Near-field Physical Layer Security: Robust Beamforming under Location Uncertainty

TL;DR

This paper develops a robust beamforming approach for near-field physical layer security systems with large-scale arrays, effectively handling imperfect eavesdropper location information to enhance secrecy and rate performance.

Contribution

It introduces a two-stage robust beamforming method that accounts for near-field angular-error amplification due to location uncertainty, improving security in practical XL-array systems.

Findings

Proposed method outperforms benchmarks in secrecy and rate trade-offs.

Near-field angular-error amplification significantly impacts beamforming robustness.

Effective for multiple users and eavesdroppers scenarios.

Abstract

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 multiple near-field legitimate users (Bobs) in the presence of multiple near-field eavesdroppers (Eves). Unlike existing works that mostly assume perfect channel state information (CSI) or location information of Eves, we consider a more practical and challenging scenario, where the locations of Bobs are perfectly known, while only imperfect location information of Eves is available at the BS. We first formulate a robust optimization problem to maximize the sum-rate of Bobs while guaranteeing a worst-case limit on the eavesdropping rate under location uncertainty. By transforming Cartesian position errors into the polar domain, we reveal an important near-field angular-error amplification effect: for the same location error, the closer the Eve, the larger the angle error, severely degrading the performance of conventional robust beamforming methods based on imperfect channel state information. To address this issue, 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 fan-shaped sub-regions, followed by the second stage to formulate and solve a refined linear-matrix-inequality (LMI)-based robust beamforming optimization problem. In addition, the proposed method is further extended to scenarios with multiple Bobs and multiple Eves. 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.