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 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 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 game theory. 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 via finding 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 Part of this work was presented in the IEEE Asilomar conference 2020, Pacific Grove, CA, USA. X. Zhang and M. Ji are with the Department of Electrical and Computer Engineering, University of Utah, Salt Lake City, UT 84112, USA (E-mail: {xiang.zhang, mingyue.ji}@utah.edu). S. Sarkar and S. K. Kasera are with the School of Computing, University of Utah, Salt Lake City, UT 84112, USA (E-mail: shamik.sarkar@utah.edu, kasera@cs.utah.edu). A. Bhuyan is with the INL Wireless Security Institute, Idaho National Laboratory, Idaho Falls, ID 83415 (E-mail: arupjyoti.bhuyan@inl.gov). Work supported through the INL Laboratory Directed Research & Development (LDRD) Program under DOE Idaho Operations Office Contract DE-AC07-05ID14517. The work of M. Ji and S. K. Kasera is also supported in part by NSF Award 1824558. ar X iv :2 01 2. 11 16 8v 1 [ cs .I T ] 2 1 D ec 2 02 0

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