Distributed Power Optimization for Security-Aware Multi-Channel Full-Duplex Communications: A Variational Inequality Framework

In this paper, we consider the physical layer security issue for the multi-channel full-duplex (FD) communications in the presence of eavesdroppers. There co-exist multiple FD pairs, where the two users in each pair perform bi-directional transmissions. The secure communication is then challenged by the users' self-interference, external interference from other pairs, and threats from the eavesdroppers. We investigate the problem from a distributed perspective and formulate the problem as a non-cooperative game, where each user optimizes their power allocation over the channels to maximize their own secrecy rate. Confirming the existence of the Nash equilibrium, we introduce an equivalent variational inequality (VI) formulation to derive the sufficient condition for the equilibrium to be unique. We then develop the iterative security-aware water-filling (ISWF) algorithm that can be implemented at each individual user in a distributed manner and prove that the condition for the unique equilibrium also claims the convergence of ISWF algorithm. Furthermore, we extend our formulation to the heterogeneous cases that there co-exist FD and half-duplex users with different security requirements in the networks, and demonstrate that they can all be covered as special cases under our formulated VI framework. Finally, we present simulation results to validate our theoretical findings.