Novel p-Median-based Formulations for Maximizing Coverage in 5G/6G Wireless Networks

In this paper, we consider the problem of maximizing user coverage for 5G/6G wireless communication networks subject to facility location and radial distance constraints. For this purpose, we propose two novel mixed-integer linear programming models which are constructed based on a classical combinatorial optimization problem referred to as the p-Median problem in the literature. In the classical p-Median problem, one seeks to find a subset of $p$ facilities in order to assign users to them while minimizing the total distance costs between users and facilities. The novelty of our proposed models is the consideration of non-overlapping radial distance constraints between antennas (facilities). In particular, our first model maximizes the total number of users. Whilst the second one includes in the objective function the maximization of users and the minimization of the number of antennas to be activated. So far we solve instances with up to 100 antennas and 1000 users with the Gurobi solver. Our preliminary numerical results indicate that the first model is harder to solve to global optimality than the second one. The numerical results obtained also show that the increase in the number of radius allowed provides more flexibility and accuracy to the model, although at a higher computational cost. Finally, we highlight that the proposed models can be used for future developments of 5G/6G networks in order to improve coverage.