We aim to secure a large-scale device-to-device (D2D) network against adversaries. The D2D network underlays a downlink cellular network to reuse the cellular spectrum and is enabled for simultaneous wireless information and power transfer (SWIPT). In the D2D network, the transmitters communicate with the receivers, and the receivers extract information and energy from their received radio-frequency (RF) signals. In the meantime, the adversaries aim to detect the D2D transmission. The D2D network applies power control and leverages the cellular signal to achieve covert communication (i.e., hide the presence of transmissions) so as to defend against the adversaries. We model the interaction between the D2D network and adversaries by using a two-stage Stackelberg game. Therein, the adversaries are the followers minimizing their detection errors at the lower stage and the D2D network is the leader maximizing its network utility constrained by the communication covertness and power outage at the upper stage. Both power splitting (PS)-based and time switch (TS)-based SWIPT schemes are explored. We characterize the spatial configuration of the large-scale D2D network, adversaries, and cellular network by stochastic geometry. We analyze the adversary's detection error minimization problem and adopt the Rosenbrock method to solve it, where the obtained solution is the best response from the lower stage. Taking into account the best response from the lower stage, we develop a bi-level algorithm to solve the D2D network's constrained network utility maximization problem and obtain the Stackelberg equilibrium. We present numerical results to reveal interesting insights.

翻译：我们旨在保护大规模设备到设备（D2D）网络免受敌方攻击。该D2D网络作为下层网络部署于下行蜂窝网络中，以复用蜂窝频谱，并支持同步无线信息与能量传输（SWIPT）。在D2D网络中，发射机与接收机进行通信，接收机从其接收到的射频（RF）信号中提取信息和能量。与此同时，敌方试图检测D2D传输。D2D网络通过功率控制并利用蜂窝信号实现隐蔽通信（即隐藏传输的存在性），从而抵御敌方攻击。我们使用两阶段Stackelberg博弈对D2D网络与敌方之间的交互进行建模。其中，敌方作为跟随者，在低层阶段最小化其检测误差；D2D网络作为领导者，在高层阶段最大化其受通信隐蔽性和功率中断约束的网络效用。我们探讨了基于功率分割（PS）和基于时间切换（TS）的两种SWIPT方案。通过随机几何刻画大规模D2D网络、敌方及蜂窝网络的空间配置。我们分析了敌方的检测误差最小化问题，并采用Rosenbrock方法进行求解，所得解即为低层阶段的最优响应。在考虑低层阶段最优响应的基础上，我们开发了一种双层算法来求解D2D网络受约束的网络效用最大化问题，并得到Stackelberg均衡。我们通过数值结果揭示了有意义的结论。