An Alternating Algorithm for Uplink Max-Min SINR in Cell-Free Massive MIMO with Local-MMSE Receiver

The problem of max-min signal-to-interference plus noise ratio (SINR) for uplink transmission of cell-free massive multiple-input multiple-output (MIMO) system is considered. We assume that the system is employed with local minimum mean square error (L-MMSE) combining. The objective is to preserve user fairness by solving max-min SINR optimization problem, by optimizing transmit power of each user equipment (UE) and weighting coefficients at central processing unit (CPU), subject to transmit power constraints of UEs. This problem is not jointly convex. Hence, we decompose original problem into two subproblems, particularly for optimizing power allocation and receiver weighting coefficients. Then, we propose an alternating algorithm to solve these two subproblems. The weighting coefficient subproblem is formulated as a generalized eigenvalue problem while power allocation subproblem is approximated as geometric programming (GP). We empirically show that the proposed algorithm achieves higher min-user uplink spectral efficiency (SE) over existing fixed power scheme which is not optimized with respect to the transmit power. Moreover, the convergence of the proposed algorithm is numerically illustrated.