Generalized Benders Decomposition to Secure Energy-Efficient Resource Allocation for Multiuser Full-Duplex Relay Cooperative Networks

In this paper, we investigate the issue of resource allocation for secure energy efficient communication in a multiuser orthogonal frequency division multiplexing (OFDM) based full-duplex (FD) relaying network in the presence of a passive eavesdropper whose channel state information (CSI) is not perfectly known. Our goal is to maximize the overall secure energy efficiency (SEE), which presents the relationship between energy consumption and secrecy performance. In the context of multiuser communications, such a resource allocation strategy jointly combines subcarrier permutation, subcarrier pair allocation, as well as power allocation altogether. The considered optimization problem is formulated as a mixed integer nonconvex programming problem, which is generally NP hard. Analyzing the property of such a problem, we first use the Dinkelbach's method to eliminate the fractional form and then exploit Generalized Benders decomposition to decouple the original problem into a master problem for pure integer programming and a primal problem for nonlinear programming. More specific, given the nonconvexity of the primal problem, we accordingly transform it into an equivalent relaxed convex problem by applying dual decomposition, alternative convex search, and difference of convex function programming. The numerical results are provided to validate the theoretical analysis and to demonstrate the effectiveness of the proposed algorithm.