A Stochastic Optimization Framework for Distributed Beam Scheduling in 5G mm-Wave Networks over Non-cooperative Operators

This paper considers the problem of distributed scheduling for 5G mm-Wave networks where the base stations (BSs) belong to different operators sharing the same spectrum without any coordination among them. We aim to design efficient distributed beam scheduling algorithms such that the network utility which is a function of the average throughput can be maximized subject to the (average and instantaneous) power consumption constraints of the base stations. We propose a Medium Access Control (MAC) and a power allocation/adaptation mechanism utilizing the Lyapunov stochastic optimization framework which can be cast into two stochastic/deterministic optimization problems, where the first one can be solved via convex optimizations and the second one can be solved by "max-weight" type algorithms or non-cooperative games. The main novelty of the proposed approach is to formulate an optimization framework that is applicable for different MAC schemes with optimizable parameters such that the optimal values of the network utility function under such different MAC schemes can be achieved for distributed beam scheduling. To illustrate the proposed approach, we consider two MAC schemes, namely, non-cooperative game and p-persistent medium access control. We conduct simulations to justify the effectiveness of the proposed optimization framework. Interestingly, the non-cooperative game based approach can converge faster but with a worse optimal value compared to that achieved by the p-persistent based scheme. Hence, in this particular case, we suggest to start with the non-cooperative game scheme and then adapt to the p-persistent based scheme.