Superresolution 2D DOA Estimation for a Rectangular Array via Reweighted Decoupled Atomic Norm Minimization

Abstract

This paper proposes a superresolution two-dimensional (2D) direction of arrival (DOA) estimation algorithm for a rectangular array based on the optimization of the atomic l0 norm and a series of relaxation formulations. The atomic l0 norm of the array response describes the minimum number of sources, which is derived from the atomic norm minimization (ANM) problem. However, the resolution is restricted and high computational complexity is incurred by using ANM for 2D angle estimation. Although an improved algorithm named decoupled atomic norm minimization (DAM) has a reduced computational burden, the resolution is still relatively low in terms of angle estimation. To overcome these limitations, we propose the direct minimization of the atomic l0 norm, which is demonstrated to be equivalent to a decoupled rank optimization problem in the positive semidefinite (PSD) form. Our goal is to solve this rank minimization problem and recover two decoupled Toeplitz matrices in which the azimuth-elevation angles of interest are encoded. Since rank minimization is an NP-hard problem, a novel sparse surrogate function is further proposed to effectively approximate the two decoupled rank functions. Then, the new optimization problem obtained through the above relaxation can be implemented via the majorization-minimization (MM) method. The proposed algorithm offers greatly improved resolution while maintaining the same computational complexity as the DAM algorithm. Moreover, it is possible to use a single snapshot for angle estimation without prior information on the number of sources, and the algorithm is robust to noise due to its iterative nature. In addition, the proposed surrogate function can achieve local convergence faster than existing functions.

Efficient Super-Resolution Two-Dimensional Harmonic Retrieval With Multiple Measurement Vectors

“…Remark 3: Although the separation and sampling conditions introduced for RR-D-ANM-R are more restrictive than those of RR-D-ANM, V-ANM and LRSCR, RR-D-ANM-R is the most computationally efficient. Moreover, when the separation and sampling conditions are too strict, the reweighted ANM techniques [51], [52] can be employed in RR-D-ANM-R to enhance the sparsity and resolution. Note in this context that the separation conditions for gridless CS methods are usually more restrictive than those of classical statistical subspace methods, while the former are more sample efficient than the latter.…”

A 2D-DOA Sparse Estimation Method with Total Variation Regularization for Spatially Extended Sources

“…Estimation of the direction of arrival is an important research issue in array signal processing, which has been widely used in radar, sonar, speech processing, and wireless communication [1][2][3][4][5][6]. At present, the main azimuth estimation methods can be divided into subspace algorithm [7], maximum likelihood algorithm [8], sparse reconstruction algorithm [9], and beamforming algorithm [10,11].…”

Crosscorrelation and DOA Estimation for L‐Shaped Array via Decoupled Atomic Norm Minimization

“…The problem of two-dimensional (2D) direction-of-arrival (DOA) estimation plays an important role in array signal processing and has attracted much interest in the area of wireless communications, radar and sonar [1][2][3][4][5][6][7]. For 2D DOA estimation, many array structures, such as rectangular arrays, circular arrays, and L-shaped arrays, have been developed.…”