Secrecy-oriented user association in ultra dense heterogeneous networks against strategically colluding adversaries

Network densification is recognized as the key technology to meet the ever growing demand of data traffic in next generation wireless networks. However the proliferation of small cell base stations (SCBSs) introduces vulnerabilities to information security, as they are prone to eavesdropping attacks. In this paper, it is studied how user association strategies can be specifically tailored to meet this security challenge in a ultra dense heterogeneous cellular network(UDHCN) with a group of colluding eavesdroppers. In particular, the situation is considered where eavesdroppers may have limited capabilities in intercepting and decoding data traffic. In this setting each eavesdropper has to make its own decision on eavesdropping targets, and they are able to take concerted actions to sabotage information security. To address this challenge, a zero sum game framework to reflect the conflicting interests of users and eavesdroppers is proposed and a user association scheme is devised that aims to maximize system sum secrecy rate against these adversaries whose actions intend to minimize sum secrecy rate. The case that all adversaries have limited eavesdropping capabilities is first considered, and it is shown that the corresponding zero sum game is indeed a bilinear game, and its Nash equilibrium solution can be readily approximated using a saddle point Frank Wolfe(SP-FW)algorithm. Then the framework is extended to the case where adversaries with a diverse configuration of eavesdropping capabilities exist. In this case, it is shown that the underlying minimax optimization problem is indeed a nonsmooth convex-nonconcave one. A two stage method is proposed by first smoothing the objective function with a Hermite cubic polynomial approximation, and then obtaining a nearly stationary solution via a recently proposed proximal point gradient descent method. Simulation results show that the proposed framework leads to significant increases in sum secrecy rate and secrecy probability against both the capability-limited adversaries and a hybrid type of adversaries.