  We study the initial beam acquisition problem in millimeter wave (mm-wave)
networks from the perspective of best arm identification in multi-armed bandits
(MABs). For the stationary environment, we propose a novel algorithm called
concurrent beam exploration, CBE, in which multiple beams are grouped based on
the beam indices and are simultaneously activated to detect the presence of the
user. The best beam is then identified using a Hamming decoding strategy. For
the case of orthogonal and highly directional thin beams, we characterize the
performance of CBE in terms of the probability of missed detection and false
alarm in a beam group (BG). Leveraging this, we derive the probability of beam
selection error and prove that CBE outperforms the state-of-the-art strategies
in this metric.
  Then, for the abruptly changing environments, e.g., in the case of moving
blockages, we characterize the performance of the classical sequential halving
(SH) algorithm. In particular, we derive the conditions on the distribution of
the change for which the beam selection error is exponentially bounded. In case
the change is restricted to a subset of the beams, we devise a strategy called
K-sequential halving and exhaustive search, K-SHES, that leads to an improved
bound for the beam selection error as compared to SH. This policy is
particularly useful when a near-optimal beam becomes optimal during the
beam-selection procedure due to abruptly changing channel conditions. Finally,
we demonstrate the efficacy of the proposed scheme by employing it in a tandem
beam refinement and data transmission scheme.
