Optimal ADMM-Based Spectrum and Power Allocation for Heterogeneous Small-Cell Networks with Hybrid Energy Supplies

Powering cellular networks with hybrid energy supplies is not only environment-friendly but can also reduce the on-grid energy consumption, thus being emerging as a promising solution for green networking. Intelligent management of spectrum and power can increase the network utility in cellular networks with hybrid energy supplies, usually at the cost of higher energy consumption. Unlike prior studies on either the network utility maximization or on-grid energy cost minimization, this paper studies the joint spectrum and power allocation problem that maximizes the system revenue in a heterogeneous small-cell network with hybrid energy supplies. Specifically, the system revenue is considered as the difference between the network utility and on-grid energy cost. By developing the convexity of the optimization problem through transformation and reparameterization, we propose a joint spectrum and power allocation algorithm based on the primal-dual arguments to obtain the optimal solution by iteratively solving the primal and dual sub-problems of the convex optimization problem. To solve the primal sub-problem, we further propose the Lagrangian maximization based on the alternating direction method of multipliers (ADMM), and derive the optimal solution in the closed-form expression at each iteration. It is shown that the proposed joint spectrum and power allocation algorithm approaches the global optimality at the rate of 1=n with n being the number of iterations. Also, the proposed ADMM-based Lagrangian maximization algorithm approaches the primal optimal solution with the time complexity of O(1=ε
_r
) iterations with ε
_r
being the termination parameter. Simulation results show that in comparison with the power control with equal frequency allocation algorithm and frequency allocation with equal power allocation algorithms the proposed algorithm increases the system revenue by over 20 and 60 percent without consuming more on-grid energy when the proportional fairness utility and the weighted sum rate utility are considered with the approximate system parameter settings, respectively. Meanwhile, in comparison with the full frequency reuse case, the proposed algorithm increases the system revenue by 20 percent at least in terms of the weighted sum rate utility, although it achieves the similar system revenue when considering the proportional fairness utility. Simulation results also show that our proposed algorithm can perform well under the realistic fast fading channel conditions.