In this paper, we investigate the problem of beam alignment in millimeter wave (mmWave) systems, and design an optimal algorithm to reduce the overhead. Specifically, due to directional communications, the transmitter and receiver beams need to be aligned, which incurs high delay overhead since without a priori knowledge of the transmitter/receiver location, the search space spans the entire angular domain. This is further exacerbated under dynamic conditions (e.g., moving vehicles) where the access to the base station (access point) is highly dynamic with intermittent on-off periods, requiring more frequent beam alignment and signal training. To mitigate this issue, we consider an online stochastic optimization formulation where the goal is to maximize the directivity gain (i.e., received energy) of the beam alignment policy within a time period. We exploit the inherent correlation and unimodality properties of the model, and demonstrate that contextual information improves the perfor 查看全文>>