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.

中文翻译：

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空中计算网络的协作干扰管理

本文考虑了一个多小区 AirComp 网络，并研究了多个小区上的最佳功率控制策略，以调节小区间干扰的影响。首先，我们考虑集中式多小区功率控制的场景，在该场景中，我们通过最小化受对单个 MSE 的一组约束的总和 MSE 来表征多小区 MSE 区域的帕累托边界。尽管 sum-MSE 最小化问题是非凸的，并且其直接求解难以处理，但我们通过等价求解一系列凸二阶锥规划可行性问题以及二分搜索来优化解决该问题。接下来，我们考虑在没有集中控制器的另一种情况下的分布式功率控制，为此提出了一种替代的基于 IT 的方法来表征相同的 MSE 帕累托边界，并启用分散的功率控制算法。相应地，每个AP只需要单独控制其关联设备的功率，但受其对相邻小区干扰的一组IT约束，而不同的AP可以通过成对的信息交换合作迭代更新IT级别，以实现帕累托最优 MSE 元组。最后，仿真结果表明，使用所提出算法的协同功率控制可以显着降低 AirComp 网络的总和 MSE。实现帕累托最优 MSE 元组。最后，仿真结果表明，使用所提出算法的协同功率控制可以显着降低 AirComp 网络的总和 MSE。实现帕累托最优 MSE 元组。最后，仿真结果表明，使用所提出算法的协同功率控制可以显着降低 AirComp 网络的总和 MSE。