  In this paper, joint resource allocation and power control for energy
efficient device-to-device (D2D) communications underlaying cellular networks
are investigated. The resource and power are optimized for maximization of the
energy efficiency (EE) of D2D communications. Exploiting the properties of
fractional programming, we transform the original nonconvex optimization
problem in fractional form into an equivalent optimization problem in
subtractive form. Then, an efficient iterative resource allocation and power
control scheme is proposed. In each iteration, part of the constraints of the
EE optimization problem is removed by exploiting the penalty function approach.
We further propose a novel two-layer approach which allows to find the optimum
at each iteration by decoupling the EE optimization problem of joint resource
allocation and power control into two separate steps. In the first layer, the
optimal power values are obtained by solving a series of maximization problems
through root-finding with or without considering the loss of cellular users'
rates. In the second layer, the formulated optimization problem belongs to a
classical resource allocation problem with single allocation format which
admits a network flow formulation so that it can be solved to optimality.
Simulation results demonstrate the remarkable improvements in terms of EE by
using the proposed iterative resource allocation and power control scheme.
