Massive multiple input multiple output(MIMO)based fully-digital receive antenna arrays bring huge amount of complexity to both traditional direction of arrival(DOA) estimation algorithms and neural network training, which is difficult to satisfy high-precision and low-latency applications in future wireless communications. To address this challenge, two estimators called OPSC and OSAP-CBAM-CNN are proposed in this paper. The computational complexity of the traditional DOA algorithm is first considered to be reduced by dividing the total set of antennas into multiple overlapped subarrays uniformly, each subarray crosses each other proportionally and performs DOA estimation to generate coarse angles, and all angles are coherently combined to get the better estimation, the final DOA estimation can given by maximum likelihood alternating projection(ML-AP) in a very small range, which has a better performance than the direct partitioning of subarrays. To further reduce the complexity of traditional estimation algorithms, deep neural networks(DNN) are utilized to offline train the relationship between the received signal covariance matrix and the estimated angles. Due to the high complexity of the training network based on large-scale arrays, in the OSAP-CBAM-CNN method, the complex network is divided into several smaller networks based on the overlapped subarray to give rough DOA estimations, followed by coherent combining and AP algorithm to get the final DOA estimation. Simulation results show that as the number of antennas goes to large-scale, the proposed methods can achieve a remarkable complexity reduction over conventional ML-AP algorithm.