This work proposes a distributed power allocation scheme to maximize energy efficiency in the uplink of multi-cell massive MIMO systems with hardware impairments at the user equipments (UEs) and imperfect channel state information at the base stations (BSS). Each UE in the network is modeled as a rational agent that engages in a generalized non-cooperative game and allocates its available transmit power to maximize its individual utility (defined as the UE's throughput per Watt of transmit power) subject to target rates and power constraints. The existence and uniqueness of the generalized Nash equilibrium of the game are studied in the asymptotic regime where the number of BS antennas and UEs grow large with a non trivial ratio. A fully distributed algorithm based on best-response dynamics and relying on large-scale fading components is proposed. Sufficient conditions to guarantee convergence to the equilibrium point are given. Numerical results are used to evaluate the performance of the proposed solution and to validate the analysis in a system of finite size.
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