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Many common instances of power control problems for cellular and cell-freemassive MIMO networks can be interpreted as max-min utility optimizationproblems involving affine interference mappings and polyhedral constraints. Weshow that these problems admit a closed-form solution which depends on thespectral radius of known matrices. In contrast, previous solutions in theliterature have been indirectly obtained using iterative algorithms based onthe bisection method, or on fixed-point iterations. Furthermore, we also showan asymptotically tight bound for the optimal utility, which in turn provides asimple rule of thumb for evaluating whether the network is operating in thenoise or interference limited regime. We finally illustrate our results byfocusing on classical max-min fair power control for cell-free massive MIMOnetworks.

Closed-form max-min power control for some cellular and cell-free massive MIMO networks