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 $1/n$ 1 / n with $n$ n being the number of iterations. Also, the proposed ADMM-based Lagrangian maximization algorithm approaches the primal optimal solution with the time complexity of $O(1/\epsilon _r)$ O ( 1 / ε r ) iterations with $\epsilon _r$ 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.

中文翻译：

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具有混合能源供应的异构小蜂窝网络的最佳基于 ADMM 的频谱和功率分配

使用混合能源为蜂窝网络供电不仅对环境友好，而且还可以降低并网能耗，因此成为一种很有前景的绿色网络解决方案。频谱和功率的智能管理可以增加混合能源供应的蜂窝网络中的网络效用，通常以更高的能耗为代价。与先前关于网络效用最大化或并网能源成本最小化的研究不同，本文研究了在具有混合能源供应的异构小蜂窝网络中最大化系统收益的联合频谱和功率分配问题。具体而言，系统收入被视为网络效用和并网能源成本之间的差额。通过通过变换和重新参数化开发优化问题的凸性，我们提出了一种基于原始对偶参数的联合频谱和功率分配算法，通过迭代求解凸优化问题的原始和对偶子问题来获得最优解。为了解决原始子问题，我们进一步提出了基于乘法器交替方向法（ADMM）的拉格朗日最大化，并在每次迭代时在闭式表达式中推导出最优解。结果表明，所提出的联合频谱和功率分配算法以 我们提出了一种基于原始对偶参数的联合频谱和功率分配算法，通过迭代求解凸优化问题的原始和对偶子问题来获得最优解。为了解决原始子问题，我们进一步提出了基于乘法器交替方向法（ADMM）的拉格朗日最大化，并在每次迭代时在闭式表达式中推导出最优解。结果表明，所提出的联合频谱和功率分配算法以 我们提出了一种基于原始对偶参数的联合频谱和功率分配算法，通过迭代求解凸优化问题的原始和对偶子问题来获得最优解。为了解决原始子问题，我们进一步提出了基于乘法器交替方向法（ADMM）的拉格朗日最大化，并在每次迭代时在闭式表达式中推导出最优解。结果表明，所提出的联合频谱和功率分配算法以$1/n$ 1 / n 和 $n$ n 是迭代次数。此外，所提出的基于 ADMM 的拉格朗日最大化算法接近原始最优解，时间复杂度为$O(1/\epsilon _r)$ 哦 ( 1 / ε r ) 迭代 $\epsilon _r$ ε r 作为终止参数。仿真结果表明，与等频分配算法和频率分配等功率分配算法相比，该算法在不消耗更多上网能量的情况下，在比例公平效用和加权和率效用分别与近似的系统参数设置一起考虑。同时，与全频率复用情况相比，所提出的算法在加权和率效用方面至少增加了20％的系统收入，尽管在考虑比例公​​平效用时它实现了类似的系统收入。