Direction of arrival (DoA) estimation of high-resolution beams is critical for cell search and maintaining communication in millimeter wave (mmWave) cellular systems. All-digital solutions for DoA estimation, however desirable for their flexibility and performance, are impractical because of their use of high-speed, power hungry Analog-Digital Converters (ADCs) at each antenna element. In this paper we take a novel approach to formulate a fully digital DoA estimation solution. Our method utilizes mmWave propagation characteristics to properly design a pilot signal that enables the reduction of the ADC speed and the number of antenna by a significant amount while achieving a desired performance goal. Our proposed method applies subspace-based methods like MUSIC on the heavily subsampled received signals, and performs the DoA estimation on a small subset of the dominant multi-paths in the channel one at a time, thus maintaining the integrity of the DoA estimation algorithm while significantly reducing computational complexity.