Direction of Arrival Estimation by Convex Optimization Methods With Unknown Sensor Gain and Phase

Direction of arrival (DOA) estimation performance severely degrades for the reasons that the perturbation from their assumed nominal complex gain values in practical sensor system. In this paper, to mitigate the effects of the uncertainty perturbation, a two-step method for joint DOAs and sensor errors estimation is proposed. In the first step, convex optimization and l
₁
norm penalties are used to conduct a second-order cone framework to estimate DOAs roughly under the assumption that all sensor gains are identity. Second, we calibrate the perturbed gains with the DOAs estimated by the first step. The iterative process of the DOAs and gains estimation is taken until convergence. Furthermore, a refinement procedure is addressed to alleviate the effects of the grid limitations to spatial locations. In the present method, no auxiliary calibrated sensors or co-operation signal source is required. And the two-step method can handle both uncorrelated signals and coherent signals, it is also a high resolution method and robust in the condition of low signal-to-noise ratio (SNR). Several aspects are taken into consideration, and numerical experimental results are given to show the advantages of the new method for the DOA estimation.