  Large-scale distributed antenna systems with many access points (APs) that
serve the users by coherent joint transmission is being considered for
5G-and-beyond networks. The technology is called Cell-free Massive MIMO and can
provide a more uniform service level to the users than a conventional cellular
topology. For a given user set, only a subset of the APs is likely needed to
satisfy the users' performance demands, particularly outside the peak traffic
hours. To find achieve an energy-efficient load balancing, we minimize the
total downlink power consumption at the APs, considering both the transmit
powers and hardware dissipation. APs can be temporarily turned off to reduce
the latter part. The formulated optimization problem is non-convex but,
nevertheless, a globally optimal solution is obtained by solving a
mixed-integer second-order cone program. Since the computational complexity is
prohibitive for real-time implementation, we also propose two low-complexity
algorithms that exploit the inherent group-sparsity and the optimized transmit
powers in the problem formulation. Numerical results manifest that our
optimization algorithms can greatly reduce the power consumption compared to
keeping all APs turned on and only minimizing the transmit powers. Moreover,
the low-complexity algorithms can effectively handle the power allocation and
AP activation for large-scale networks.
