This paper considers a multi-cell AirComp network and investigates the
optimal power control policies over multiple cells to regulate the effect of
inter-cell interference. First, we consider the scenario of centralized
multi-cell power control, where we characterize the Pareto boundary of the
multi-cell MSE region by minimizing the sum MSE subject to a set of constraints
on individual MSEs. Though the sum-MSE minimization problem is non-convex and
its direct solution intractable, we optimally solve this problem via
equivalently solving a sequence of convex second-order cone program feasibility
problems together with a bisection search. Next, we consider distributed power
control in the other scenario without a centralized controller, for which an
alternative IT-based method is proposed to characterize the same MSE Pareto
boundary, and enable a decentralized power control algorithm. Accordingly, each
AP only needs to individually control the power of its associated devices, but
subject to a set of IT constraints on their interference to neighboring cells,
while different APs can cooperate in iteratively updating the IT levels by
pairwise information exchange, to achieve a Pareto-optimal MSE tuple. Last,
simulation results demonstrate that cooperative power control using the
proposed algorithms can substantially reduce the sum MSE of AirComp networks.

本文研究多小区 AirComp 网络的功率控制策略，包括中心化多小区功率控制和分布式功率控制。该文提出了一种基于集成电路的方法来解决无中心控制的情况并证明了该算法的有效性，模拟结果表明，采用所提出的算法的协作功率控制可以大幅减少 AirComp 网络的总均方误差。