Optimal Power Allocation for Over-the-Air Computation With Correlated Data

Over-the-air computation (AirComp) exploits superposition property of wireless multiple access channels for effective sensing data collection. Existing works on AirComp assume statistically independent sensing data, although in practice sensing data may be correlated with one another. Considering correlated sensing data, we formulate a power allocation optimization problem for achieving the minimum computation mean square error. We transform the formulated problem into a fractional quadratically constrained quadratic problem and propose a semidefinite programming-based scheme to obtain the optimal power allocation factors. It is shown through simulation results that our proposed scheme outperforms the full-power and channel-inversion schemes.