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Beamfocusing and Power Allocation for AN-Based PLS in Multiuser XL-MIMO with Multiple Eavesdroppers

Xiangjun Ma, Ali Arshad Nasir, Daniel Benevides da Costa

TL;DR

This work tackles secure downlink transmission in near-field XL-MIMO with multiple LUEs and EUEs by jointly designing NF beamfocusing and AN-aided power allocation to maximize the minimum secrecy rate $SR_{\min}$. An alternating optimization framework is proposed, using successive convex approximation (SCA) for the beamfocusing matrix $\mathbf{W}$ and golden-section search (GSS) for the power split $\epsilon$, while accounting for both perfect and unknown EUE CSI. The key contributions include a two-stage beamfocusing design that yields high SR by generating focused LUE beams and complementary null-space AN patterns, and a robust power-allocation strategy that adapts to CSI conditions. Results show that null-space AN substantially improves SR in the NF regime, with performance approaching the perfect-CSI upper bound at high transmit power, underscoring the practical viability of AN-based PLS in NF XL-MIMO for 6G networks.

Abstract

This paper investigates the downlink (DL) physical layer security (PLS) in a near-field (NF) extra-large multiple-input multiple-output MIMO (XL-MIMO) system. To enhance the secrecy rate (SR), null-space artificial noise (AN) is transmitted alongside the confidential message, ensuring orthogonality with legitimate user equipment (LUE) channels. The objective is to maximize the minimum SR by optimizing the NF beamfocusing matrix and power allocation between the signal and AN, considering various channel state information (CSI) conditions and transmit power constraints. The proposed approach uses successive convex approximation (SCA) for beamfocusing optimization and golden section search (GSS) for power allocation. The following open questions are addressed: (i) Can AN transmission further enhance SR for multiple LUEs in the presence of multiple eavesdropping user equipment (EUEs)? (ii) Can null-space AN transmission achieve attractive SR performance even without CSI availability for EUEs? Both questions are affirmatively answered and explored in detail, with an algorithm presented for joint beamfocusing design and AN-aided power allocation. The proposed method outperforms state-of-the-art approaches that either omit AN transmission or rely on maximal-ratio transmission (MRT) for beamfocusing.

Beamfocusing and Power Allocation for AN-Based PLS in Multiuser XL-MIMO with Multiple Eavesdroppers

TL;DR

This work tackles secure downlink transmission in near-field XL-MIMO with multiple LUEs and EUEs by jointly designing NF beamfocusing and AN-aided power allocation to maximize the minimum secrecy rate . An alternating optimization framework is proposed, using successive convex approximation (SCA) for the beamfocusing matrix and golden-section search (GSS) for the power split , while accounting for both perfect and unknown EUE CSI. The key contributions include a two-stage beamfocusing design that yields high SR by generating focused LUE beams and complementary null-space AN patterns, and a robust power-allocation strategy that adapts to CSI conditions. Results show that null-space AN substantially improves SR in the NF regime, with performance approaching the perfect-CSI upper bound at high transmit power, underscoring the practical viability of AN-based PLS in NF XL-MIMO for 6G networks.

Abstract

This paper investigates the downlink (DL) physical layer security (PLS) in a near-field (NF) extra-large multiple-input multiple-output MIMO (XL-MIMO) system. To enhance the secrecy rate (SR), null-space artificial noise (AN) is transmitted alongside the confidential message, ensuring orthogonality with legitimate user equipment (LUE) channels. The objective is to maximize the minimum SR by optimizing the NF beamfocusing matrix and power allocation between the signal and AN, considering various channel state information (CSI) conditions and transmit power constraints. The proposed approach uses successive convex approximation (SCA) for beamfocusing optimization and golden section search (GSS) for power allocation. The following open questions are addressed: (i) Can AN transmission further enhance SR for multiple LUEs in the presence of multiple eavesdropping user equipment (EUEs)? (ii) Can null-space AN transmission achieve attractive SR performance even without CSI availability for EUEs? Both questions are affirmatively answered and explored in detail, with an algorithm presented for joint beamfocusing design and AN-aided power allocation. The proposed method outperforms state-of-the-art approaches that either omit AN transmission or rely on maximal-ratio transmission (MRT) for beamfocusing.

Paper Structure

This paper contains 11 sections, 1 theorem, 17 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Channel Model
  4. Problem Formulation Assuming Perfect CSI of EUEs
  5. Proposed Optimization Scheme
  6. Beamforcusing Matrix Optimization
  7. Power Allocation Optimization
  8. Simulation Results and Discussion
  9. SR with Power Allocation
  10. SR with Transmit Power Budget
  11. Conclusion

Key Result

Lemma 1

For $\mathbf{g}_1\in\mathbb{C}^{1\times{N}_1}$ and $\mathbf{g}_2\in\mathbb{C}^{1\times{N}_2}$, we have $f_1^{(t)}(\mathbf{g}_1,\mathbf{g}_2)\leq\ln\left(1+\frac{\|\mathbf{g}_1\|^2}{\|\mathbf{g}_2\|^2+\sigma^2}\right)\leq{f}_2^{(t)}(\mathbf{g}_1,\mathbf{g}_2)$, where

Figures (3)

  • Figure 1: DL secrecy transmission of XL-MIMO.
  • Figure 2: Secrecy performance of the considered XL-MIMO. (a) Beam patterns of the received power of signal and AN. (b) Minimum SR versus power allocation $\epsilon$.
  • Figure 3: Minimum SR versus transmit power budget $P_\mathrm{b}$ for the proposed beamfocusing matrix.

Theorems & Definitions (2)

  • Lemma 1
  • Remark 1