This paper presents an efficient gridless sparse reconstruction algorithm for the coprime planar array in two-dimensional (2-D) direction-of-arrival (DOA) estimation problem. According to the equivalent second-order statistic signals derived from the covariance matrix of the coprime planar array, we construct a virtual 2-D difference co-array extended from the coprime line arrays along two directions. The virtual array has a double-sized array aperture leading to an increased number of degree-of-freedoms (DOFs). To address the discontinuity of the virtual planar array, and to reduce the computation complexity for the increased array size, decoupled atomic norm minimization approach is investigated to interpolate the missing sensors without discarding any virtual sensors. The problem of decoupled atomic norm minimization can be solved by semidefinite programming with significantly lower computational cost. Besides, the ratio of the number of missing sensors to full sensors in the interpolated virtual uniform array is smaller than that of the physical coprime array, which further improves the recovery accuracy of decoupled atomic norm minimization algorithm. The numerical examples are provided to demonstrate the practical ability of the proposed method in terms of DOF, computational complexity, and DOA estimation error. INDEX TERMS Coprime planar array, decoupled atomic norm, direction-of-arrival (DOA), degree-of-freedom (DOF).

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Two-dimensional (2D) direction-of-arrival (DOA) estimation with arbitrary planar sparse array has attracted more interest in massive multiple-input multiple-output application. The research on this issue recently has been advanced with the development of atomic norm technique, which provides super resolution methods for DOA estimation, when the number of snapshots is limited. In this paper, we study the problem of 2D DOA estimation from the sparse array with the sensors randomly selected from uniform rectangular array. In order to identify all azimuth and elevation angles of the incident sources jointly, the 2D atomic norm approach is proposed, which can be solved by semidefinite programming. However, the computational cost of 2D atomic norm is high. To address this issue, our work further reduces the computational complexity of the problem significantly by utilizing the atomic norm approximation method based on the concept of multiple measurement vectors. The numerical examples are provided to demonstrate the practical ability of the proposed method to reduce computational complexity and retain the estimation performance as compared to the competitors.

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