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

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.

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

In this paper, 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.