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A Green Downlink Power Allocation Scheme for Cell-Free Massive MIMO Systems

In this article, we consider the problem of downlink power allocation in a cell-free massive multiple-input multiple-output (m-MIMO) communication system under spectral efficiency (SE) constraints for the users. From the perspective of green communications, the power allocation is formulated as an optimization problem where the aim is to maximize the sum SE as the objective function, while limiting the transmission power of each access point (AP) and imposing lower and upper bounds on the achievable SEs of different users. The resulting optimization problem is non-convex since the objective function is non-concave and the upper bounding constraints on user SEs are non-convex. To address these difficulties, we first derive a closed-form lower bound on the sum SE (objective function) and prove that it is a quasi-concave function. Then, we relax the unwieldy upper bounding constraints on the user SEs by replacing them with linear functions, which renders the optimization problem convex. An optimal solution to the relaxed problem is finally obtained by solving a sequence of convex feasibility programs. We evaluate the performance of the proposed downlink power allocation scheme through Monte Carlo simulations under the uncorrelated and correlated shadow fading models. The results show that for both models, the proposed algorithm can lead to a significant reduction in total power consumption compared to a benchmark approach, while accurately allocating power to the APs so that the SE constraint of each user is satisfied within the imposed bounds.