Joint Secure Transceiver Design for an Untrusted MIMO Relay Assisted Over-the-Air Computation Networks With Perfect and Imperfect CSI

In this paper, we investigate the physical layer security of an untrusted relay assisted over-the-air computation (AirComp) network, where each node is equipped with multiple antennas and the relay is operated in an amplify-and-forward mode. The relay receives the data from each sensor and sends them to the access point (AP) in the first and second time slot, respectively. The AP applies artificial noise (AN) to protect the aggregation of sensors’ data from being wiretapped by the untrusted relay in the first time slot. In particular, we are interested in minimizing the computation distortion measured by the mean-squared error (MSE) via jointly optimizing beamforming matrices at all nodes, subject to the MSE constraint at the relay and individual power constraints at the AP, the relay and each sensor. In the case of the perfect channel state information (CSI), we convert the nonconvex MSE minimization problem into a difference-of-convex (DC) form and propose a constrained concave-convex procedure that can obtain a local minimum to solve the DC problem. We also generalize the framework to an imperfect CSI case where the additional interference term due to incomplete interference cancellation is considered, and the nonconvex robust MSE minimization problem is solved by a proposed inexact block coordinate descent algorithm. Numerical results are presented to show the effectiveness of our proposed schemes.