Over-the-Air Computation with Spatial-and-Temporal Correlated Signals

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.