Massive multiple-input multiple-output (MIMO) systems equipped with a high number of antenna elements are becoming one of the most exciting emerging technologies in next-generation wireless communication systems. The use of a high number of anten-nas makes it challenging to implement separate radio frequency front-end circuits for each antenna due to hardware cost and power consumption restrictions. To make massive MIMO feasible, an ef-ficient solution is to perform hybrid beamforming that compresses the received signals at the MIMO receiver before the signals are dig-itized. We have proposed optimized compressive measurement by maximizing the mutual information between the compressed mea-surement and the signal directions-of-arrival (DOAs) by utilizing a coarse a priori probability distribution of the signal DOAs. Despite its superior performance to effectively reduce the number of required front-end circuits, the requirement of a coarse a priori distribution of signal DOAs makes it difficult to apply in some situations where such information is unavailable. In this paper, we propose a data-driven approach based on neural network to iteratively update the signal DOA distribution. The neural network estimate signal DOA spectrum, which is then fed back to refine the prior information, thereby making this method practical even in the situations where no prior information of the signal DOAs is available.