Rank Minimization-Based Toeplitz Reconstruction for DoA Estimation Using Coprime Array

• Published in: IEEE communications letters Vol. 25; no. 7; pp. 2265 - 2269
• Main Authors: Liu, Shengheng, Mao, Zihuan, Zhang, Yimin D., Huang, Yongming
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Arrays; convex optimization; Covariance matrices; Covariance matrix; Direction finding; Direction of arrival; direction of arrival (DoA); Direction-of-arrival estimation; Estimation; Minimization; Optimization; parameter estimation; Reconstruction; Sensor arrays; Sensors; sparse array; Spatial resolution; Toeplitz matrix
• ISSN: 1089-7798; 1558-2558
• DOI: 10.1109/LCOMM.2021.3075227

In this letter, we address the problem of direction finding using coprime array, which is one of the most preferred sparse array configurations. Motivated by the fact that non-uniform element spacing hinders full utilization of the underlying information in the receive signals, we propose a direction-of-arrival (DoA) estimation algorithm based on low-rank reconstruction of the Toeplitz covariance matrix. The atomic-norm representation of the measurements from the interpolated virtual array is considered, and the equivalent dual-variable rank minimization problem is formulated and solved using a cyclic optimization approach. The recovered covariance matrix enables the application of conventional subspace-based spectral estimation algorithms, such as MUSIC, to achieve enhanced DoA estimation performance. The estimation performance of the proposed approach, in terms of the degrees-of-freedom and spatial resolution, is examined. We also show the superiority of the proposed method over the competitive approaches in the root-mean-square error sense.