Joint Optimization of Secure Over-the-Air Computation and Reliable Multicasting Assisted by a MIMO Untrusted Two-Way Relay

In this article, we investigate the joint optimization of secure Over-the-Air Computation (AirComp) and reliable multicasting assisted by a multiple-input–multiple-output-untrusted two-way relay, where artificial noise is employed at the access point (AP) to interfere the relay for ensuring secure AirComp. We aim to minimize the computation distortion at the AP by jointly designing the transmit variables of all the nodes and the aggregation variables at the AP and relay, under the secure AirComp constraint, the reliable multicasting constraint, and the transmit power constraints of all the nodes. We consider two scenarios that perfect and imperfect channel state information (CSI) are available. For the former, the formulated optimization problem is highly nonconvex, and we propose an effective block coordinate descent (BCD)-penalty successive convex approximation (penaltySCA) method to solve the nonconvex problem. For the latter, we model the imperfect CSI by using the worst case criterion and the formulated robust optimization problem is much more challenging than its counterpart with perfect CSI. To solve the robust problem effectively, we first transform it into a deterministic optimization problem by employing some powerful mathematical lemmas and then apply the proposed BCD-penaltySCA method to solve the reformulated deterministic problem. The proposed methods are shown by simulations to significantly reduce the computation distortion compared with other benchmarks under considering secure AirComp and reliable multicasting.