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

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. INDEX TERMS Coprime planar array, decoupled atomic norm, direction-of-arrival (DOA), degree-of-freedom (DOF).

Joint DoA-Range Estimation Using Space-Frequency Virtual Difference Coarray

“…Remark 4: If we consider a multiple measurement vector (MMV) form of the virtual signal [29], the covariance-based formulation and similar DANM methods [36] can also be developed. To further reduce the computational complexity, the methodology of compressed sensing can be combined with DANM [37].…”

“…In the second set of simulations, statistical results in terms of the RMSE are used to compare the estimation accuracy of CMT-BCS, SST, DANM and CRM. The covariance-based DANM methods, normal DANM (NDANM) [36], and low rank structured covariance reconstruction DANM (LRSCR-DANM) [37] are also included for comparison. The RMSE of a certain parameter ξ is defined as…”

A Two-Dimensional Direction Finding Method Based on Non-Uniform Array

“…Therefore, in the case of having many array elements and a large number of snapshots, the amount of calculation from the ESPRIT algorithm to solve the CM and EVD operations will increase significantly. In recent years, new twodimensional DOA estimation methods based on the L-shaped array have been proposed [20][21][22][23][24][25][26][27][28][29][30][31], such as the joint singular value decomposition (JSVD) algorithm [20], the cross correlation matrix ESPRIT (CCM-ESPRIT) algorithm [21], the joint angle estimation algorithm for finding the root of polynomials [22], and the improved PM algorithm for twodimensional L-shaped arrays [23]. In [24], an algorithm that uses two parallel nested arrays was proposed.…”

“…A method that can effectively estimate the coherent signal received by the coprime array is proposed in [25], which uses the Toeplitz matrix and the nuclear norm minimization problem to analyze the coherent signal. In reference to the DOA estimation problem of a two-dimensional coprime planar array, Lu proposed a meshless sparse reconstruction algorithm using decoupled atomic norm minimization theory, which reduces the complexity of the algorithm [26]. In [27], a fast-convergent trilinear decomposition method is applied to the two-dimensional DOA estimation of multiple signals of a generalized coprime planar array composed of two rectangular uniform planar sub-arrays problem, which has good estimation performance.…”

Two-Dimensional Separable Gridless Direction-of-Arrival Estimation Based on Finite Rate of Innovation

“…A decoupled ANM model is established to reduce the dimension of positive semidefinite matrix, and successfully applied in the field of spectrum estimation, which can be regarded as the DOA estimation problem in the case of single snapshot [18]. In [19], the decoupled ANM model is extended to the case of multi snapshots, and combined with coprime planar array (CPPA), which can effectively increase the degree of freedom (DOF) and improve the estimation accuracy as a result of expanding the array aperture.…”