Direction of arrival estimation for sparse arrays with gain-phase errors in nonuniform noise environment

The emerging sparse arrays achieve enhanced direction of arrival (DOA) estimation by flexibly deploying sensors and fully extracting the structural information contained in the incident sources. However, the existing DOA estimation algorithms for sparse arrays typically yield satisfactory performance only in ideal or single non-ideal scenarios. In this work, we address the issue of DOA estimation for sparse arrays under the coexistence of gain-phase errors and nonuniform noise. The analysis of the negative impact of these two types of non-idealities on virtual array processing motivates us to develop new algorithm. Specifically, with the perturbation of gain-phase errors, a least squares optimization program is first constructed to solve the nonuniform noise power. Then, based on the initial gain errors obtained by exploiting the diagonal entries in the denoised covariance matrix, we implement the iterative estimation of DOAs and gain-phase errors with the aid of the eigenstructure-based subspace approach. To improve the DOA estimation accuracy, we formulate the difference coarray interpolation problem and introduce the truncated nuclear norm minimization to recover the missing information. The developed algorithm can overcome the effects of gain-phase errors and nonuniform noise simultaneously. Numerical simulations demonstrate that the developed algorithm outperforms its competitors.