Max-Min Fairness Optimization in Uplink Cell-Free Massive MIMO Using Meta-Heuristics

One of the most promising technologies to be employed in beyond 5G networks is based on the concept of cell-free (CF) massive MIMO, in which a predetermined set of access points (APs) jointly cooperate in the data transmission and reception to/from the user equipment (UE). In order to efficiently manage radio resources, the CF central processing unit implement uplink power control policies. These policies aim to optimize a given network utility function. In this paper, we investigate the max-min fairness optimization problem, in which the spectral efficiency performance of the UE with the worst channel conditions is prioritized, taking into account a per-UE power constraint and assuming linear maximum ratio combining at APs. Existing solutions have typically relied on second-order cone programming with convex approximations, which exhibit high computational complexity and scalability issues. Therefore, meta-heuristics (MHs) are explored as alternative optimization schemes, capable of providing (near)-optimal solutions with reasonable computational effort. Three MH approaches with different operation principles are compared. Numerical results show that the differential evolution algorithm exhibits the best trade-off between solution quality and run time, being able to reach (near)-optimal solutions faster than the bisection approach while coping with the scalability issues of the geometric programming-based algorithm.