The paper is dedicated to the multipath angle of arrival (AOA) estimation problem in millimeter wave (mmWave) 5G NR communication system. The case of a phased antenna array with a single digital port is considered. In this scenario, the conventional highly accurate subspace-based algorithms cannot be applied because of hardware restrictions. We proposed a novel subspace-based algorithm called power-based root minimal polynomial method (PR-MPM) that uses the spatial power spectrum to get an approximation of the signal correlation matrix. The power spectrum is measured via the conventional beam sweeping procedure over a finite number of directions. The efficiency of the proposed method is studied using the high-realistic ray-tracing-based channel model applied in mmWave IEEE 802.11ay standard. Simulation results show that AOAs can be precisely estimated using only single-port power measurement.