Optimal Multicasting in Dual mmWave/$\mu$Wave 5G NR Deployments With Multi-Beam Directional Antennas

The design of multicast services in the fifth-generation (5G) New Radio (NR) deployments is hampered by the directional nature of antenna radiation patterns. This complexity is further compounded by the emergence of new deployment options, such as dual millimeter wave (mmWave) and microwave $(\mu$ Wave) base station (BS) deployments, as well as new antenna design solutions. In this paper, the resource allocation task for multicast services in dual mmWave/ $\mu$ Wave deployments with multi-beam directional antennas is addressed as a multi-period variable cost and size bin packing problem. We solve this problem and characterize the globally optimal solution. To decrease complexity, we then propose and test the simulated annealing approximation and relaxation techniques, i.e., local branching and relaxation-induced neighborhood search heuristic. Our results show that for the considered system parameters, the properties of the optimal solution depend on the density of dual-mode BS deployment and BS deployment type. We observe a transition point at which the system shifts from primarily utilizing mmWave resources to exclusively using $\mu$ Wave BS. Furthermore, the optimal number of beams is upper limited by 3 for mmWave and by 2 for $\mu$ Wave BSs. The efficiency of resource utilization is also affected by the utilized numerology and technology selection priority. Finally, we show that the simulated annealing technique allows for decreasing the solution complexity at the expense of slightly overestimating the amount of resources.