We develop a deep learning framework for Direction of Arrival (DOA) estimation. The sparse power spectrum inspires us, and the first shows that the columns of the array covariance matrix can be formulated as undersampled linear measurements of the spatial spectrum. Secondly, we introduce a Deep Neural Network (DNN) that learns potential inverse transformation from large training dataset. Our proposed DNN-based framework provides a larger aperture with a small number of antennas. Moreover, we reduce the hardware complexity and allow reconfig-urability of the receiver channels. Our solution is able to estimate a number of closely spaced targets larger than the number of receiver channels. Through numerical simulations, our proposed method overmatches the most advanced DOA estimation methods based on deep learning, particularly with limited snapshot and low signal-to-noise ratio (SNR) situations.