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

Abstract : A cell-free Massive multiple-input multiple-output (MIMO) 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 (SINR) problem is formulated for optimization of receiver filter coefficients at a central processing unit (CPU), 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 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 existing schemes in the literature. Index Terms-Cell-free Massive MIMO, max-min resource allocation, geometric programming, uplink-downlink duality, convex optimization, generalized eigenvalue problem.
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Manijeh Bashar, Kanapathippillai Cumanan, Alister Burr, Merouane Debbah, Hien Quoc Ngo. On the Uplink Max–Min SINR of Cell-Free Massive MIMO Systems. IEEE Transactions on Wireless Communications, Institute of Electrical and Electronics Engineers, 2019, 18 (4), pp.2021-2036. ⟨10.1109/TWC.2019.2892463⟩. ⟨hal-02904783⟩

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