This paper considers the fundamental power allocation problem in cell-free massive mutiple-input and multiple-output (MIMO) systems which aims at maximizing the total energy efficiency (EE) under a sum power constraint at each access point (AP) and a quality-of-service (QoS) constraint at each user. Existing solutions for this optimization problem are based on solving a sequence of second-order cone programs (SOCPs), whose computational complexity scales dramatically with the network size. Therefore, they are not implementable for practical large-scale cell-free massive MIMO systems. To tackle this issue, we propose an iterative power control algorithm based on the frame work of an accelerated projected gradient (APG) method. In particular, each iteration of the proposed method is done by simple closed-form expressions, where a penalty method is applied to bring constraints into the objective in the form of penalty functions. Finally, the convergence of the proposed algorithm is analytically proved and numerically compared to the known solution based on SOCP. Simulations results demonstrate that our proposed power control algorithm can achieve the same EE as the existing SOCPs-based method, but more importantly, its run time is much lower (one to two orders of magnitude reduction in run time, compared to the SOCPs-based approaches).

中文翻译：

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大规模无细胞大规模 MIMO 中的能效最大化：一种投影梯度方法

本文考虑了无蜂窝大规模多输入多输出 (MIMO) 系统中的基本功率分配问题，其目标是在每个接入点 (AP) 的总功率约束下最大化总能量效率 (EE) 和质量每个用户的服务（QoS）约束。此优化问题的现有解决方案基于求解一系列二阶锥程序 (SOCP)，其计算复杂度随网络规模显着增加。因此，它们不适用于实际的大规模无细胞大规模 MIMO 系统。为了解决这个问题，我们提出了一种基于加速投影梯度（APG）方法框架的迭代功率控制算法。特别是，所提出方法的每次迭代都是通过简单的封闭式表达式完成的，其中应用惩罚方法以惩罚函数的形式将约束带入目标。最后，分析证明了该算法的收敛性，并与基于SOCP的已知解进行了数值比较。仿真结果表明，我们提出的功率控制算法可以实现与现有基于 SOCPs 的方法相同的 EE，但更重要的是，它的运行时间要低得多（与基于 SOCPs 的方法相比，运行时间减少一到两个数量级）方法）。