Optimal Design and Coverage for 5G Networks Operating in the mmWave Frequency Spectrum Using Mathematical Programming

This paper presents two mathematical optimization models to solve problems related to the design and planning of 5G wireless communications networks using millimeter wave frequency spectrum. The first one allows for maximizing the number of covered users while minimizing the distances between each pair of base stations, and the distances required to connect each user to a unique base station. In this model, the number of base stations is fixed. The second model allows for optimizing the same objective function as the first one with an additional term used to minimize the total number of base stations required for the coverage. Notice that the problem to be addressed presents a high path loss. Consequently, the transmission distances should be reduced for different coverage transmission radii. Our models assume the existence of line-of-sight (LOS) for the links between the users and the base stations. Finally, we consider 10 instances with a maximum of 50 candidate location sites for the base stations and a maximum of 300 users for radial transmission distances of 150 and 200 meters. Our numerical results show that the proposed models can solve all the instances to optimality in a short CPU time effort.