An Eigenstructure Method for Estimating DOA and Sensor Gain-Phase Errors

In this paper, we consider the problem of direction of arrival (DOA) estimation in the presence of sensor gain-phase errors. Under some mild assumptions, we propose a new DOA estimation method based on the eigendecomposition of a covariance matrix which is constructed by the dot product of the array output vector and its conjugate. By combining the new DOA estimation with the conventional gain-phase error estimation, a method is proposed to simultaneously estimate the DOA and gain-phase errors without joint iteration. Theoretical analysis shows that the proposed method performs independently of phase errors and thus behaves well regardless of phase errors. However, the resolution capability of the proposed method is lower than that of the method in [A. J. Weiss and B. Friedlander, “Eigenstructure methods for direction finding with sensor gain and phase uncertainties,” Circuits Systems Signal Process., vol. 9, no. 3, pp. 271-300, 1990], named as the WF method. In order to improve the resolution capability and maintain phase error independence, a combined strategy is developed using the proposed and WF methods. The advantage of the proposed methods is that they are independent of phase errors, leading to the cancellation of phase error calibration during the operation life of an array. Moreover, the proposed methods avoid the problem of suboptimal convergence which occurs in the WF method. The drawbacks of the proposed methods are their high computational complexity and their requirement for the condition that at least two signals are spatially far from each other, and they are not applicable to a linear array. Simulation results verify the effectiveness of the proposed methods.