  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.
