  Over-the-air computation (AirComp), which leverages the superposition
property of wireless multiple-access channel (MAC) and the mathematical tool of
function representation, has been considered as a promising technique for
effective collection and computation of massive sensor data in wireless Big
Data applications. In most of the existing work on AirComp, optimal
system-parameter design is commonly considered under the peak-power constraint
of each sensor. In this paper, we propose an optimal transmitter-receiver
(Tx-Rx) parameter design problem to minimize the computation mean-squared error
(MSE) of an AirComp system under the sum-power constraint of the sensors. We
solve the non-convex problem and obtain a closed-form solution. Also, we
investigate another problem that minimizes the sum power of the sensors under
the constraint of computation MSE. Our results show that in both of the
problems, the sensors with poor and good channel conditions should use less
power than the ones with moderate channel conditions.
