Reconfigurable Intelligent Surface-Assisted Key Generation for Millimeter-Wave Multi-User Systems

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.