In antenna array based radar applications, it is often desirable to choose an optimum subarray from a full array to achieve a balance between hardware cost and resolution. Moreover, in a cognitive radar system, the sparse subarrays are chosen based on the target scenario at that instant. Recently, a deep-learning based antenna selection technique was proposed for a single target scenario. In this paper, we extend this approach to multiple targets and assess the performance of state-of-the-art direction of arrival estimation techniques in conjunction with the proposed antenna selection method. To optimally choose the subarrays based on the target DOAs, we design a convolutional neural network which accepts the array covariance matrix as an input and selects the best sparse subarray that minimizes the error. Once the optimum sparse subarray is obtained, the signals from the selected antennas are used to estimate the DOAs. We provide numerical simulations to validate the performance of the proposed cognitive array selection strategy. We show that the proposed approach outperforms random sparse antenna selection and it leads to a higher DOA estimation accuracy by 6 dB.