Unbiased Over-the-Air Computation via Retransmissions

Over-the-air computation (AirComp) has recently emerged as an efficient analog method for data acquisition from wireless sensor devices. In essence, AirComp exploits the signal superposition property of a multiple access channel to estimate functions of the transmitted data points. Unless devices are excluded from participation, state-of-the-art AirComp methods do not achieve unbiased function computation, thereby introducing systematic errors in the acquired function. In this paper, we propose a new AirComp scheme that employs retransmissions to achieve probabilistically unbiased function computation. We solve a power control problem that minimizes the bias subject to a peak transmission power constraint. We show that the optimal power control follows a greedy structure that maximizes the devices' contribution to the received function at every retransmission. Numerical results show that the proposed scheme can achieve unbiased function computation with a few retransmissions and drastically reduce the mean squared error in the function estimation compared to the current state-of-the-art.