Precoding Design for Key Generation in Extremely Large-Scale MIMO Near-Field Multi-User Systems

This paper develops a physical layer key generation (PLKG) scheme that utilizes artificial randomness in extremely large-scale multiple-input multiple-output (XL-MIMO) near-field multi-user communications to produce shared secret keys for legitimate users. Unlike traditional PLKG schemes, which rely on the variation of wireless channels, this approach introduces noise power via the precoding vectors to create dynamic fluctuations in the line-of-sight (LoS) channels, emulating the rapid changes typically observed in fast-fading channels. This artificial randomness ensures that the user equipment (UEs) can generate secret keys while effectively preventing potential eavesdropping from malicious eavesdroppers. In particular, a novel channel probing protocol is designed, enabling multiple UEs to simultaneously agree on secret keys with the base station (BS) using non-orthogonal pilots, which exploits the difference in the distances and spatial angles of UEs in near-field communications. Secondly, to maximize the secret key rate, an alternating optimization algorithm is proposed, solving two sub-optimization problems. The first sub-problem employs the singular value decomposition (SVD) method to identify the legitimate space and its orthogonal subspace for generating secret keys and preventing eavesdropping attacks, respectively. Subsequently, a Dinkelbach method-based power allocation algorithm is developed to allocate noise power to these two spaces. The second sub-problem uses a water-filling algorithm to implement power allocation among multiple UEs. Finally, to address the issue of precoding noise not being considered in the alternating optimization problem, a deep learning-based method is introduced, which further improves the performance of the scheme. Simulations demonstrate the efficiency of the proposed PLKG scheme over existing schemes.