Joint Secure Beamforming and Power Splitting Design for MIMO Relay Assisted Over-the-Air Computation Networks With Imperfect CSI

In this paper, we consider a physical layer security issue in a multiple-input multiple-output (MIMO) relay assisted over-the-air computation (AirComp) network, where sensors send their sensing data to the access point (AP) via a harvest and forward relay, and an eavesdropper (Eve) attempts to wiretap the aggregation result of sensors’ sensing signals. In the first time slot, the AP applies artificial noise (AN) to protect the aggregation result from being wiretapped by the Eve, and the relay harvests energy from the received signal according to the power splitting protocol. In the second time slot, the relay forwards the received signal, containing AN and sensors’ sensing signals, to the AP. The channel state information (CSI) between each node is assumed to be imperfect, and the channel uncertainties are molded as bounded errors. Specifically, we investigate a joint secure beamforming and power splitting design to minimize the worst-case mean-square error (MSE) at the AP, subject to the worst-case MSE constraint of the Eve and the worst-case transmit power constraints at each node. Different from the common approach that ignores the higher-order terms of channel uncertainties caused by cascade channels, by exploiting the block coordinate descent (BCD) algorithm, cutting set (CS) method and constrained concave-convex procedure (CCCP), we propose a BCD-CS-CCCP algorithm attempting to solve the robust optimization problem while retaining the higher-order terms of channel uncertainties. Numerical results indicate the effectiveness of our proposed schemes.