  Next generation wireless networks face the challenge of increasing energy
consumption while satisfying the unprecedented increase in the data rate
demand. To address this problem, we propose a utility-based energy-efficient
resource allocation algorithm for the downlink transmissions in heterogeneous
networks (HetNets). We consider the fractional frequency reuse (FFR) method in
order to mitigate the intra- and inter-cell interference. The proposed
algorithm divides the resource allocation problem into frequency and power
assignment problems and sequentially solves them. The proposed power control
algorithm uses the gradient ascent method to control the transmit power of
macrocell base stations as most of the power in the network is consumed there.
We also present the optimality conditions of the resource allocation problem
and the convergence of the proposed algorithm. We study the performance of the
proposed algorithm in a Long Term Evolution (LTE) system. Our simulation
results demonstrate that the proposed algorithm provides substantial
improvements in the energy efficiency and throughput of the network.
