  Communication in high frequencies such as millimeter wave and terahertz
suffer from high path-loss and intense shadowing which necessitates beamforming
for reliable data transmission. On the other hand, at high frequencies the
channels are sparse and consist of few spatial clusters. Therefore, beam
alignment (BA) strategies are used to find the direction of these channel
clusters and adjust the width of the beam used for data transmission. In this
work, a single-user uplink scenario where the channel has one dominant cluster
is considered. It is assumed that the user transmits a set of BA packets over a
fixed duration. Meanwhile, the base-station (BS) uses different probing beams
to scan different angular regions. Since the BS measurements are noisy, it is
not possible to find a narrow beam that includes the angle of arrival (AoA) of
the user with probability one. Therefore, the BS allocates a narrow beam to the
user which includes the AoA of the user with a predetermined error probability
while minimizing the expected beamwidth of the allocated beam. Due to
intractability of this noisy BA problem, here this problem is posed as an
end-to-end optimization of a deep neural network (DNN) and effects of different
loss functions are discussed and investigated. It is observed that the proposed
DNN based BA, at high SNRs, achieves a performance close to that of the optimal
BA when there is no-noise and for all SNRs, outperforms state-of-the-art.
