Abstract
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.
Highlights
The problem of two-dimensional (2-D) direction-of-arrival (DOA) estimation is encountered in a variety of array signal processing applications, such as radar, sonar, massive multiple-input multiple-output (MIMO) systems in 5G, etc
We propose a novel decoupled atomic norm minimization (ANM) approach based on the 2-D co-array model of covariance matrix, leading to an excellent performance
All simulations are carried out on the basis of the coprime array consisting of two sparse uniform rectangular arrays (URAs) with 3 × 3 and 5 × 5 elements respectively
Summary
The problem of two-dimensional (2-D) direction-of-arrival (DOA) estimation is encountered in a variety of array signal processing applications, such as radar, sonar, massive multiple-input multiple-output (MIMO) systems in 5G, etc In these systems, the 2-D planar array antennas provide the flexibilities of sources by jointly estimating the elevation and azimuth angles of incident signals [1]. Many researchers have done much effort on DOA estimation problems by some common classical methods, such as multiple signal classification (MUSIC) [2] and estimation of signal parameters via rotational invariance techniques (ESPRIT) [3] These investigations mainly focus on the DOA estimation application with L-shape arrays and uniform rectangular arrays (URAs) [4]–[6]. It is important to investigate algorithms to improve the performance of DOA estimation by utilizing the characteristics of co-array effectively
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