Abstract
Over-the-air computation (AirComp) has been shown to provide a significantly higher efficiency than the traditional separating communication and computation tasks in the large-scale wireless sensor network. However, the presence of the malicious active eavesdropper in the network poses a severe security threat, as the eavesdropper can not only intercept aggregated information but also interfere with legitimate transmissions. To address the issue, we first derive the closed-form expressions that characterize both the approximation level and the security level of AirComp in the presence of active eavesdropping. Then, we jointly design the power allocation, the sensor selection, the artificial noise, and the receiver filter to minimize the approximation level subject to the required security level and the power budget constraint. Finally, the penalty dual decomposition scheme is proposed to solve the approximation level minimization problem, which is NP-hard due to the integer-programming nature and coupling properties of the optimization variables. Numerical results show that our scheme significantly outperforms the existing method.