This paper comprehensively studies the physical layer security in frequency division duplex multi-antenna cellular systems, where the multi-antenna base stations (BSs), legitimate users (LUs), and eavesdroppers are all randomly located. Each BS employs artificial-noise (AN)-aided multi-user linear beamforming with limited channel state information feedback. Based on the stochastic geometry theory, we first derive an analytical expression of a lower bound on the ergodic secrecy rate (ESR) of the typical LU without assuming asymptotes for any system parameter. We then develop a tight closed-form approximation on the optimal number of feedback bits to maximize a lower bound on the per-user net ESR, which takes into consideration the cost of uplink spectral efficiency for limited feedback. Moreover, the power allocation coefficient between message-bearing signals and AN can be optimized by using a bisection search method. Our main finding is that, the optimum number of feedback bits scales linearly with the path-loss exponent and the number of antennas, and scales logarithmically with the channel coherence time. The derived analytical results can also provide system-level insights into the ESR performance of the multi-antenna random cellular networks with limited feedback and the optimal system design. Numerical results are also presented to verify the obtained results.

中文翻译：

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多天线蜂窝系统中的物理层安全：反馈率和功率分配的联合优化

本文全面研究了频分双工多天线蜂窝系统中的物理层安全性，其中多天线基站（BS）、合法用户（LU）和窃听者都是随机分布的。每个 BS 采用人工噪声 (AN) 辅助的多用户线性波束成形，并具有有限的信道状态信息反馈。基于随机几何理论，我们首先推导了典型LU的遍历保密率（ESR）下界的解析表达式，而不假设任何系统参数的渐近线。然后，我们对最佳反馈比特数开发了一个紧密的封闭形式近似，以最大化每用户净 ESR 的下限，其中考虑了有限反馈的上行链路频谱效率成本。而且，消息承载信号与AN之间的功率分配系数可以通过二分搜索法进行优化。我们的主要发现是，最佳反馈比特数与路径损耗指数和天线数量成线性关系，并与信道相干时间成对数关系。推导出的分析结果还可以为具有有限反馈和最佳系统设计的多天线随机蜂窝网络的 ESR 性能提供系统级洞察。还给出了数值结果以验证获得的结果。推导出的分析结果还可以为具有有限反馈和最佳系统设计的多天线随机蜂窝网络的 ESR 性能提供系统级洞察。还给出了数值结果以验证获得的结果。推导出的分析结果还可以为具有有限反馈和最佳系统设计的多天线随机蜂窝网络的 ESR 性能提供系统级洞察。还给出了数值结果以验证获得的结果。