Direction-of-arrival (DOA) estimation for arbitrary array structures in the presence of mutual coupling (MC) is an important problem for antenna arrays. Previous methods in the literature are usually proposed for certain array geometries and show limited performance at low SNR or for small number of snapshots. In this paper, compressed sensing is used to exploit the joint-sparsity of the array model to estimate both DOA and MC coefficients with a single snapshot for an unstructured array where the antennas are placed arbitrarily in space. A joint-sparse recovery algorithm for a single snapshot (JSR-SS) is presented by embedding the source DOA angles and MC coefficients into a joint-sparse vector. A dictionary matrix is defined by considering the symmetricity of the MC matrix for the unstructured antenna array. The proposed method is extended to the multiple snapshots, and the joint-sparse recovery algorithm with multiple snapshots (JSR-MS) is developed. A new joint-sparsity structure, namely, joint-block-sparsity is introduced to take advantage of the structure in the composite matrix involving both DOA and MC coefficients. 1-D and 2-D DOA estimation performance of the proposed methods is provided in comparison to the conventional sparse recovery techniques, subspace methods, and the Cramer-Rao lower bound. It is shown that the proposed methods perform significantly better than the alternative methods. (C) 2016 Elsevier Inc. All rights reserved.