Over-the-Air Computing With Imperfect CSI: Design and Performance Optimization

Over-the-air computing (AirComp) has recently attracted considerable attention as an efficient method of data fusion by integrating uncoded communication transmissions with computation thanks to the signal superposition offered by the multiple access channels. However, appropriate processing is required to neutralize the wireless channel effect. As, internet-of-things (IoT) applications through low-cost devices is the main target of AirComp, perfect availability of channel state information (CSI) is not always practical, there is the need to investigate the effect of imperfect CSI on AirComp. Specifically, we present novel closed-form expressions for tight approximations that can be used to design and evaluate AirComp systems. Furthermore, we design a general optimization framework that takes into account both magnitude and phase errors in the CSI. Finally, a pilot retransmission policy is designed, that offers trade-off between resources cost and the gain in the accuracy of the computations. In order to validate its application, a utility function of the cost of retransmission is introduced, namely, Retransmission Policy Cost (RPC), which can incorporate the power or throughput cost opposing to the expected gain of the selected policy. Simulations show the deterioration caused by the imperfect CSI and highlight the added value of the proposed policy under various system conditions.