  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.
