This paper studies the energy-efficient power allocation problem for physical-layer security in multi-user (MU) distributed massive multiple-input multiple-output (MIMO) systems. A new metric called global average secrecy energy efficiency (GASEE) is proposed to measure the MU secrecy energy efficiency (SEE) with a single eavesdropper (Eve). We first derive closed-form expressions for the signal to interference-plus-noise ratios (SINRs) of legitimate users and the Eve with pilot contamination. Under a power consumption model that incorporates transmit power, backhaul power, remote antenna unit (RAU) circuit and signal processing power, and with transmit power constraints as well as SINR constraints for both users and the Eve, the GASEE maximization problem is formulated as a joint optimization of power allocation, RAU clustering, RAU selection and artificial noise (AN) selection. The formulated problem is a mixed integer nonlinear program (MINLP), which is solved by a double-loop procedure. In the outer loop, the denominator of objective is approximated as a linear function. In the inner loop, an efficient algorithm is proposed to find a near-optimal solution to the approximated problem by solving a sequence of sub-problems. Simulation results demonstrate that the proposed algorithm converges fast and achieves a higher GASEE than some heuristics.

中文翻译：

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多用户分布式大规模MIMO系统的保密能效优化

本文研究了多用户 (MU) 分布式大规模多输入多输出 (MIMO) 系统中物理层安全的节能功率分配问题。提出了一种称为全球平均保密能效 (GASEE) 的新指标，用于测量单个窃听者 (Eve) 的 MU 保密能效 (SEE)。我们首先推导出合法用户的信号干扰加噪声比 (SINR) 和带有导频污染的 Eve 的封闭形式表达式。在包含发射功率、回程功率、远程天线单元 (RAU) 电路和信号处理能力的功耗模型下，在用户和 Eve 的发射功率约束以及 SINR 约束下，GASEE 最大化问题被公式化为功率分配联合优化，RAU 聚类，RAU 选择和人工噪声 (AN) 选择。公式化的问题是一个混合整数非线性规划 (MINLP)，它是通过一个双循环程序解决的。在外循环中，目标的分母近似为线性函数。在内部循环中，提出了一种有效的算法，通过解决一系列子问题来找到近似问题的近似最优解。仿真结果表明，所提出的算法收敛速度快，并且比一些启发式算法实现了更高的 GASEE。提出了一种有效的算法，通过解决一系列子问题来找到近似问题的近似最优解。仿真结果表明，所提出的算法收敛速度快，并且比一些启发式算法实现了更高的 GASEE。提出了一种有效的算法，通过解决一系列子问题来找到近似问题的近似最优解。仿真结果表明，所提出的算法收敛速度快，并且比一些启发式算法实现了更高的 GASEE。