Physical-layer key generation (PKG) exploits the reciprocity and randomness of wireless channels to generate a symmetric key between two legitimate communication ends. However, in multi-cell systems, PKG suffers from severe pilot contamination due to the reuse of pilots in different cells. In this paper, we invoke multiple reconfigurable intelligent surfaces (RISs) for adaptively shaping the environment and enhancing the PKG performance. To this end, we formulate an optimization problem to maximize the weighted sum key rate (WSKR) by jointly optimizing the precoding matrices at the base stations (BSs) and the phase shifts at the RISs. For addressing the non-convexity of the problem, we derive an upper bound of the WSKR and prove its tightness. To tackle the upper bound maximization problem, we apply an alternating optimization (AO)-based algorithm to divide the joint optimization into two sub-problems. We apply the Lagrangian dual approach based on the Karush-Kuhn-Tucker (KKT) conditions for the sub-problem of precoding matrices and adopt a projected gradient ascent (PGA) algorithm for the sub-problem of phase shifts. Simulation results confirm the near-optimal performance of the proposed algorithm and the effectiveness of RISs for improving the WSKR via mitigating pilot contamination.

翻译：物理层密钥生成（PKG）利用无线信道的互易性和随机性在合法通信双方之间生成对称密钥。然而在多小区系统中，由于导频在不同小区中的复用，PKG面临严重的导频污染问题。本文引入多个可重构智能表面（RIS）对环境进行自适应调控以提升PKG性能。为此，我们构建了一个优化问题，通过联合优化基站（BS）的预编码矩阵和RIS的相位偏移来最大化加权和密钥速率（WSKR）。针对该问题的非凸性，我们推导出WSKR的上界并证明其紧致性。为解决该上界最大化问题，我们采用基于交替优化（AO）的算法将联合优化分解为两个子问题。针对预编码矩阵子问题应用基于Karush-Kuhn-Tucker（KKT）条件的拉格朗日对偶方法，针对相位偏移子问题采用投影梯度上升（PGA）算法。仿真结果证实了所提算法的近优性能以及RIS通过缓解导频污染提升WSKR的有效性。