Polar-domain multi-user key generation in near-field communications

Given the substantial increase in the number of antennas in extremely large-scale antenna array (ELAA) systems, polar-domain channel modeling has been introduced to capture both angular and distance information in near-field environments. The fine-grained polar-domain channel provides additional sources of randomness, making it well-suited for physical layer key generation (PLKG). To minimize the pilot overhead in multi-user key generation and leverage the randomness from the polar-domain channel paths, we implement a zero-forcing (ZF)-based precoding scheme to mitigate the inter-path and inter-user interference. Using ZF precoding, we derive an analytical expression for the sum secret key rate (SKR) as a function of the power allocation variables, and then optimize these variables in the presence of eavesdroppers. Since the ZF method may not fully eliminate interference with imperfect channel state information (CSI), there could be correlation between the measurements of polar-domain channel paths and users. We present a channel decorrelation and reciprocity compensation approach that leverages principal component analysis (PCA) and deep neural networks (DNNs) to mitigate channel correlation issues. Specifically, PCA is first applied at the base station (BS) to decorrelate the composite CSI vector that aggregates the CSI of all users. Following this preprocessing, a DNN is trained to learn the mapping from the decorrelated uplink CSI to the corresponding original downlink CSI. This trained DNN then reconstructs a new version of the downlink CSI, enhancing the cross-correlation between the BS and the users’ CSI, thereby improving uplink/downlink reciprocity. Our simulations evaluate the effectiveness of the DNN-based reciprocity compensation by assessing the normalized mean squared error (NMSE) and the correlation between uplink and downlink CSI, the bit disagreement ratio (BDR) and the randomness of secret keys after quantization.