  Device-to-device (D2D) communications recently have attracted much attention
for its potential capability to improve spectral efficiency underlaying the
existing heterogeneous networks (HetNets). Due to no sophisticated control, D2D
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 the D2D communication underlaying
HetNets which consist of high power nodes and low power nodes. The optimization
objective function with transmit bit rate and power constraints, which is
non-convex and hard to be directly derived, is firstly transformed into matrix
form. Then the equivalent convex form of the optimization problem is derived
according to the 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 Lagrange function. Numerical
results show that the proposed radio resource allocation solution significantly
improves the secure capacity with a fast convergence speed.
