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.

Future Internet-of-Things applications may require both high-quality wireless data aggregation and communication simultaneously. In this paper, we propose an integrated over-the-air computation (AirComp) and non-orthogonal multiple access (NOMA) communication scheme in a wireless uplink system, which consists of a data fusion center, a base station, and associated multiple users. Each user participates in AirComp and information transmission simultaneously. The data fusion center is responsible for wireless data aggregation and the base station is responsible for data collection of all users. Our aim is to minimize the computation mean square error (CMSE) at the data fusion center while satisfying the total transmission rate requirement at the base station. The formulated optimization problem is non-convex. To solve the problem, we propose a one-dimensional search based globally optimal solution, an alternating optimization based locally optimal solution, and a generalized Rayleigh quotient based globally optimal solution. Numerical results illustrate that although the locally optimal solution has the shortest average program execution time (PET), it achieves the suboptimal system performance. The generalized Rayleigh quotient based globally optimal solution, which addresses the CMSE minimization problem in a different manner, has much lower average PET than the one-dimensional search based globally optimal solution.

In this paper, we investigate joint optimization of secure 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 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 to 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.

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.