Physical-layer key generation (PKG) based on channel reciprocity has recently emerged as a new technique to establish secret keys between devices. Most works focus on pairwise communication scenarios with single or small-scale antennas. However, the fifth generation (5G) wireless communications employ massive multiple-input multiple-output (MIMO) to support multiple users simultaneously, bringing serious overhead of reciprocal channel acquisition. This paper presents a multi-user secret key generation in massive MIMO wireless networks. We provide a beam domain channel model, in which different elements represent the channel gains from different transmit directions to different receive directions. Based on this channel model, we analyze the secret key rate and derive a closed-form expression under independent channel conditions. To maximize the sum secret key rate, we provide the optimal conditions for the Kronecker product of the precoding and receiving matrices and propose an algorithm to generate these matrices with pilot reuse. The proposed optimization design can significantly reduce the pilot overhead of the reciprocal channel state information acquisition. Furthermore, we analyze the security under the channel correlation between user terminals (UTs), and propose a low overhead multi-user secret key generation with non-overlapping beams between UTs. Simulation results demonstrate the near-optimal performance of the proposed precoding and receiving matrices design and the advantages of the non-overlapping beam allocation.

中文翻译：

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TDD 多用户大规模 MIMO 无线网络的和密钥速率最大化


基于通道互易性的物理层密钥生成（PKG）最近出现作为在设备之间建立秘密密钥的新技术。大多数工作集中于使用单个或小规模天线的成对通信场景。然而，第五代（5G）无线通信采用大规模多输入多输出（MIMO）来同时支持多个用户，带来了严重的相互信道获取开销。本文提出了大规模 MIMO 无线网络中的多用户密钥生成方法。我们提供了一个波束域信道模型，其中不同的元素表示从不同发射方向到不同接收方向的信道增益。基于该信道模型，我们分析了密钥率并推导了独立信道条件下的封闭式表达式。为了最大化总密钥率，我们为预编码和接收矩阵的克罗内克乘积提供了最佳条件，并提出了一种通过导频重用生成这些矩阵的算法。所提出的优化设计可以显着减少交互信道状态信息获取的导频开销。此外，我们分析了用户终端（UT）之间的信道相关性下的安全性，并提出了一种在UT之间具有非重叠波束的低开销多用户密钥生成方法。仿真结果证明了所提出的预编码和接收矩阵设计的接近最优的性能以及非重叠波束分配的优点。