Abstract: The issue of single-snapshot direction of arrival (DOA) estimation is researched based on the sparse representation of array output model. In practical application, the number of targets is far less than the number of array elements, and the DOAs of signals are sparse in the space, so the conventional array output model can be reconstructed as a sparse representation model. The the single-snapshot DOA estimation algorithm based on the l₁-norm minimization (L1-min) is proposed. The algorithm translates the optimization problem of sparse parameters into a second-order cone programming (SOCP) framework. The selection criterion of the regularization parameters in this approach is analyzed. The proposed algorithm shows an improved robustness to limited snapshots, coherent sources, and closely spaced sources. Simulations show the effectiveness of the L1-min algorithm.