Beamforming and Power Optimization for User Fairness in Cell-Free MIMO Systems

Cell-free (CF) massive multiple-input multiple-output (MIMO) systems are expected to provide high spectral efficiency to all users, regardless of their locations, when equipped with a large number of evenly distributed access points (APs) in the area of coverage. In this paper, we investigate beamforming and power allocation schemes in CF MIMO systems to achieve user fairness, while maintaining high spectral efficiency without degrading the performance of users with good channel conditions, even as the number of users scales up. The system models and optimization problems for both downlink and uplink are described in a unified mathematical framework. For achieving user fairness, three different approaches are used, i.e., maximizing the minimum received signal power, minimizing the maximum interference power, and maximizing the minimum of signal to interference and noise ratio (SINR). By decoupling beamforming and power allocation problems, the beamforming problems can be formulated as the generalized eigenvalue problems, and the optimal solutions correspond to well-known schemes such as maximum ratio, zero-forcing, and minimum mean square error combining/transmission. In addition to beamforming, we provide closed-form solutions for optimal power allocation by incorporating additional objectives such as minimum total transmit power or evenly balanced SINR when needed. Our performance comparison suggests that to achieve evenly high data rates for all users irrespective of their locations or the number of users, active interference suppression is necessary instead of relying on maximum ratio combining/transmission even with many APs employed.