Beam Alignment and User Scheduling in mmWave Networks under Mobility

In this paper, we study beam alignment in a millimeter wave (mmWave) network with multiple users, and consider an optimal transmission scheduling algorithm. The problem is posed as an infinite horizon average cost constrained Markov decision process (CMDP) with the goal of minimizing the average beam alignment overhead subject to the average rate constraint on each user. By using a structural result derived from the Lagrangian formulation of the CMDP, we show that the optimal policy should keep scheduling the users that are scheduled in the previous time slot unless an abrupt change in the beam direction happens. Using this result, the complexity of the problem decreases to polynomial in the number of users. We also provide a heuristic deterministic algorithm that achieves (1+ ∊) approximation of the optimal solution, with smaller ∊ at the cost of longer transmission interval of each user.