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Device-to-device (D2D) communications have recently attracted much attention for the potential capability to improve spectral efficiency (SE) underlaying the existing heterogeneous networks (HetNets). Due to no sophisticated control, D2D-worked user equipments (DUEs) themselves cannot resist eavesdropping or security attacks. It is urgent to maximize the secure capacity for both cellular users and DUEs. This paper formulates the radio resource-allocation problem to maximize the secure capacity of DUEs for D2D communication underlaying HetNets, which consist of high-power nodes (HPNs) and low-power nodes (LPNs). The optimization objective function with transmit bit rate and power constraints, which is nonconvex and hard to directly derive, is first transformed into a matrix form. Then, the equivalent convex form of the optimization problem is derived according to Perron–Frobenius theory. A heuristic iterative algorithm based on the proximal theory is proposed to solve this equivalent convex problem through evaluating the proximal operator of the Lagrange function. Numerical results show that the proposed radio resource-allocation solution significantly improves the secure capacity with a fast convergence speed. [ABSTRACT FROM PUBLISHER]