Underdetermined Direction-of-Arrival Estimation with Coprime Array via Atomic Norm Minimization

The coprime array provides the possibility of resolving more signals than the sensors for the direction-of-arrival (DOA) estimation application. However, the non-consecution of its virtual array raises challenges for making full use of the degree of freedom (DOF). In this paper, we propose a new underdetermined DOA estimation method with coprime array where the non-consecutive virtual array can be converted into a virtual uniform linear array (ULA) with the same aperture. Firstly, all elements in the vectorized signal covariance matrix corresponding to the same virtual array positions are averaged to construct the output signals of the virtual array. Then, an atomic norm minimization (ANM) based optimization problem is formed for denoising the output signals of the virtual array and for interpolating the missing signals at the virtual array holes. At last, the ANM problem is solved by the semidefinite programming (SDP) and the DOAs are obtained by applying the subspace method on the reconstructed signal covariance matrix of the interpolated virtual ULA. The proposed algorithm is gridless and makes full use of the DOF and the information provided by the coprime array. The simulation results compared with the other representative methods are given to demonstrate the superiority of the proposed method with respect to the resolution and estimation accuracy.