  This paper proposes a deep learning approach to the adaptive and sequential
beamforming design problem for the initial access phase in a mmWave environment
with a single-path channel. For a single-user scenario where the problem is
equivalent to designing the sequence of sensing beamformers to learn the angle
of arrival (AoA) of the dominant path, we propose a novel deep neural network
(DNN) that designs the adaptive sensing vectors sequentially based on the
available information so far at the base station (BS). By recognizing that the
AoA posterior distribution is a sufficient statistic for solving the initial
access problem, we use the posterior distribution as the input to the proposed
DNN for designing the adaptive sensing strategy. However, computing the
posterior distribution can be computationally challenging when the channel
fading coefficient is unknown. To address this issue, this paper proposes to
use an estimate of the fading coefficient to compute an approximation of the
posterior distribution. Further, this paper shows that the proposed DNN can
deal with practical beamforming constraints such as the constant modulus
constraint. Numerical results demonstrate that compared to the existing
adaptive and non-adaptive beamforming schemes, the proposed DNN-based adaptive
sensing strategy achieves a significantly better AoA acquisition performance.
