Robust Secrecy Competition with Aggregate Interference Constraint in Small-Cell Networks

In this article, we address the security issue in a tiered small-cell network aiming at security optimization for small-cell users (SUEs) to defend against eavesdropping. Meanwhile, the transmissions from small-cell base stations (SBSs) are subject to the aggregate interference constraints of macro-cell users (MUEs). In particular, we consider two-fold information uncertainties in small cells, i.e., the uncertainties regarding the eavesdroppers and interference channels to the MUEs. As such, the SBSs compete for robust secrecy rate with robust protection for the MUEs. We adopt the generalized robust Nash equilibrium problem (GRNEP) formulation, for which we confirm the existence of equilibrium and analyze the condition for the uniqueness with variational inequality-Assisted analysis. Furthermore, to solve for the equilibrium, we introduce the pricing mechanism and decompose the original GRNEP as a nonlinear complementarity problem with a priced NEP, where the former provides solution of price coefficients and the latter for resource allocation strategies based on given prices. Finally, extensive simulation results are provided to demonstrate the impacts of the interference constraint and uncertainties upon the security performance of an individual SUE and the overall network, which also corroborate the effectiveness of our proposal in security provisioning for the SUEs and interference protection for the MUEs.