On the Uplink Max–Min SINR of Cell-Free Massive MIMO Systems

A cell-free massive multiple-input multiple-output system is considered using a max-min approach to maximize the minimum user rate with per-user power constraints. First, an approximated uplink user rate is derived based on channel statistics. Then, the original max-min signal-to-interference-plus-noise ratio problem is formulated for the optimization of receiver filter coefficients at a central processing unit and user power allocation. To solve this max-min non-convex problem, we decouple the original problem into two sub-problems, namely, receiver filter coefficient design and power allocation. The receiver filter coefficient design is formulated as a generalized Eigenvalue problem, whereas the geometric programming (GP) is used to solve the user power allocation problem. Based on these two sub-problems, an iterative algorithm is proposed, in which both problems are alternately solved while one of the design variables is fixed. This iterative algorithm obtains a globally optimum solution, whose optimality is proved through establishing an uplink-downlink duality. Moreover, we present a novel sub-optimal scheme which provides a GP formulation to efficiently and globally maximize the minimum uplink user rate. The numerical results demonstrate that the proposed scheme substantially outperforms the existing schemes in the literature.