A Game With Randomly Distributed Eavesdroppers in Wireless Ad Hoc Networks: A Secrecy EE Perspective

We study energy-efficient secure communication using the combined approach of game theory and stochastic geometry in a large-scale wireless network, where legitimate transmitters (Alice nodes) and eavesdroppers (Eve nodes) are randomly distributed in space. We consider the following two scenarios according to the Eve tier's strategy: I) the Eve tier activates all its nodes to maximally eavesdrop the confidential messages of the Alice tier; and II) the Eve tier activates only a portion of its nodes to maximize its energy efficiency (EE) in eavesdropping according to the Alice tier's node activation. In Scenario I, we propose an alternating optimization scheme that maximizes the secrecy EE of the Alice tier by controlling the node-activation probability, the confidential message rate, the redundancy rate, and the number of active antennas. Simulation result shows that the proposed scheme can achieve the optimal secrecy EE. In Scenario II, we study an energy-efficient node activation game between the Alice tier and the Eve tier, where the former and the latter control their node-activation probabilities to maximize the secrecy EE and the eavesdropping EE, respectively. We show that the node activation game admits a unique Nash equilibrium. The node-activation probabilities of the Alice tier and the Eve tier at the Nash equilibrium can be used to estimate their network lifetimes, which are important information for the energy-efficient secure network design. Simulation result shows that the best-response dynamics converges to the Nash equilibrium within a few iterations.