In this paper, the problem of direction-of-arrival (DoA) estimation for a hybrid array of subarrays is considered in millimeter-wave communication systems. Unlike much prior work using the outputs from the analog subarrays with symbol-wise processing, the proposed framework jointly exploits multiple outputs in time domain for high-resolution DoA estimation. With block-wise processing, the proposed method designs an optimal hybrid combiner maximizing beamforming gain, while reducing a receiver complexity based on fast Fourier transform filtering for each blocked signal. The performance of the proposed method is analyzed, including estimation performance with a limited training signal, training overhead, and computational complexity. An extension of the proposed method to a uniform planar array case is also discussed. Numerical results show the effectiveness of the proposed algorithm.INDEX TERMS Millimeter-wave, DoA estimation, hybrid beamforming, array of subarrays I. INTRODUCTION