  This paper studies the problem of distributed beam scheduling for 5G
millimeter-Wave (mm-Wave) cellular networks where base stations (BSs) belonging
to different operators share the same spectrum without centralized coordination
among them. Our goal is to design efficient distributed scheduling algorithms
to maximize the network utility, which is a function of the achieved throughput
by the user equipment (UEs), subject to the average and instantaneous power
consumption constraints of the BSs. We propose a Media Access Control (MAC) and
a power allocation/adaptation mechanism utilizing the Lyapunov stochastic
optimization framework and non-cooperative games. In particular, we first
decompose the original utility maximization problem into two sub-optimization
problems for each time frame, which are a convex optimization problem and a
non-convex optimization problem, respectively. By formulating the distributed
scheduling problem as a non-cooperative game where each BS is a player
attempting to optimize its own utility, we provide a distributed solution to
the non-convex sub-optimization problem via finding the Nash Equilibrium (NE)
of the game whose weights are determined optimally by the Lyapunov optimization
framework. Finally, we conduct simulation under various network settings to
show the effectiveness of the proposed game-based beam scheduling algorithm in
comparison to that of several reference schemes.
