Robust Beamforming for Near-Field Physical Layer Security under Location Uncertainty

In this paper, we study robust beamforming design for near-field physical-layer-security (PLS) systems, where a base station (BS) equipped with an extremely large-scale array (XL-array) serves near-field legitimate user (Bob) in the presence of near-field eavesdropper (Eve). Unlike existing works mostly assuming perfect channel state information (CSI) or location information of Eve, we consider the scenario where the location of Bob is perfectly known, while only imperfect location information of Eve is available at the BS. Specifically, we formulate a robust optimization problem to maximize the achievable rate of Bob while guaranteeing a worst-case limit on the eavesdropping rate under location uncertainty. To overcome the limitations of conventional methods, we first establish the conditions for which the first-order Taylor approximation of the near-field channel steering vector under location uncertainty is largely accurate. Then, we propose a two-stage robust beamforming method, which first partitions the uncertainty region into multiple sub-regions, followed by the second stage to formulate and solve a refined linear-matrix-inequality (LMI)-based robust beamforming optimization problem. Finally, numerical results validate that the proposed method achieves a superior trade-off between rate performance and secrecy robustness, hence significantly outperforming existing benchmarks under Eve location uncertainty.