A Non-cooperative Game-based Distributed Beam Scheduling for 5G mm-Wave Networks

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 any centralized coordination among them. Our goal is to design efficient distributed beam scheduling algorithms to maximize the network utility, which is a function of the achieved throughput by the user equipment (UEs), subject to average and instantaneous transmit power 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 transform 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 in which each BS is a player attempting to optimize its own utility, we provide a distributed solution to the non-convex sub-optimization problem by solving the Nash Equilibrium (NE) of the scheduling game. We prove the existence of NE and provide sufficient conditions guaranteeing the uniqueness of NE by utilizing the equivalence between the non-cooperative game and the Variational Inequality (VI) problem. A corresponding parallel updating algorithm for finding the NE is proposed which is proved to globally converge. Finally, we conduct simulation under various network settings to show the effectiveness of the proposed game-based beam scheduling algorithm in comparison to several baseline MAC schemes including $p$-persistent and CSMA/CA MAC protocols.