Selective channel inversion protocol for over-the-air computation

This paper introduces a novel selective channel inversion (SCI) protocol for over-the-air computation (AirComp) networks. The proposed SCI protocol reduces the overhead associated with channel state information (CSI) by broadcasting a predefined channel threshold. Furthermore, it improves mean squared error (MSE) performance by permitting transmission only from sensor nodes with favorable channel conditions. For an arbitrary channel distribution, an exact closed-form expression for the MSE is derived, from which an asymptotic expression for a large number of sensor nodes is obtained. Numerical results demonstrate that the asymptotic expression closely matches the exact result, even for a relatively small number of sensor nodes. An optimization problem is formulated to determine the optimal channel threshold under Nakagami- m fading channels, and it is analytically proven that the problem is convex. An algorithm for dynamically determining the threshold under arbitrary channel distributions is also presented. Numerical results demonstrate that SCI AirComp outperforms CI AirComp in scenarios with low signal-to-noise ratio (SNR), high fading severity, and a large number of sensor nodes. 2018 The Korean Institute of Communications and Information Sciences. Publishing Services by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ).