Physical layer key generation (PLKG) leverages wireless channels to produce secret keys for legitimate users. However, in millimetre-wave (mmWave) frequency bands, the presence of blockage significantly reduces the key rate (KR) of a PLKG system. To address this issue, we introduce reconfigurable intelligent surfaces (RISs) as a potential solution for constructing RIS-reflected channels, thereby enhancing the KR. Our study focuses on the beam-domain channel model and exploits the sparsity of mmWave bands to enhance the randomness of secret keys. To relieve pilot overhead in multi-user systems, we employ a compressed sensing (CS) algorithm to estimate angular information and propose a channel probing protocol with the full-array configuration for acquiring the beam-domain channel. We derive the analytical expressions for the KR in the case of full-array configuration. To optimize the KR, we design the phase shift and precoding vectors based on the obtained angular information. Furthermore, we employ a water-filling algorithm that relies on the Karush-Kuhn-Tucker (KKT) conditions to optimize power allocation for estimating the beam-domain channel with the same channel variance. When channel variances of the beam-domain channel differ, we design a deep-learning-based power allocation method for a more complex problem. What is more, we design a sub-array configuration scheme that exploits the difference in spatial angles between users to reduce pilot overhead and derive the analytical expression for the KR. Through extensive simulations, we demonstrate that our proposed PLKG schemes outperform existing methods.

中文翻译：

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毫米波多用户系统的可重构智能表面辅助密钥生成

物理层密钥生成 (PLKG) 利用无线通道为合法用户生成密钥。然而，在毫米波 (mmWave) 频段中，阻塞的存在会显着降低 PLKG 系统的密钥速率 (KR)。为了解决这个问题，我们引入可重构智能表面（RIS）作为构建 RIS 反射通道的潜在解决方案，从而增强 KR。我们的研究重点是波束域信道模型，并利用毫米波频段的稀疏性来增强密钥的随机性。为了减轻多用户系统中的导频开销，我们采用压缩感知（CS）算法来估计角度信息，并提出一种具有全阵列配置的信道探测协议来获取波束域信道。我们推导了全阵列配置情况下 KR 的解析表达式。为了优化 KR，我们根据获得的角度信息设计相移和预编码向量。此外，我们采用了一种依赖于Karush-Kuhn-Tucker（KKT）条件的注水算法来优化功率分配，以估计具有相同信道方差的波束域信道。当波束域信道的信道方差不同时，我们针对更复杂的问题设计了一种基于深度学习的功率分配方法。更重要的是，我们设计了一种子阵列配置方案，利用用户之间的空间角度差异来减少导频开销并推导 KR 的解析表达式。通过广泛的模拟，我们证明了我们提出的 PLKG 方案优于现有方法。