Efficient Gridless 2-D Direction-of-Arrival Estimation for Coprime Array Based on Decoupled Atomic Norm Minimization

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.