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.

翻译：我们从多臂赌博机(MABs)中最佳臂识别角度研究毫米波网络的初始波束获取问题。针对静止环境，提出一种名为并发波束探索(CBE)的新算法，该算法根据波束索引对多个波束进行分组并同时激活以检测用户存在性，随后采用汉明译码策略识别最佳波束。对于正交且高度定向的窄波束场景，我们以波束组(BG)内漏检概率和虚警概率为指标表征CBE性能。基于此，推导出波束选择错误概率，并证明CBE在此指标上优于现有最优策略。针对突变环境（如移动遮挡情况），我们刻画了经典顺序二分(SH)算法的性能特征。具体而言，推导了波束选择错误呈指数级有界时变化分布所需满足的条件。当变化局限于部分波束时，设计了一种名为K-顺序二分穷举搜索(K-SHES)的策略，相较于SH算法显著提升了波束选择错误的界值。该策略在因信道条件突变导致近最优波束在波束选择过程中变为最优波束时尤为有效。最后，通过将该方案应用于串联波束细化与数据传输中，验证了所提方法的有效性。