Device-to-device (D2D) communications recently have attracted much attentionfor its potential capability to improve spectral efficiency underlaying theexisting heterogeneous networks (HetNets). Due to no sophisticated control, D2Duser equipments (DUEs) themselves cannot resist eavesdropping or securityattacks. It is urgent to maximize the secure capacity for both cellular usersand DUEs. This paper formulates the radio resource allocation problem tomaximize the secure capacity of DUEs for the D2D communication underlayingHetNets which consist of high power nodes and low power nodes. The optimizationobjective function with transmit bit rate and power constraints, which isnon-convex and hard to be directly derived, is firstly transformed into matrixform. Then the equivalent convex form of the optimization problem is derivedaccording to the Perron-Frobenius theory. A heuristic iterative algorithm basedon the proximal theory is proposed to solve this equivalent convex problemthrough evaluating the proximal operator of Lagrange function. Numericalresults show that the proposed radio resource allocation solution significantlyimproves the secure capacity with a fast convergence speed.
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