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

• Published in: IEEE transactions on signal processing Vol. 70; p. 1
• Main Authors: Mao, Zihuan, Liu, Shengheng, Zhang, Yimin D., Han, Leixin, Huang, Yongming
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Arrays; atomic norm; coprime array; Covariance matrices; Covariance matrix; degree-of-freedom; Direction of arrival; direction-of-arrival estimation; Estimation; frequency diverse array; Frequency diversity; Interpolation; Mathematical analysis; Minimization; Optimization; parameter estimation; Sensor arrays; Sensors; Signal processing algorithms
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2022.3173150

In this paper, we address the problem of joint direction-of-arrival (DoA) and range estimation using frequency diverse coprime array (FDCA). By incorporating the coprime array structure and coprime frequency offsets, a two-dimensional space-frequency virtual difference coarray corresponding to uniform array and uniform frequency offset is considered to increase the number of degrees-of-freedom (DoFs). However, the reconstruction of the doubly-Toeplitz covariance matrix is computationally prohibitive. To solve this problem, we propose an interpolation algorithm based on decoupled atomic norm minimization (DANM), which converts the coarray signal to a simple matrix form. On this basis, a relaxation-based optimization problem is formulated to achieve joint DoA-range estimation with enhanced DoFs. The reconstructed coarray signal enables application of existing subspace-based spectral estimation methods. The proposed DANM problem is further reformulated as an equivalent rank-minimization problem which is solved by cyclic rank minimization. This approach avoids the approximation errors introduced in nuclear norm-based approach, thereby achieving superior root-mean-square error which is closer to the Cramer-Rao bound. The effectiveness of proposed method is confirmed by theoretical analyses and numerical simulations.