In high-speed vehicular communications, e.g., a high-speed train system, the beam between the base station and user is frequently misaligned, resulting in a huge amount of associated overheads. As a result, beam alignment is often challenging. This paper presents a new approach to beam alignment in millimeter wave high-speed train systems. The core idea of our approach is using Bayesian multi-armed bandit (MAB) in the beam search process, where we refer to the beams as arms. Furthermore, there exists an unimodal structure of the mean received signal strength (referred to as mean rewards) over the available beams (or arms). To this end, we develop an algorithm named Bayesian-Best Arm with Unimodality (B-BAU) that identifies the best arm with high confidence within a fixed-budget by exploiting the unimodal structure of the mean rewards over the arms. In the proposed method, by approximating the signal on each beam direction as a Gaussian random variable, for the Gaussian rewards with a Gaussian prior, we show that the expected probability that B-BAU misidentifies the optimal arm is upper bounded as O (1/ √), where is the budget. We then develop an algorithm for its frequentist counterpart named F-BAU. We demonstrate that F-BAU and B-BAU outperform the state-of-the-art algorithms through extensive simulations. While F-BAU is parameter-free, B-BAU performs better with the prior information.

One of the core problems in millimeter wave (mmWave) massive multiple-input-single-output (MISO) communication systems, which significantly affects the data rate, is the misalignment of the beam direction of the transmitter towards the receiver. In this paper, we investigate strategies that identify the best beam within a fixed duration of time. To this end, we develop an algorithm, named Unimodal Bandit for Best Beam (UB3), that exploits the unimodal structure of the mean received signal strength as a function of the available beams and identifies the best beam within a fixed time duration using pure exploration strategies. We derive an upper bound on the probability of misidentifying the best beam, and we prove that the upper bound is of the order O (log 2 K exp {−αnA}), where K is the number of beams, A is a problem-dependent constant, and αn is the number of pilots used in the channel estimation phase. In contrast, when the unimodal structure is not exploited, the error probability is of order O (log 2 K exp {−αnA/(K log K)}). Thus, by exploiting the unimodal structure, we achieve a much better error probability, which depends only logarithmically on K. We demonstrate that UB3 outperforms the state-of-the-art algorithms through extensive simulations.