Robust Joint Design for Integrated Communication and Over-the-Air Computation in Cooperative Cognitive Relay Networks

The rapid growth of wireless devices for communication and computation in wireless networks makes spectrum scarcity an increasingly prominent challenge. To alleviate this issue, we investigate a cooperative cognitive relay network, which consists of a primary network aiming at communication and a secondary network assisted by multiple cognitive relays responsible for over-the-air computation (AirComp), where the secondary network helps relay the signals for the primary network in exchange for opportunity of using the spectrum of the primary network, to transmit its own information. Considering the scenario where only imperfect channel state information (CSI) is available, we try to minimize the worst-case computation mean square error of the AirComp network while ensuring the quality-of-service of the primary network, by jointly designing the transmit coefficients of the sensors, the amplify-and-forward coefficients of the relays and the beamforming vector of the access point. The formulated robust optimization problem is challenging due to the imperfect CSI and highly-coupled variables. By employing the cutting-set (CS) method and the concave-convex constrained procedure (CCCP), we propose an effective CS-CCCP algorithm to solve the robust problem. Numerical results demonstrate the superiority of our proposed scheme over the baseline methods.