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

Chao Zhou, Changsheng You, Cong Zhou, Chengwen Xing, Jianhua Zhang

TL;DR

This work tackles robust beamforming for near-field PLS with XL-arrays under imperfect Eve location information. It reveals an angular-error amplification effect in the near-field and develops a two-stage method that partitions the Eve uncertainty region and uses refined LMIs based on first-order Taylor expansions to achieve tractable, lower-complexity robust design. The approach is extended to multi-Bob and multi-Eve scenarios, with numerical results showing superior secrecy robustness and rate performance compared to benchmarks. The proposed framework offers practical robustness for secure high-resolution near-field communications and motivates extensions to XL-IRS and integrated sensing and communications systems.

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.

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

TL;DR

This work tackles robust beamforming for near-field PLS with XL-arrays under imperfect Eve location information. It reveals an angular-error amplification effect in the near-field and develops a two-stage method that partitions the Eve uncertainty region and uses refined LMIs based on first-order Taylor expansions to achieve tractable, lower-complexity robust design. The approach is extended to multi-Bob and multi-Eve scenarios, with numerical results showing superior secrecy robustness and rate performance compared to benchmarks. The proposed framework offers practical robustness for secure high-resolution near-field communications and motivates extensions to XL-IRS and integrated sensing and communications systems.

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.
Paper Structure (27 sections, 6 theorems, 64 equations, 11 figures)

This paper contains 27 sections, 6 theorems, 64 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Prior Works
  3. Far-field PLS
  4. Near-field PLS
  5. Contributions
  6. System Model and Problem Formulation
  7. Channel Model
  8. Location Error Model
  9. Signal Model
  10. Problem Formulation
  11. Single-Bob-Single-Eve Scenario
  12. Conventional Methods
  13. Sampling-based method
  14. Error-bound-based method
  15. Proposed Method
  16. ...and 12 more sections

Key Result

Proposition 1

For the error-bound-based method, given $\Gamma$, the error bound $\varepsilon_{\rm Tayl}^{(\rm ub)}$ in Exp:TaylorBoundofvec, and estimated Eve location $(\hat{\theta}_{\rm E},\hat{r}_{\rm E})$, the beamforming vector $\mathbf{w}$ should satisfy $\|\mathbf{w}\|_{2}^2 \le \Gamma/(\varepsilon_{\rm Ta

Figures (11)

  • Figure 1: An XL-array enabled near-field PLS system.
  • Figure 2: Schematic of near-field angular-error amplification.
  • Figure 3: CSV error bound, and corresponding achievable rate and transmit power.
  • Figure 4: $\|\Delta\mathbf{a}_{\rm E} \|_{2}^{2}$ versus angle error and range error.
  • Figure 5: Schematic of the sub-region partitioning.
  • ...and 6 more figures

Theorems & Definitions (11)

  • Proposition 1
  • proof
  • Lemma 1: CSV error in the range domain
  • proof
  • Lemma 2: CSV error in the angle domain
  • proof
  • Proposition 2: Conditions for accurate first-order Taylor approximation
  • proof
  • Proposition 3: Refined LMI reformulation
  • proof
  • ...and 1 more