  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.
