Uncertainties

Conventional direction-of-arrival (DOA) estimation based on compressed sensing assumes that the true DOAs are on the discretized grid. However, the accuracy of DOA estimation will deteriorate since most DOAs don't lie on the grid. This problem is also called off-grid problem or grid mismatch. Besides the grid mismatch problem, another problem should not be overlooked is the existence of the sensors imperfections, such as the gain/phase uncertainties. In order to solve these problems, an iterative reweighted-total least squares (IR-TLS) DOA estimation method based on compressed sensing (CS) is proposed. Firstly, the original problem is transformed into a total least-squares (TLS) framework. An alternating descent algorithm is then developed. The DOAs are estimated and the grid is refined through an iterative reweighted method. Then the gain/phase uncertainties are updated with the estimated DOAs and refined grid through iterations. Simulation results are provided to show that the proposed IR-TLS method can help improving the accuracy of off-grid DOA estimation with less computational complexity.