Over-the-Air Computation Systems: Optimal Design with Sum-Power Constraint

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.