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.

中文翻译：

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小蜂窝网络中具有综合干扰约束的鲁棒保密竞争

在本文中，我们针对小型蜂窝用户网络（SUE）进行安全性优化，以防止窃听，从而解决了小型蜂窝网络中的安全性问题。同时，来自小小区基站（SBS）的传输受到宏小区用户（MUE）的总干扰约束。特别是，我们考虑了小型小区中的两倍信息不确定性，即有关MUE的窃听者和干扰通道的不确定性。这样，SBS争夺强大的保密率，同时为MUE提供强大的保护。我们采用广义鲁棒纳什均衡问题（GRNEP）公式，为此我们确认了均衡的存在，并通过变分不等式辅助分析来分析唯一性的条件。此外，为了解决平衡问题，我们介绍了定价机制，并将原始GRNEP分解为具有定价NEP的非线性互补问题，其中前者提供价格系数的解决方案，后者提供基于给定价格的资源分配策略。最后，提供了广泛的仿真结果，以证明干扰约束和不确定性对单个SUE和整个网络的安全性能的影响，也证实了我们的建议在SUE的安全配置和MUE的干扰保护方面的有效性。 。