A Non-cooperative Game-based Approach to Distributed Beam Scheduling in Millimeter-Wave Networks

This paper considers the problem of distributed beam scheduling in millimeter-Wave (mmWave) cellular networks with non-cooperating service operators sharing the spectrum. The base stations (BSs) may belong to different operators so there is no coordination or centralized control among them. Our goal is to design efficient distributed beam scheduling schemes to optimize the network-level utility defined as the sum of the logarithm of the average throughput of the users. Utilizing the Lyapunov optimization theory, the network utility optimization problem can be cast into two sub-problems to be solved iteratively in each frame. The second sub-problem is non-convex and challenging to solve in general. To this end, we propose a non-cooperative game-based beam scheduling and power allocation scheme in which the BSs are modeled as players that aim to optimize their individual payoff. The Nash Equilibrium (NE) then provides a distributed (approximate) solution to the second sub-problem. We prove the existence of NE and identify sufficient conditions guaranteeing the uniqueness of NE by establishing an equivalence of the formulated game to a variational inequality problem. A parallel power update algorithm is proposed with assured convergence. Numerical evaluation demonstrates the superiority of the proposed approach over several baselines.