Over-the-air computation (AirComp) leveraging the superposition property of wireless multiple-access channel (MAC), is a promising technique for effective data collection and computation of large-scale wireless sensor measurements in Internet of Things applications. Most existing work on AirComp only considered computation of spatial-and-temporal independent sensor signals, though in practice different sensor measurement signals are usually correlated. In this letter, we propose an AirComp system with spatial-and-temporal correlated sensor signals, and formulate the optimal AirComp policy design problem for achieving the minimum computation mean-squared error (MSE). We develop the optimal AirComp policy with the minimum computation MSE in each time step by utilizing the current and the previously received signals. We also propose and optimize a low-complexity AirComp policy in closed form with the performance approaching to the optimal policy.

中文翻译：

---

使用时空相关信号进行空中计算

利用无线多路访问信道 (MAC) 的叠加特性的空中计算 (AirComp) 是一种很有前途的技术，可用于在物联网应用中对大规模无线传感器测量进行有效的数据收集和计算。AirComp 上的大多数现有工作仅考虑计算空间和时间独立的传感器信号，尽管实际上不同的传感器测量信号通常是相关的。在这封信中，我们提出了一个具有时空相关传感器信号的 AirComp 系统，并制定了实现最小计算均方误差 (MSE) 的最优 AirComp 策略设计问题。我们通过利用当前和先前接收到的信号，在每个时间步中以最小的计算 MSE 开发最佳 AirComp 策略。