Tree Formation with Physical Layer Security Considerations in Wireless Multi-Hop Networks

Physical layer security has emerged as a promising technique that complements existing cryptographic approaches and enables the securing of wireless transmissions against eavesdropping. In this paper, the impact of optimizing physical layer security metrics on the architecture and interactions of the nodes in multi-hop wireless networks is studied. In particular, a game-theoretic framework is proposed using which a number of nodes interact and choose their optimal and secure communication paths in the uplink of a wireless multi-hop network, in the presence of eavesdroppers. To this end, a tree formation game is formulated in which the players are the wireless nodes that seek to form a network graph among themselves while optimizing their multi-hop secrecy rates or the path qualification probabilities, depending on their knowledge of the eavesdroppers' channels. To solve this game, a distributed tree formation algorithm is proposed and is shown to converge to a stable Nash network. Simulation results show that the proposed approach yields significant performance gains in terms of both the average bottleneck secrecy rate per node and the average path qualification probability per node, relative to classical best-channel algorithms and the single-hop star network. The results also assess the properties and characteristics of the resulting Nash networks.