Cooperative Interference Management for Over-the-Air Computation Networks

Recently, over-the-air computation (AirComp) has emerged as an efficient solution for access points (APs) to aggregate distributed data from many edge devices (e.g., sensors) by exploiting the waveform superposition property of multiple access (uplink) channels. While prior work focuses on the single-cell setting where inter-cell interference is absent, this article considers a multi-cell AirComp network limited by such interference and investigates the optimal policies for controlling devices' transmit power to minimize the mean squared errors (MSEs) in aggregated signals received at different APs. First, we consider the scenario of centralized multi-cell power control. To quantify the fundamental AirComp performance tradeoff among different cells, 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 show that this problem can be optimally solved via equivalently solving a sequence of convex second-order cone program (SOCP) feasibility problems together with a bisection search. This results in an efficient algorithm for computing the optimal centralized multi-cell power control, which optimally balances the interference-and-noise-induced errors and the signal misalignment errors unique for AirComp. Next, we consider the other scenario of distributed power control, e.g., when there lacks a centralized controller. In this scenario, we introduce a set of interference temperature (IT) constraints, each of which constrains the maximum total inter-cell interference power between a specific pair of cells. Accordingly, each AP only needs to individually control the power of its associated devices for single-cell MSE minimization, but subject to a set of IT constraints on their interference to neighboring cells. By optimizing the IT levels, the distributed power control is shown to provide an alternative method for characterizing the same multi-cell MSE Pareto boundary as the centralized counterpart. Building on this result, we further propose an efficient algorithm for different APs to cooperate in iteratively updating the IT levels to achieve a Pareto-optimal MSE tuple, by pairwise information exchange. Last, simulation results demonstrate that cooperative power control using the proposed algorithms can substantially reduce the sum MSE of AirComp networks compared with the conventional single-cell approaches.